Subgroups — C₂×C₃×#5594 #11910209

Order 1152.

3147 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×C₃²×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#953	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#937	C₂	1	3	yes	maximal, complemented
4	C₂×C₃×#936	C₂	1	3	yes	maximal, complemented
5	C₃×#5594	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#885	C₂	1	6	yes	maximal, complemented
7	C₂×C₃×H(3,𝔽₄)	—	3	1	no	maximal
8	C₂×#5594	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	1	yes	characteristic, complemented
10	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₃²×D₄	C₂²	1	3	yes	—
12	C₂²×C₃×#67	C₂²	1	6	yes	—
13	C₂²×C₃×Dic₆	C₂²	1	3	yes	complemented
14	C₃²×#120	C₂²	1	8	yes	complemented
15	C₂×C₃²×C₂²⋊C₄	C₂²	1	3	yes	complemented
16	C₃×#953	C₂²	1	16	yes	complemented
17	C₂×C₃×#217	C₂²	1	6	yes	complemented
18	C₂×C₃×#217	C₂²	1	3	yes	complemented
19	C₃×#937	C₂²	1	24	yes	complemented
20	C₃×#936	C₂²	1	24	yes	complemented
21	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	6	yes	complemented
22	C₂×C₃×C₄×Dic₃	C₂²	1	3	yes	complemented
23	C₃×#885	C₂²	1	48	yes	complemented
24	C₃×H(3,𝔽₄)	—	3	16	no	—
25	C₂×C₃×#124	—	3	3	no	—
26	C₂×C₃×#124	—	3	6	no	—
27	C₂×C₃×#120	—	2	1	no	—
28	C₂×C₃×#120	—	3	3	no	—
29	C₂×C₃×#120	—	3	2	no	—
30	C₂×C₃×#120	D₃	1	1	yes	characteristic, complemented
31	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#953	C₂×C₃	1	2	yes	complemented
33	C₂×#937	C₂×C₃	1	3	yes	complemented
34	C₂×#936	C₂×C₃	1	3	yes	complemented
35	#5594	C₂×C₃	1	16	yes	direct product factor
36	C₂×#885	C₂×C₃	1	6	yes	complemented
37	C₂⁴×C₃²	—	4	6	no	—
38	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
39	C₂⁴×C₃²	C₂³	1	3	yes	—
40	C₂⁴×C₃²	C₂³	1	4	yes	complemented
41	C₂³×C₃×D₃	—	4	6	no	—
42	C₂³×C₃×D₃	C₂³	1	2	yes	—
43	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
44	C₂×C₃²×D₄	—	4	6	no	—
45	C₂×C₃²×D₄	C₂³	1	12	yes	—
46	C₂²×C₃²×C₄	C₂³	1	3	yes	—
47	C₂×C₃×#67	—	4	12	no	—
48	C₂×C₃×#67	C₂³	1	24	yes	—
49	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
50	C₂×C₃×Dic₆	—	4	6	no	—
51	C₂×C₃×Dic₆	C₂³	1	12	yes	complemented
52	C₃²×C₂²⋊C₄	C₂³	1	12	yes	complemented
53	C₃×#217	C₂³	1	24	yes	complemented
54	C₃×#217	C₂³	1	12	yes	complemented
55	C₃×(C₂×D₃)⋊C₄	C₂³	1	24	yes	complemented
56	C₃×C₄×Dic₃	C₂³	1	12	yes	complemented
57	C₂×H(3,𝔽₄)	—	3	1	no	Sylow
58	C₂⁵×C₃	—	2	1	no	—
59	C₂⁵×C₃	—	3	1	no	—
60	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic, complemented
61	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic, complemented
62	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
63	C₂²×C₃×Q₈	—	3	3	no	—
64	C₂²×C₃×D₄	—	2	3	no	—
65	C₂²×C₃×D₄	—	3	6	no	—
66	C₂²×C₃×D₄	C₂×D₃	1	3	yes	—
67	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
68	C₂²×#67	C₂²×C₃	1	6	yes	—
69	C₂²×Dic₆	C₂²×C₃	1	3	yes	complemented
70	C₃×#124	—	3	24	no	—
71	C₃×#124	—	3	48	no	—
72	C₃×#120	—	2	8	no	—
