Subgroups — C₂×C₃×#4867 #11867006

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#897	C₂	1	2	yes	maximal
4	C₂×C₃²×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#810	C₂	1	2	yes	maximal, complemented
6	C₃×#4867	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#470	—	3	1	no	maximal
8	C₂×#4867	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
14	C₂×C₃×C₄⋊Dic₃	—	2	2	no	—
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×Dic₁₂	—	2	4	no	—
17	C₂×C₃×Dic₁₂	C₂²	1	4	yes	complemented
18	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
19	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
20	C₃×#897	—	2	4	no	—
21	C₃×#897	C₂²	1	8	yes	—
22	C₃²×#106	C₂²	1	4	yes	complemented
23	C₃×#810	C₂²	1	8	yes	complemented
24	C₂²×C₃×Q₁₆	—	3	1	no	—
25	C₂²×C₃×M₁₆	—	3	1	no	—
26	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
27	C₂²×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
29	C₂×#897	C₂×C₃	1	2	yes	—
30	C₃×#470	—	3	8	no	—
31	C₂×C₃×#106	—	2	1	no	—
32	C₂×C₃×#106	D₃	1	1	yes	characteristic, complemented
33	C₂×C₃×#106	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#103	—	3	2	no	—
35	C₂×#810	C₂×C₃	1	2	yes	complemented
36	#4867	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	—	2	2	no	—
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₃	—	2	2	no	—
41	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₃	—	2	2	no	—
43	C₂×C₃×C₄×D₃	—	2	2	no	—
44	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
45	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
46	C₂×C₃×Dic₆	—	2	4	no	—
47	C₂×C₃×Dic₆	—	2	4	no	—
48	C₂×C₃×Dic₆	—	2	2	no	—
49	C₂×C₃×Dic₆	C₂³	1	4	yes	—
50	C₂×C₃²×C₈	D₄	1	4	yes	—
51	C₂×C₃²×C₈	C₂³	1	2	yes	—
52	C₃²×C₄⋊C₄	—	2	2	no	—
53	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
54	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
55	C₃×C₄⋊Dic₃	—	2	8	no	—
56	C₂×C₃×C₃⋊C₈	—	2	2	no	—
57	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
58	C₃×Dic₁₂	—	2	8	no	—
59	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
60	C₂×#470	—	3	1	no	Sylow
61	C₂²×C₃×Q₈	—	3	2	no	—
62	C₂³×C₃×C₄	—	3	1	no	—
63	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
64	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
65	C₂×C₃×Q₁₆	—	3	4	no	—
66	C₂×C₃×Q₁₆	—	6	4	no	—
67	C₂×C₃×M₁₆	—	3	4	no	—
68	C₂×C₃×M₁₆	—	6	4	no	—
69	C₂²×C₃×C₈	—	2	1	no	—
70	C₂²×C₃×C₈	—	3	1	no	—
71	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₃×C₂²⋊Q₈	—	3	8	no	—
74	C₃×C₂²⋊Q₈	—	6	4	no	—
75	C₂×C₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₃×C₄⋊C₄	—	6	2	no	—
77	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
78	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
80	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
81	C₂×C₄⋊Dic₃	—	2	2	no	—
82	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×Dic₁₂	—	2	4	no	—
84	C₂×Dic₁₂	C₂²×C₃	1	4	yes	complemented
85	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
86	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
87	#897	—	2	4	no	—
88	#897	C₂²×C₃	1	8	yes	—
89	C₃×#106	—	2	4	no	—
90	C₃×#106	C₂×D₃	1	4	yes	complemented
91	C₃×#106	C₂²×C₃	1	4	yes	complemented
92	C₃×#103	—	3	8	no	—
