Subgroups — C₂²×C₃×#935 #11900357

Order 1152.

4617 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#217	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#935	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃×#123	—	3	1	no	maximal
8	C₂²×#935	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
10	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×D₄	—	2	8	no	—
12	C₂²×C₃²×D₄	C₂²	1	12	yes	—
13	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×Dic₃	—	2	8	no	—
15	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
16	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
17	C₂³×C₃×Dic₃	C₂²	1	12	yes	complemented
18	C₂×C₃×#217	C₂²	1	24	yes	complemented
19	C₂×C₃×#217	C₂²	1	12	yes	complemented
20	C₃×#935	C₂²	1	64	yes	direct product factor
21	C₂×C₃×Dic₃⋊C₄	C₂²	1	24	yes	complemented
22	C₂³×C₃×D₄	—	2	1	no	—
23	C₂³×C₃×D₄	D₃	1	1	yes	characteristic
24	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
25	C₂⁴×C₃×C₄	—	3	1	no	—
26	C₂⁴×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#123	—	3	24	no	—
28	C₂²×C₃×C₄⋊C₄	—	3	2	no	—
29	C₂²×C₃×C₂²⋊C₄	—	3	2	no	—
30	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
31	C₂²×#217	C₂×C₃	1	2	yes	complemented
32	C₂²×#217	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#935	C₂×C₃	1	24	yes	direct product factor
34	C₂²×Dic₃⋊C₄	C₂×C₃	1	2	yes	complemented
35	C₂⁴×C₃²	—	2	8	no	—
36	C₂⁴×C₃²	—	2	4	no	—
37	C₂⁴×C₃²	—	2	8	no	—
38	C₂⁴×C₃²	D₄	1	8	yes	—
39	C₂⁴×C₃²	C₂³	1	6	yes	—
40	C₂⁴×C₃²	C₂³	1	6	yes	—
41	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
42	C₂×C₃²×D₄	—	2	48	no	—
43	C₂×C₃²×D₄	C₂³	1	16	yes	—
44	C₂²×C₃²×C₄	—	2	4	no	—
45	C₂²×C₃²×C₄	C₂³	1	6	yes	—
46	C₂²×C₃×Dic₃	—	2	8	no	—
47	C₂²×C₃×Dic₃	—	2	48	no	—
48	C₂²×C₃×Dic₃	—	2	8	no	—
49	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
50	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
51	C₂²×C₃×Dic₃	C₂³	1	16	yes	complemented
52	C₃×#217	C₂³	1	16	yes	complemented
53	C₃×#217	C₂³	1	32	yes	complemented
54	C₃×Dic₃⋊C₄	C₂³	1	32	yes	complemented
55	C₂²×#123	—	3	1	no	Sylow
56	C₂⁵×C₃	—	2	1	no	—
57	C₂⁵×C₃	—	2	1	no	—
58	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
59	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
60	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
61	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₃×D₄	—	2	16	no	—
63	C₂²×C₃×D₄	—	2	8	no	—
64	C₂²×C₃×D₄	—	2	8	no	—
65	C₂²×C₃×D₄	—	2	12	no	—
66	C₂²×C₃×D₄	C₂×D₃	1	12	yes	—
67	C₂²×C₃×D₄	C₂²×C₃	1	12	yes	—
68	C₂³×C₃×C₄	—	2	1	no	—
69	C₂³×C₃×C₄	—	3	12	no	—
70	C₂³×C₃×C₄	—	3	2	no	—
71	C₂³×C₃×C₄	—	3	2	no	—
72	C₂³×C₃×C₄	—	6	8	no	—
73	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