73	C₃×#120	—	3	16	no	—
74	C₃×#120	—	3	24	no	—
75	C₃×#120	C₂×D₃	1	8	yes	complemented
76	C₃×#120	C₂²×C₃	1	8	yes	complemented
77	C₂×C₃×C₂²⋊C₄	—	2	3	no	—
78	C₂×C₃×C₂²⋊C₄	—	3	3	no	—
79	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
80	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
81	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	3	yes	complemented
82	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
83	C₂×C₃×C₄²	—	3	3	no	—
84	#953	C₂²×C₃	1	16	yes	complemented
85	C₂×#217	C₂²×C₃	1	6	yes	complemented
86	C₂×#217	C₂²×C₃	1	3	yes	complemented
87	#937	C₂²×C₃	1	24	yes	complemented
88	#936	C₂²×C₃	1	24	yes	complemented
89	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	6	yes	complemented
90	C₂×C₄×Dic₃	C₂²×C₃	1	3	yes	complemented
91	#885	C₂²×C₃	1	48	yes	complemented
92	C₂³×C₃²	—	2	6	no	—
93	C₂³×C₃²	—	2	6	no	—
94	C₂³×C₃²	—	2	12	no	—
95	C₂³×C₃²	—	4	12	no	—
96	C₂³×C₃²	—	4	16	no	—
97	C₂³×C₃²	C₂⁴	1	2	yes	—
98	C₂³×C₃²	C₂⁴	1	6	yes	—
99	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
100	C₂²×C₃×D₃	—	2	12	no	—
101	C₂²×C₃×D₃	—	4	12	no	—
102	C₂²×C₃×D₃	—	4	16	no	—
103	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
104	C₃²×D₄	—	4	12	no	—
105	C₂×C₃²×C₄	—	2	6	no	—
106	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
107	C₃×#67	—	4	24	no	—
108	C₂×C₃×Dic₃	—	2	12	no	—
109	C₂×C₃×Dic₃	C₂⁴	1	12	yes	—
110	C₃×Dic₆	—	4	12	no	—
111	H(3,𝔽₄)	—	3	16	no	—
112	C₂×#124	—	3	3	no	—
113	C₂×#124	—	3	6	no	—
114	C₂×#120	—	3	2	no	—
115	C₂×#120	—	3	3	no	—
116	C₂×#120	C₃×D₃	1	1	yes	characteristic, complemented
117	C₂⁴×C₃	—	2	3	no	—
118	C₂⁴×C₃	—	2	1	no	—
119	C₂⁴×C₃	—	2	4	no	—
120	C₂⁴×C₃	—	3	2	no	—
121	C₂⁴×C₃	—	3	4	no	—
122	C₂⁴×C₃	—	4	6	no	—
123	C₂⁴×C₃	—	4	6	no	—
124	C₂⁴×C₃	—	4	12	no	—
125	C₂⁴×C₃	—	12	6	no	—
126	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
127	C₂⁴×C₃	C₂²×D₃	1	3	yes	—
128	C₂⁴×C₃	C₂²×D₃	1	4	yes	complemented
129	C₂⁴×C₃	C₂³×C₃	1	3	yes	—
130	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
131	C₂⁴×C₃	C₂³×C₃	1	4	yes	complemented
132	C₂³×D₃	—	4	6	no	—
133	C₂³×D₃	C₂³×C₃	1	2	yes	—
134	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
135	C₂×C₃×Q₈	—	3	12	no	—
136	C₂×C₃×Q₈	—	12	6	no	—
137	C₂×C₃×D₄	—	2	12	no	—
138	C₂×C₃×D₄	—	3	24	no	—
139	C₂×C₃×D₄	—	4	6	no	—
140	C₂×C₃×D₄	—	4	6	no	—
141	C₂×C₃×D₄	—	4	12	no	—
142	C₂×C₃×D₄	—	12	12	no	—
143	C₂×C₃×D₄	C₂²×D₃	1	12	yes	—
144	C₂×C₃×D₄	C₂³×C₃	1	12	yes	—
145	C₂²×C₃×C₄	—	2	3	no	—
146	C₂²×C₃×C₄	—	3	6	no	—
147	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
148	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
149	C₂×#67	—	4	12	no	—
150	C₂×#67	C₂³×C₃	1	24	yes	—
151	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
152	C₂×Dic₆	—	4	6	no	—
153	C₂×Dic₆	C₂³×C₃	1	12	yes	complemented
154	C₃×C₂²⋊C₄	—	2	12	no	—
155	C₃×C₂²⋊C₄	—	3	12	no	—
156	C₃×C₂²⋊C₄	—	3	24	no	—
157	C₃×C₂²⋊C₄	—	3	24	no	—
158	C₃×C₂²⋊C₄	C₂²×D₃	1	12	yes	complemented