93	#810	C₂²×C₃	1	8	yes	complemented
94	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₃×D₃	—	2	2	no	—
96	C₂²×C₃×D₃	—	2	4	no	—
97	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
98	C₂×C₃²×C₄	—	2	4	no	—
99	C₂×C₃²×C₄	—	4	4	no	—
100	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
101	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	#41	1	2	yes	—
103	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₂×C₃×Dic₃	—	2	4	no	—
106	C₂×C₃×Dic₃	—	4	4	no	—
107	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
108	C₃×C₄×D₃	—	2	4	no	—
109	C₃×C₄×D₃	—	2	2	no	—
110	C₃×C₄×D₃	—	2	2	no	—
111	C₃×Dic₆	—	2	4	no	—
112	C₃×Dic₆	—	2	4	no	—
113	C₃×Dic₆	—	4	4	no	—
114	C₃²×C₈	C₂×D₄	1	4	yes	—
115	C₃×C₃⋊C₈	—	2	2	no	—
116	C₂²×Q₁₆	—	3	1	no	—
117	C₂²×M₁₆	—	3	1	no	—
118	C₂×C₂²⋊Q₈	—	3	2	no	—
119	#470	—	3	8	no	—
120	C₂×#106	C₃×D₃	1	1	yes	characteristic, complemented
121	C₂×#103	—	3	2	no	—
122	C₂⁴×C₃	—	3	1	no	—
123	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
124	C₂×C₃×Q₈	—	3	4	no	—
125	C₂×C₃×Q₈	—	6	2	no	—
126	C₂×C₃×Q₈	—	6	4	no	—
127	C₂×C₃×Q₈	—	6	4	no	—
128	C₂²×C₃×C₄	—	2	2	no	—
129	C₂²×C₃×C₄	—	2	2	no	—
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	3	1	no	—
132	C₂²×C₃×C₄	—	3	2	no	—
133	C₂²×C₃×C₄	—	3	2	no	—
134	C₂²×C₃×C₄	—	4	2	no	—
135	C₂²×C₃×C₄	—	6	2	no	—
136	C₂²×C₃×C₄	—	6	2	no	—
137	C₂²×C₃×C₄	—	6	2	no	—
138	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂²×Dic₃	—	2	2	no	—
141	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
142	C₂×C₄×D₃	—	2	2	no	—
143	C₂×C₄×D₃	—	2	2	no	—
144	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
145	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
146	C₂×Dic₆	—	2	4	no	—
147	C₂×Dic₆	—	2	4	no	—
148	C₂×Dic₆	—	2	2	no	—
149	C₂×Dic₆	C₂³×C₃	1	4	yes	—
150	C₃×Q₁₆	—	6	8	no	—
151	C₃×M₁₆	—	6	8	no	—
152	C₂×C₃×C₈	—	2	4	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	3	2	no	—
155	C₂×C₃×C₈	—	6	2	no	—
156	C₂×C₃×C₈	D₁₂	1	4	yes	—
157	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
158	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
159	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
160	C₃×C₄⋊C₄	—	2	2	no	—
161	C₃×C₄⋊C₄	—	2	2	no	—
162	C₃×C₄⋊C₄	—	2	4	no	—
163	C₃×C₄⋊C₄	—	4	2	no	—
164	C₃×C₄⋊C₄	—	6	8	no	—
165	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
166	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
167	C₃×C₂²⋊C₄	—	6	8	no	—
168	(C₂×D₃)⋊C₄	—	2	8	no	—
169	C₄⋊Dic₃	—	2	8	no	—
170	C₂×C₃⋊C₈	—	2	2	no	—
171	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
172	Dic₁₂	—	2	8	no	—
173	ΓL(1,𝔽₂₅)	—	2	8	no	—
174	C₂²×C₃²	#121	1	2	yes	—
175	C₂²×C₃²	#137	1	4	yes	—
176	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₃×D₃	—	2	2	no	—
178	C₂×C₃×D₃	—	2	4	no	—
179	C₂×C₃×D₃	—	4	4	no	—
180	C₃²×C₄	—	4	4	no	—
181	C₃²×C₄	#121	1	2	yes	—
182	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
183	C₃²×C₄	C₂×#41	1	1	yes	characteristic
184	C₃×Dic₃	—	2	2	no	—
185	C₃×Dic₃	—	4	4	no	—
186	C₂²×Q₈	—	3	2	no	—
187	C₂³×C₄	—	3	1	no	—
188	C₂×Q₁₆	—	3	4	no	—
189	C₂×Q₁₆	—	6	4	no	—
190	C₂×M₁₆	—	3	4	no	—
191	C₂×M₁₆	—	6	4	no	—
192	C₂²×C₈	—	3	1	no	—
193	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