74	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂³×Dic₃	—	2	8	no	—
76	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
77	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
78	C₂³×Dic₃	C₂²×C₃	1	12	yes	complemented
79	C₃×#123	—	3	64	no	—
80	C₂×C₃×C₄⋊C₄	—	3	24	no	—
81	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
82	C₂×C₃×C₂²⋊C₄	—	3	24	no	—
83	C₂×#217	C₂²×C₃	1	12	yes	complemented
84	C₂×#217	C₂²×C₃	1	24	yes	complemented
85	#935	C₂²×C₃	1	64	yes	direct product factor
86	C₂×Dic₃⋊C₄	C₂²×C₃	1	24	yes	complemented
87	C₂³×C₃²	—	2	12	no	—
88	C₂³×C₃²	—	2	32	no	—
89	C₂³×C₃²	—	2	24	no	—
90	C₂³×C₃²	—	2	24	no	—
91	C₂³×C₃²	—	4	16	no	—
92	C₂³×C₃²	C₂×D₄	1	24	yes	—
93	C₂³×C₃²	C₂×D₄	1	4	yes	—
94	C₂³×C₃²	#41	1	8	yes	—
95	C₂³×C₃²	C₂⁴	1	4	yes	—
96	C₂³×C₃²	C₂⁴	1	4	yes	—
97	C₂³×C₃²	C₂⁴	1	3	yes	—
98	C₃²×D₄	—	2	32	no	—
99	C₂×C₃²×C₄	—	2	12	no	—
100	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
101	C₂×C₃×Dic₃	—	2	24	no	—
102	C₂×C₃×Dic₃	—	2	32	no	—
103	C₂×C₃×Dic₃	—	2	24	no	—
104	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
105	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
106	C₂³×D₄	C₃×D₃	1	1	yes	characteristic
107	C₂⁴×C₄	—	3	1	no	—
108	C₂×#123	—	3	24	no	—
109	C₂²×C₄⋊C₄	—	3	2	no	—
110	C₂²×C₂²⋊C₄	—	3	1	no	—
111	C₂²×C₂²⋊C₄	—	3	2	no	—
112	C₂⁴×C₃	—	2	8	no	—
113	C₂⁴×C₃	—	2	8	no	—
114	C₂⁴×C₃	—	2	8	no	—
115	C₂⁴×C₃	—	2	8	no	—
116	C₂⁴×C₃	—	2	4	no	—
117	C₂⁴×C₃	—	2	4	no	—
118	C₂⁴×C₃	—	2	8	no	—
119	C₂⁴×C₃	—	2	8	no	—
120	C₂⁴×C₃	—	2	1	no	—
121	C₂⁴×C₃	—	2	6	no	—
122	C₂⁴×C₃	—	2	6	no	—
123	C₂⁴×C₃	—	4	8	no	—
124	C₂⁴×C₃	—	4	8	no	—
125	C₂⁴×C₃	#67	1	8	yes	—
126	C₂⁴×C₃	C₃×D₄	1	8	yes	—
127	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
128	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
129	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
130	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
131	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
132	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₃×D₄	—	2	96	no	—
134	C₂×C₃×D₄	—	2	48	no	—
135	C₂×C₃×D₄	—	2	48	no	—
136	C₂×C₃×D₄	—	2	16	no	—
137	C₂×C₃×D₄	C₂²×D₃	1	16	yes	—
138	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
139	C₂²×C₃×C₄	—	2	8	no	—
140	C₂²×C₃×C₄	—	2	4	no	—
141	C₂²×C₃×C₄	—	2	4	no	—
142	C₂²×C₃×C₄	—	2	6	no	—
143	C₂²×C₃×C₄	—	3	12	no	—
144	C₂²×C₃×C₄	—	3	12	no	—
145	C₂²×C₃×C₄	—	3	16	no	—
146	C₂²×C₃×C₄	—	6	8	no	—
147	C₂²×C₃×C₄	—	6	48	no	—
148	C₂²×C₃×C₄	—	6	8	no	—
149	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
150	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
151	C₂²×Dic₃	—	2	8	no	—
152	C₂²×Dic₃	—	2	48	no	—
153	C₂²×Dic₃	—	2	8	no	—
154	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