159	C₃×C₂²⋊C₄	C₂³×C₃	1	12	yes	complemented
160	C₃×C₄²	—	3	12	no	—
161	#217	C₂³×C₃	1	24	yes	complemented
162	#217	C₂³×C₃	1	12	yes	complemented
163	(C₂×D₃)⋊C₄	C₂³×C₃	1	24	yes	complemented
164	C₄×Dic₃	C₂³×C₃	1	12	yes	complemented
165	C₂²×C₃²	—	2	6	no	—
166	C₂²×C₃²	—	2	12	no	—
167	C₂²×C₃²	—	2	6	no	—
168	C₂²×C₃²	—	4	16	no	—
169	C₂²×C₃²	—	4	12	no	—
170	C₂²×C₃²	—	4	4	no	—
171	C₂²×C₃²	H(5,𝔽₂)	1	6	yes	—
172	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
173	C₂×C₃×D₃	—	2	12	no	—
174	C₂×C₃×D₃	—	4	16	no	—
175	C₂×C₃×D₃	—	4	8	no	—
176	C₃²×C₄	—	2	6	no	—
177	C₃×Dic₃	—	2	12	no	—
178	C₂⁵	—	3	1	no	—
179	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic, complemented
180	C₂²×Q₈	—	3	3	no	—
181	C₂²×D₄	—	3	6	no	—
182	C₂²×D₄	C₂×C₃×D₃	1	3	yes	—
183	#124	—	3	24	no	—
184	#124	—	3	48	no	—
185	#120	—	3	16	no	—
186	#120	—	3	24	no	—
187	#120	C₂×C₃×D₃	1	8	yes	complemented
188	C₂×C₂²⋊C₄	—	3	3	no	—
189	C₂×C₂²⋊C₄	—	3	6	no	—
190	C₂×C₂²⋊C₄	—	3	6	no	—
191	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	3	yes	complemented
192	C₂×C₄²	—	3	3	no	—
193	C₂³×C₃	—	2	12	no	—
194	C₂³×C₃	—	2	6	no	—
195	C₂³×C₃	—	2	6	no	—
196	C₂³×C₃	—	2	12	no	—
197	C₂³×C₃	—	2	12	no	—
198	C₂³×C₃	—	2	6	no	—
199	C₂³×C₃	—	2	6	no	—
200	C₂³×C₃	—	2	1	no	—
201	C₂³×C₃	—	2	6	no	—
202	C₂³×C₃	—	2	2	no	—
203	C₂³×C₃	—	3	4	no	—
204	C₂³×C₃	—	4	12	no	—
205	C₂³×C₃	—	4	6	no	—
206	C₂³×C₃	—	4	12	no	—
207	C₂³×C₃	—	4	12	no	—
208	C₂³×C₃	—	4	24	no	—
209	C₂³×C₃	—	4	32	no	—
210	C₂³×C₃	—	4	16	no	—
211	C₂³×C₃	—	4	16	no	—
212	C₂³×C₃	—	6	12	no	—
213	C₂³×C₃	—	12	12	no	—
214	C₂³×C₃	—	12	16	no	—
215	C₂³×C₃	C₂³×D₃	1	2	yes	—
216	C₂³×C₃	C₂³×D₃	1	6	yes	—
217	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
218	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
219	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
220	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
221	C₂²×D₃	—	2	12	no	—
222	C₂²×D₃	—	4	12	no	—
223	C₂²×D₃	—	4	16	no	—
224	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
225	C₃×Q₈	—	12	12	no	—
226	C₃×D₄	—	4	12	no	—
227	C₃×D₄	—	4	12	no	—
228	C₃×D₄	—	4	24	no	—
229	C₃×D₄	—	12	24	no	—
230	C₂×C₃×C₄	—	2	6	no	—
231	C₂×C₃×C₄	—	2	6	no	—
232	C₂×C₃×C₄	—	2	6	no	—
233	C₂×C₃×C₄	—	3	12	no	—
234	C₂×C₃×C₄	—	4	6	no	—
235	C₂×C₃×C₄	—	6	12	no	—
236	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
237	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
238	#67	—	4	24	no	—
239	C₂×Dic₃	—	2	12	no	—
240	C₂×Dic₃	C₂⁴×C₃	1	12	yes	—
241	Dic₆	—	4	12	no	—
242	C₂×C₃²	—	4	6	no	—
243	C₂×C₃²	—	4	2	no	—
244	C₂×C₃²	H(3,𝔽₄)	1	4	yes	complemented
245	C₂×C₃²	C₂×H(5,𝔽₂)	1	3	yes	—
246	C₃×D₃	—	4	4	no	—
247	C₂⁴	—	3	2	no	—
248	C₂⁴	—	3	4	no	—
249	C₂⁴	—	4	6	no	—
250	C₂⁴	—	12	6	no	—
251	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂⁴	C₂²×C₃×D₃	1	3	yes	—
253	C₂⁴	C₂²×C₃×D₃	1	4	yes	complemented
254	C₂×Q₈	—	3	12	no	—
255	C₂×Q₈	—	12	6	no	—