194	C₂²⋊Q₈	—	3	8	no	—
195	C₂²⋊Q₈	—	6	4	no	—
196	C₂×C₄⋊C₄	—	6	2	no	—
197	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
198	C₂×C₂²⋊C₄	—	6	2	no	—
199	#106	C₂×C₃×D₃	1	4	yes	complemented
200	#103	—	3	8	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	3	2	no	—
203	C₂³×C₃	—	6	2	no	—
204	C₂³×C₃	—	6	4	no	—
205	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
206	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂²×D₃	—	2	2	no	—
208	C₂²×D₃	—	2	4	no	—
209	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
210	C₃×Q₈	—	6	4	no	—
211	C₃×Q₈	—	6	4	no	—
212	C₃×Q₈	—	12	4	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	3	2	no	—
220	C₂×C₃×C₄	—	4	4	no	—
221	C₂×C₃×C₄	—	4	4	no	—
222	C₂×C₃×C₄	—	4	4	no	—
223	C₂×C₃×C₄	—	6	2	no	—
224	C₂×C₃×C₄	—	6	4	no	—
225	C₂×C₃×C₄	—	6	2	no	—
226	C₂×C₃×C₄	—	6	2	no	—
227	C₂×C₃×C₄	—	6	4	no	—
228	C₂×C₃×C₄	—	8	4	no	—
229	C₂×C₃×C₄	—	12	4	no	—
230	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
231	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	#239	1	2	yes	—
233	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
234	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄	C₃×#41	1	2	yes	—
236	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
238	C₂×Dic₃	—	2	2	no	—
239	C₂×Dic₃	—	2	4	no	—
240	C₂×Dic₃	—	4	4	no	—
241	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
242	C₄×D₃	—	2	4	no	—
243	C₄×D₃	—	2	2	no	—
244	C₄×D₃	—	2	2	no	—
245	Dic₆	—	2	4	no	—
246	Dic₆	—	2	4	no	—
247	Dic₆	—	4	4	no	—
248	C₃×C₈	—	2	4	no	—
249	C₃×C₈	—	6	2	no	—
250	C₃×C₈	C₂×D₁₂	1	4	yes	—
251	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
252	C₃⋊C₈	—	2	2	no	—
253	C₂×C₃²	#470	1	4	yes	complemented
254	C₂×C₃²	C₂×#121	1	1	yes	characteristic
255	C₂×C₃²	C₂×#137	1	2	yes	—
256	C₃×D₃	—	4	2	no	—
257	C₂⁴	—	3	1	no	—
258	C₂×Q₈	—	3	4	no	—
259	C₂×Q₈	—	6	2	no	—
260	C₂×Q₈	—	6	4	no	—
261	C₂×Q₈	—	6	4	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	3	1	no	—
264	C₂²×C₄	—	3	2	no	—
265	C₂²×C₄	—	3	2	no	—
266	C₂²×C₄	—	6	2	no	—
267	C₂²×C₄	—	6	2	no	—
268	C₂²×C₄	—	6	2	no	—
269	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
270	Q₁₆	—	6	8	no	—
271	M₁₆	—	6	8	no	—
272	C₂×C₈	—	3	2	no	—
273	C₂×C₈	—	6	2	no	—
274	C₂×C₈	C₃×D₁₂	1	4	yes	—
275	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	6	8	no	—
278	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
279	C₂²⋊C₄	—	6	8	no	—
280	C₂²×C₃	—	2	2	no	—
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	6	4	no	—
284	C₂²×C₃	—	6	2	no	—
285	C₂²×C₃	—	12	4	no	—
286	C₂²×C₃	#895	1	2	yes	—
287	C₂²×C₃	#915	1	4	yes	—
288	C₂²×C₃	C₃×#121	1	2	yes	—
289	C₂²×C₃	C₃×#137	1	4	yes	—
290	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
291	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
292	C₂×D₃	—	2	4	no	—
293	C₂×D₃	—	2	2	no	—
294	C₂×D₃	—	4	4	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	4	4	no	—
299	C₃×C₄	—	4	4	no	—
300	C₃×C₄	—	6	2	no	—
301	C₃×C₄	—	8	4	no	—
302	C₃×C₄	—	12	4	no	—
303	C₃×C₄	#895	1	2	yes	—
304	C₃×C₄	C₃×#121	1	2	yes	—
305	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
306	C₃×C₄	C₂×#239	1	1	yes	characteristic
307	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