155	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
156	C₂²×Dic₃	C₂³×C₃	1	16	yes	complemented
157	C₃×C₄⋊C₄	—	3	32	no	—
158	C₃×C₂²⋊C₄	—	3	16	no	—
159	C₃×C₂²⋊C₄	—	3	32	no	—
160	#217	C₂³×C₃	1	16	yes	complemented
161	#217	C₂³×C₃	1	32	yes	complemented
162	Dic₃⋊C₄	C₂³×C₃	1	32	yes	complemented
163	C₂²×C₃²	—	2	4	no	—
164	C₂²×C₃²	—	2	48	no	—
165	C₂²×C₃²	—	2	8	no	—
166	C₂²×C₃²	—	2	8	no	—
167	C₂²×C₃²	—	4	24	no	—
168	C₂²×C₃²	#123	1	16	yes	complemented
169	C₂²×C₃²	C₂²×D₄	1	8	yes	—
170	C₂²×C₃²	C₂²×D₄	1	6	yes	—
171	C₂²×C₃²	C₂×#41	1	12	yes	—
172	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
173	C₃²×C₄	—	2	4	no	—
174	C₃×Dic₃	—	2	8	no	—
175	C₃×Dic₃	—	2	8	no	—
176	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
178	C₂²×D₄	—	2	8	no	—
179	C₂²×D₄	C₂×C₃×D₃	1	12	yes	—
180	C₂³×C₄	—	3	2	no	—
181	C₂³×C₄	—	3	2	no	—
182	C₂³×C₄	—	3	12	no	—
183	C₂³×C₄	—	6	8	no	—
184	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
185	#123	—	3	64	no	—
186	C₂×C₄⋊C₄	—	3	24	no	—
187	C₂×C₂²⋊C₄	—	3	12	no	—
188	C₂×C₂²⋊C₄	—	3	24	no	—
189	C₂³×C₃	—	2	32	no	—
190	C₂³×C₃	—	2	32	no	—
191	C₂³×C₃	—	2	24	no	—
192	C₂³×C₃	—	2	24	no	—
193	C₂³×C₃	—	2	24	no	—
194	C₂³×C₃	—	2	24	no	—
195	C₂³×C₃	—	2	12	no	—
196	C₂³×C₃	—	2	12	no	—
197	C₂³×C₃	—	2	24	no	—
198	C₂³×C₃	—	2	3	no	—
199	C₂³×C₃	—	2	4	no	—
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	—	2	8	no	—
202	C₂³×C₃	—	2	4	no	—
203	C₂³×C₃	—	2	24	no	—
204	C₂³×C₃	—	4	32	no	—
205	C₂³×C₃	—	4	24	no	—
206	C₂³×C₃	—	4	24	no	—
207	C₂³×C₃	—	4	32	no	—
208	C₂³×C₃	—	4	16	no	—
209	C₂³×C₃	—	4	16	no	—
210	C₂³×C₃	#237	1	8	yes	—
211	C₂³×C₃	C₂×#67	1	24	yes	—
212	C₂³×C₃	C₂×#67	1	4	yes	—
213	C₂³×C₃	C₂×C₃×D₄	1	24	yes	—
214	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
215	C₂³×C₃	C₃×#41	1	8	yes	—
216	C₂³×C₃	C₂³×D₃	1	4	yes	—
217	C₂³×C₃	C₂³×D₃	1	4	yes	—
218	C₂³×C₃	C₂³×D₃	1	3	yes	—
219	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
220	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
221	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
222	C₃×D₄	—	2	64	no	—
223	C₃×D₄	—	2	32	no	—
224	C₃×D₄	—	2	32	no	—
225	C₂×C₃×C₄	—	2	24	no	—
226	C₂×C₃×C₄	—	2	12	no	—
227	C₂×C₃×C₄	—	2	12	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	3	8	no	—
230	C₂×C₃×C₄	—	3	8	no	—
231	C₂×C₃×C₄	—	6	24	no	—
232	C₂×C₃×C₄	—	6	32	no	—
233	C₂×C₃×C₄	—	6	24	no	—
234	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
235	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
236	C₂×Dic₃	—	2	24	no	—
237	C₂×Dic₃	—	2	32	no	—
238	C₂×Dic₃	—	2	24	no	—
239	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
240	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
241	C₂×C₃²	—	2	8	no	—
242	C₂×C₃²	—	4	4	no	—