256	C₂×D₄	—	3	24	no	—
257	C₂×D₄	—	4	6	no	—
258	C₂×D₄	—	12	12	no	—
259	C₂×D₄	C₂²×C₃×D₃	1	12	yes	—
260	C₂²×C₄	—	3	6	no	—
261	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
262	C₂²⋊C₄	—	3	12	no	—
263	C₂²⋊C₄	—	3	24	no	—
264	C₂²⋊C₄	—	3	24	no	—
265	C₂²⋊C₄	C₂²×C₃×D₃	1	12	yes	complemented
266	C₄²	—	3	12	no	—
267	C₂²×C₃	—	2	12	no	—
268	C₂²×C₃	—	2	6	no	—
269	C₂²×C₃	—	2	6	no	—
270	C₂²×C₃	—	2	12	no	—
271	C₂²×C₃	—	2	12	no	—
272	C₂²×C₃	—	2	6	no	—
273	C₂²×C₃	—	2	6	no	—
274	C₂²×C₃	—	2	6	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	4	12	no	—
277	C₂²×C₃	—	4	6	no	—
278	C₂²×C₃	—	4	24	no	—
279	C₂²×C₃	—	4	32	no	—
280	C₂²×C₃	—	4	16	no	—
281	C₂²×C₃	—	4	16	no	—
282	C₂²×C₃	—	4	4	no	—
283	C₂²×C₃	—	4	12	no	—
284	C₂²×C₃	—	4	12	no	—
285	C₂²×C₃	—	4	4	no	—
286	C₂²×C₃	—	6	12	no	—
287	C₂²×C₃	—	8	4	no	—
288	C₂²×C₃	—	12	16	no	—
289	C₂²×C₃	—	12	8	no	—
290	C₂²×C₃	#1004	1	6	yes	—
291	C₂²×C₃	C₃×H(5,𝔽₂)	1	6	yes	—
292	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
293	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
294	C₂×D₃	—	2	12	no	—
295	C₂×D₃	—	4	16	no	—
296	C₂×D₃	—	4	8	no	—
297	C₃×C₄	—	2	6	no	—
298	C₃×C₄	—	2	6	no	—
299	C₃×C₄	—	4	6	no	—
300	C₃×C₄	—	6	12	no	—
301	Dic₃	—	2	12	no	—
302	C₃²	C₂×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
303	C₂³	—	2	6	no	—
304	C₂³	—	2	6	no	—
305	C₂³	—	2	12	no	—
306	C₂³	—	3	4	no	—
307	C₂³	—	4	12	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	6	12	no	—
310	C₂³	—	12	12	no	—
311	C₂³	—	12	16	no	—
312	C₂³	C₂³×C₃×D₃	1	2	yes	—
313	C₂³	C₂³×C₃×D₃	1	6	yes	—
314	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
315	Q₈	—	12	12	no	—
316	D₄	—	4	12	no	—
317	D₄	—	12	24	no	—
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	3	12	no	—
320	C₂×C₄	—	6	12	no	—
321	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
322	C₂×C₃	—	2	4	no	—
323	C₂×C₃	—	2	3	no	—
324	C₂×C₃	—	4	12	no	—
325	C₂×C₃	—	4	2	no	—
326	C₂×C₃	—	4	6	no	—
327	C₂×C₃	—	4	6	no	—
328	C₂×C₃	—	4	2	no	—
329	C₂×C₃	—	8	2	no	—
330	C₂×C₃	—	12	4	no	—
331	C₂×C₃	#5594	1	4	yes	direct product factor
332	C₂×C₃	C₃×H(3,𝔽₄)	1	4	yes	complemented
333	C₂×C₃	C₂×#1004	1	3	yes	—
334	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
335	D₃	—	4	4	no	—
336	C₂²	—	2	6	no	—
337	C₂²	—	2	6	no	—
338	C₂²	—	2	12	no	—
339	C₂²	—	4	16	no	—
340	C₂²	—	4	12	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	6	12	no	—
343	C₂²	—	12	16	no	—
344	C₂²	—	12	8	no	—
345	C₂²	C₃×#1004	1	6	yes	—
346	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
347	C₄	—	2	6	no	—
348	C₄	—	6	12	no	—
349	C₃	—	2	1	no	—
350	C₃	C₂×#5594	1	1	yes	characteristic, direct product factor
351	C₃	C₂×C₃×H(3,𝔽₄)	1	1	yes	characteristic, complemented
352	C₂	—	4	6	no	—
353	C₂	—	4	2	no	—
354	C₂	—	12	4	no	—
355	C₂	C₃×#5594	1	4	yes	direct product factor
356	C₂	C₂×C₃×#1004	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#120	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#120	D₃