308	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
309	Dic₃	—	2	2	no	—
310	Dic₃	—	4	4	no	—
311	C₃²	C₂×#470	1	1	yes	characteristic, complemented, Sylow
312	C₂³	—	3	2	no	—
313	C₂³	—	6	2	no	—
314	C₂³	—	6	4	no	—
315	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
316	Q₈	—	6	4	no	—
317	Q₈	—	6	4	no	—
318	Q₈	—	12	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	3	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	6	2	no	—
323	C₂×C₄	—	6	4	no	—
324	C₂×C₄	—	6	2	no	—
325	C₂×C₄	—	6	2	no	—
326	C₂×C₄	—	6	4	no	—
327	C₂×C₄	—	12	4	no	—
328	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
329	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
330	C₂×C₄	C₃×#239	1	2	yes	—
331	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
332	C₈	—	6	2	no	—
333	C₈	C₂×C₃×D₁₂	1	4	yes	—
334	C₂×C₃	—	2	2	no	—
335	C₂×C₃	—	2	1	no	—
336	C₂×C₃	—	2	4	no	—
337	C₂×C₃	—	12	2	no	—
338	C₂×C₃	#4867	1	4	yes	direct product factor
339	C₂×C₃	C₃×#470	1	4	yes	complemented
340	C₂×C₃	C₂×#895	1	1	yes	characteristic
341	C₂×C₃	C₂×#915	1	2	yes	—
342	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
343	C₂×C₃	C₂×C₃×#137	1	2	yes	—
344	D₃	—	4	2	no	—
345	C₂²	—	6	4	no	—
346	C₂²	—	6	2	no	—
347	C₂²	—	12	4	no	—
348	C₂²	C₃×#895	1	2	yes	—
349	C₂²	C₃×#915	1	4	yes	—
350	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
351	C₄	—	4	4	no	—
352	C₄	—	6	2	no	—
353	C₄	—	12	4	no	—
354	C₄	C₃×#895	1	2	yes	—
355	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
356	C₄	C₂×C₃×#239	1	1	yes	characteristic
357	C₃	—	2	1	no	—
358	C₃	C₂×#4867	1	1	yes	characteristic, direct product factor
359	C₃	C₂×C₃×#470	1	1	yes	characteristic, complemented
360	C₂	—	12	2	no	—
361	C₂	C₃×#4867	1	4	yes	direct product factor
362	C₂	C₂×C₃×#895	1	1	yes	characteristic
363	C₂	C₂×C₃×#915	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#106	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂³×C₃×D₃	D₄
hypercenter	C₂×C₃×#106	D₃
hypocenter	C₃	C₂×C₃×#470
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#106

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Dic₁₂	C₂	semidirect
4. C₂×C₃²×#106	C₂	semidirect
5. C₂×C₃×#810	C₂	semidirect
6. C₃×#4867	C₂	direct (N × H)
8. C₂×#4867	C₃	direct (N × H)
17. C₂×C₃×Dic₁₂	C₂²	semidirect
22. C₃²×#106	C₂²	semidirect
23. C₃×#810	C₂²	semidirect
27. C₂²×Dic₁₂	C₂×C₃	semidirect
32. C₂×C₃×#106	D₃	semidirect
33. C₂×C₃×#106	C₂×C₃	semidirect
35. C₂×#810	C₂×C₃	semidirect
36. #4867	C₂×C₃	direct (N × H)
84. C₂×Dic₁₂	C₂²×C₃	semidirect
90. C₃×#106	C₂×D₃	semidirect
91. C₃×#106	C₂²×C₃	semidirect
93. #810	C₂²×C₃	semidirect
120. C₂×#106	C₃×D₃	semidirect
199. #106	C₂×C₃×D₃	semidirect
253. C₂×C₃²	#470	semidirect
311. C₃²	C₂×#470	semidirect
338. C₂×C₃	#4867	direct (N × H)
339. C₂×C₃	C₃×#470	semidirect
358. C₃	C₂×#4867	direct (N × H)
359. C₃	C₂×C₃×#470	semidirect
361. C₂	C₃×#4867	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×C₃×Dic₁₂	2
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂×C₃×#897	2
C₂×C₃²×#106	2
C₂×C₃×#810	2
C₃×#4867	2
C₂×C₃×#470	3
C₂×#4867	3

Subgroups — C2×C3×#4867 #11867006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4867 #11867006