243	C₂×C₃²	C₂×#123	1	12	yes	complemented
244	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
245	C₂×C₃²	C₂²×#41	1	2	yes	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	2	8	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	C₃×#67	1	8	yes	—
250	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
251	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
252	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
253	C₂×D₄	—	2	48	no	—
254	C₂×D₄	C₂²×C₃×D₃	1	16	yes	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	3	12	no	—
257	C₂²×C₄	—	3	12	no	—
258	C₂²×C₄	—	3	16	no	—
259	C₂²×C₄	—	6	8	no	—
260	C₂²×C₄	—	6	48	no	—
261	C₂²×C₄	—	6	8	no	—
262	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
263	C₄⋊C₄	—	3	32	no	—
264	C₂²⋊C₄	—	3	16	no	—
265	C₂²⋊C₄	—	3	32	no	—
266	C₂²×C₃	—	2	8	no	—
267	C₂²×C₃	—	2	8	no	—
268	C₂²×C₃	—	2	48	no	—
269	C₂²×C₃	—	2	48	no	—
270	C₂²×C₃	—	2	8	no	—
271	C₂²×C₃	—	2	8	no	—
272	C₂²×C₃	—	2	4	no	—
273	C₂²×C₃	—	2	4	no	—
274	C₂²×C₃	—	2	8	no	—
275	C₂²×C₃	—	2	16	no	—
276	C₂²×C₃	—	2	12	no	—
277	C₂²×C₃	—	2	6	no	—
278	C₂²×C₃	—	2	8	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	4	48	no	—
281	C₂²×C₃	—	4	8	no	—
282	C₂²×C₃	—	4	8	no	—
283	C₂²×C₃	—	4	48	no	—
284	C₂²×C₃	—	4	24	no	—
285	C₂²×C₃	—	4	24	no	—
286	C₂²×C₃	#935	1	16	yes	direct product factor
287	C₂²×C₃	C₃×#123	1	16	yes	complemented
288	C₂²×C₃	C₂×#237	1	12	yes	—
289	C₂²×C₃	C₂²×#67	1	8	yes	—
290	C₂²×C₃	C₂²×#67	1	6	yes	—
291	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
292	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
293	C₂²×C₃	C₂×C₃×#41	1	12	yes	—
294	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
295	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
296	C₃×C₄	—	2	8	no	—
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	6	8	no	—
300	C₃×C₄	—	6	8	no	—
301	Dic₃	—	2	8	no	—
302	Dic₃	—	2	8	no	—
303	C₃²	C₂²×#123	1	1	yes	characteristic, complemented, Sylow
304	C₂³	—	2	32	no	—
305	C₂³	—	2	24	no	—
306	C₂³	—	2	24	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	4	16	no	—
309	C₂³	C₃×#237	1	8	yes	—
310	C₂³	C₂×C₃×#67	1	24	yes	—
311	C₂³	C₂×C₃×#67	1	4	yes	—
312	C₂³	C₂³×C₃×D₃	1	4	yes	—
313	C₂³	C₂³×C₃×D₃	1	4	yes	—
314	C₂³	C₂³×C₃×D₃	1	3	yes	—
315	D₄	—	2	32	no	—
316	C₂×C₄	—	2	12	no	—
317	C₂×C₄	—	3	8	no	—
318	C₂×C₄	—	3	8	no	—
319	C₂×C₄	—	6	24	no	—
320	C₂×C₄	—	6	32	no	—
321	C₂×C₄	—	6	24	no	—
322	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
323	C₂×C₃	—	2	8	no	—
324	C₂×C₃	—	2	8	no	—
325	C₂×C₃	—	2	12	no	—
326	C₂×C₃	—	2	2	no	—
327	C₂×C₃	—	2	1	no	—
328	C₂×C₃	—	4	8	no	—
329	C₂×C₃	—	4	8	no	—
330	C₂×C₃	—	4	4	no	—
331	C₂×C₃	—	4	4	no	—
332	C₂×C₃	C₂×#935	1	12	yes	direct product factor