hypocenter	C₃	C₂×C₃×H(3,𝔽₄)
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#120	C₂	semidirect
2. C₂×C₃×#953	C₂	semidirect
3. C₂×C₃×#937	C₂	semidirect
4. C₂×C₃×#936	C₂	semidirect
5. C₃×#5594	C₂	direct (N × H)
6. C₂×C₃×#885	C₂	semidirect
8. C₂×#5594	C₃	direct (N × H)
9. C₂⁵×C₃²	C₂²	semidirect
10. C₂⁴×C₃×D₃	C₂²	semidirect
13. C₂²×C₃×Dic₆	C₂²	semidirect
14. C₃²×#120	C₂²	semidirect
15. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
16. C₃×#953	C₂²	semidirect
17. C₂×C₃×#217	C₂²	semidirect
18. C₂×C₃×#217	C₂²	semidirect
19. C₃×#937	C₂²	semidirect
20. C₃×#936	C₂²	semidirect
21. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
22. C₂×C₃×C₄×Dic₃	C₂²	semidirect
23. C₃×#885	C₂²	semidirect
30. C₂×C₃×#120	D₃	semidirect
31. C₂×C₃×#120	C₂×C₃	semidirect
32. C₂×#953	C₂×C₃	semidirect
33. C₂×#937	C₂×C₃	semidirect
34. C₂×#936	C₂×C₃	semidirect
35. #5594	C₂×C₃	direct (N × H)
36. C₂×#885	C₂×C₃	semidirect
40. C₂⁴×C₃²	C₂³	semidirect
43. C₂³×C₃×D₃	C₂³	semidirect
51. C₂×C₃×Dic₆	C₂³	semidirect
52. C₃²×C₂²⋊C₄	C₂³	semidirect
53. C₃×#217	C₂³	semidirect
54. C₃×#217	C₂³	semidirect
55. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
56. C₃×C₄×Dic₃	C₂³	semidirect
60. C₂⁵×C₃	C₂×D₃	semidirect
61. C₂⁵×C₃	C₂²×C₃	semidirect
62. C₂⁴×D₃	C₂²×C₃	semidirect
69. C₂²×Dic₆	C₂²×C₃	semidirect
75. C₃×#120	C₂×D₃	semidirect
76. C₃×#120	C₂²×C₃	semidirect
81. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
82. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
84. #953	C₂²×C₃	semidirect
85. C₂×#217	C₂²×C₃	semidirect
86. C₂×#217	C₂²×C₃	semidirect
87. #937	C₂²×C₃	semidirect
88. #936	C₂²×C₃	semidirect
89. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
90. C₂×C₄×Dic₃	C₂²×C₃	semidirect
91. #885	C₂²×C₃	semidirect
116. C₂×#120	C₃×D₃	semidirect
128. C₂⁴×C₃	C₂²×D₃	semidirect
131. C₂⁴×C₃	C₂³×C₃	semidirect
134. C₂³×D₃	C₂³×C₃	semidirect
153. C₂×Dic₆	C₂³×C₃	semidirect
158. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
159. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
161. #217	C₂³×C₃	semidirect
162. #217	C₂³×C₃	semidirect
163. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
164. C₄×Dic₃	C₂³×C₃	semidirect
179. C₂⁵	C₂×C₃×D₃	semidirect
187. #120	C₂×C₃×D₃	semidirect
191. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
244. C₂×C₃²	H(3,𝔽₄)	semidirect
253. C₂⁴	C₂²×C₃×D₃	semidirect
265. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
302. C₃²	C₂×H(3,𝔽₄)	semidirect
331. C₂×C₃	#5594	direct (N × H)
332. C₂×C₃	C₃×H(3,𝔽₄)	semidirect
350. C₃	C₂×#5594	direct (N × H)
351. C₃	C₂×C₃×H(3,𝔽₄)	semidirect
355. C₂	C₃×#5594	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×C₃²×#120	2
C₂×C₃×#953	2
C₂×C₃×#937	2
C₂×C₃×#936	2
C₃×#5594	2
C₂×C₃×#885	2
C₂×C₃×H(3,𝔽₄)	3
C₂×#5594	3

Subgroups — C2×C3×#5594 #11910209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5594 #11910209