333	C₂×C₃	C₂×C₃×#123	1	12	yes	complemented
334	C₂×C₃	C₂²×#237	1	2	yes	—
335	C₂×C₃	C₂³×#67	1	1	yes	characteristic
336	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
337	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
338	C₂²	—	2	48	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	8	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	24	no	—
343	C₂²	C₃×#935	1	16	yes	direct product factor
344	C₂²	C₂×C₃×#237	1	12	yes	—
345	C₂²	C₂²×C₃×#67	1	8	yes	—
346	C₂²	C₂²×C₃×#67	1	6	yes	—
347	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
348	C₄	—	2	4	no	—
349	C₄	—	6	8	no	—
350	C₄	—	6	8	no	—
351	C₃	—	2	1	no	—
352	C₃	C₂²×#935	1	1	yes	characteristic, direct product factor
353	C₃	C₂²×C₃×#123	1	1	yes	characteristic, complemented
354	C₂	—	2	8	no	—
355	C₂	—	4	4	no	—
356	C₂	C₂×C₃×#935	1	12	yes	direct product factor
357	C₂	C₂²×C₃×#237	1	2	yes	—
358	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting, prime radical	C₂³×C₃²×D₄	C₂
socle	C₂⁴×C₃²	C₂³
hypercenter	C₂³×C₃×D₄	D₃
hypocenter	C₃	C₂²×C₃×#123
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₃×Dic₃	C₂	semidirect
3. C₂²×C₃×#217	C₂	semidirect
4. C₂²×C₃×#217	C₂	semidirect
5. C₂×C₃×#935	C₂	direct (N × H)
6. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
8. C₂²×#935	C₃	direct (N × H)
17. C₂³×C₃×Dic₃	C₂²	semidirect
18. C₂×C₃×#217	C₂²	semidirect
19. C₂×C₃×#217	C₂²	semidirect
20. C₃×#935	C₂²	direct (N × H)
21. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
26. C₂⁴×Dic₃	C₂×C₃	semidirect
31. C₂²×#217	C₂×C₃	semidirect
32. C₂²×#217	C₂×C₃	semidirect
33. C₂×#935	C₂×C₃	direct (N × H)
34. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
51. C₂²×C₃×Dic₃	C₂³	semidirect
52. C₃×#217	C₂³	semidirect
53. C₃×#217	C₂³	semidirect
54. C₃×Dic₃⋊C₄	C₂³	semidirect
78. C₂³×Dic₃	C₂²×C₃	semidirect
83. C₂×#217	C₂²×C₃	semidirect
84. C₂×#217	C₂²×C₃	semidirect
85. #935	C₂²×C₃	direct (N × H)
86. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
156. C₂²×Dic₃	C₂³×C₃	semidirect
160. #217	C₂³×C₃	semidirect
161. #217	C₂³×C₃	semidirect
162. Dic₃⋊C₄	C₂³×C₃	semidirect
168. C₂²×C₃²	#123	semidirect
243. C₂×C₃²	C₂×#123	semidirect
286. C₂²×C₃	#935	direct (N × H)
287. C₂²×C₃	C₃×#123	semidirect
303. C₃²	C₂²×#123	semidirect
332. C₂×C₃	C₂×#935	direct (N × H)
333. C₂×C₃	C₂×C₃×#123	semidirect
343. C₂²	C₃×#935	direct (N × H)
352. C₃	C₂²×#935	direct (N × H)
353. C₃	C₂²×C₃×#123	semidirect
356. C₂	C₂×C₃×#935	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃²×D₄	2
C₂⁴×C₃×Dic₃	2
C₂²×C₃×#217	2
C₂×C₃×#935	2
C₂²×C₃×Dic₃⋊C₄	2
C₂²×C₃×#123	3
C₂²×#935	3

Subgroups — C22×C3×#935 #11900357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#935 #11900357