Subgroups — C₂²×C₃×#929 #11900363

Order 1152.

4617 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#929	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂²×C₃×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃×#123	—	3	1	no	maximal
8	C₂²×#929	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
10	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
11	C₂³×C₃²×C₄	—	2	8	no	—
12	C₂³×C₃²×C₄	C₂²	1	2	yes	—
13	C₂³×C₃²×C₄	C₂²	1	12	yes	complemented
14	C₂²×C₃×#67	—	2	8	no	—
15	C₂²×C₃×#67	C₂²	1	12	yes	—
16	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
17	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×#217	C₂²	1	12	yes	complemented
19	C₃×#929	C₂²	1	64	yes	direct product factor
20	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	24	yes	complemented
21	C₂×C₃×Dic₃⋊C₄	C₂²	1	24	yes	complemented
22	C₂³×C₃×D₄	—	3	1	no	—
23	C₂⁴×C₃×C₄	—	2	1	no	—
24	C₂⁴×C₃×C₄	D₃	1	1	yes	characteristic, complemented
25	C₂⁴×C₃×C₄	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂³×#67	C₂×C₃	1	1	yes	characteristic
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	1	yes	characteristic, complemented
32	C₂×#929	C₂×C₃	1	24	yes	direct product factor
33	C₂²×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	complemented
34	C₂²×Dic₃⋊C₄	C₂×C₃	1	2	yes	complemented
35	C₂⁴×C₃²	—	2	8	no	—
36	C₂⁴×C₃²	D₄	1	8	yes	—
37	C₂⁴×C₃²	C₂³	1	6	yes	—
38	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
39	C₂³×C₃×D₃	—	2	4	no	—
40	C₂³×C₃×D₃	—	2	8	no	—
41	C₂³×C₃×D₃	C₂³	1	6	yes	—
42	C₂²×C₃²×C₄	—	2	8	no	—
43	C₂²×C₃²×C₄	—	2	48	no	—
44	C₂²×C₃²×C₄	C₂³	1	12	yes	—
45	C₂²×C₃²×C₄	C₂³	1	16	yes	complemented
46	C₂×C₃×#67	—	2	48	no	—
47	C₂×C₃×#67	C₂³	1	16	yes	—
48	C₂²×C₃×Dic₃	—	2	4	no	—
49	C₂²×C₃×Dic₃	—	2	8	no	—
50	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
51	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
52	C₃×#217	C₂³	1	16	yes	complemented
53	C₃×(C₂×D₃)⋊C₄	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	—	3	1	no	—
58	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
59	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
60	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₃×D₄	—	3	12	no	—
62	C₂²×C₃×D₄	—	6	8	no	—
63	C₂³×C₃×C₄	—	2	16	no	—
64	C₂³×C₃×C₄	—	2	8	no	—
65	C₂³×C₃×C₄	—	2	8	no	—
66	C₂³×C₃×C₄	—	2	2	no	—
67	C₂³×C₃×C₄	—	2	12	no	—
68	C₂³×C₃×C₄	—	3	1	no	—
69	C₂³×C₃×C₄	—	3	2	no	—
70	C₂³×C₃×C₄	C₂×D₃	1	2	yes	—
71	C₂³×C₃×C₄	C₂×D₃	1	12	yes	complemented
72	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
73	C₂³×C₃×C₄	C₂²×C₃	1	12	yes	complemented
74	C₂²×#67	—	2	8	no	—
75	C₂²×#67	C₂²×C₃	1	12	yes	—
76	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
77	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
78	C₃×#123	—	3	64	no	—
79	C₂×C₃×C₄⋊C₄	—	3	24	no	—
80	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
81	C₂×C₃×C₂²⋊C₄	—	3	24	no	—
82	C₂×#217	C₂²×C₃	1	12	yes	complemented
83	#929	C₂²×C₃	1	64	yes	direct product factor
84	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	24	yes	complemented
85	C₂×Dic₃⋊C₄	C₂²×C₃	1	24	yes	complemented
86	C₂³×C₃²	—	2	32	no	—
87	C₂³×C₃²	—	2	24	no	—
88	C₂³×C₃²	C₂×D₄	1	24	yes	—
89	C₂³×C₃²	C₂×D₄	1	4	yes	—
90	C₂³×C₃²	#41	1	8	yes	—
91	C₂³×C₃²	C₂⁴	1	4	yes	—
92	C₂³×C₃²	C₂⁴	1	3	yes	—
93	C₂²×C₃×D₃	—	2	12	no	—
94	C₂²×C₃×D₃	—	2	24	no	—
95	C₂²×C₃×D₃	—	4	16	no	—
96	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
97	C₂×C₃²×C₄	—	2	24	no	—
98	C₂×C₃²×C₄	—	2	32	no	—
99	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
100	C₃×#67	—	2	32	no	—
101	C₂×C₃×Dic₃	—	2	12	no	—
102	C₂×C₃×Dic₃	—	2	24	no	—
103	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
104	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
105	C₂³×D₄	—	3	1	no	—
106	C₂⁴×C₄	C₃×D₃	1	1	yes	characteristic, complemented
107	C₂×#123	—	3	24	no	—
108	C₂²×C₄⋊C₄	—	3	2	no	—
109	C₂²×C₂²⋊C₄	—	3	1	no	—
110	C₂²×C₂²⋊C₄	—	3	2	no	—
111	C₂⁴×C₃	—	2	16	no	—
112	C₂⁴×C₃	—	2	8	no	—
113	C₂⁴×C₃	—	2	8	no	—
114	C₂⁴×C₃	—	2	8	no	—
115	C₂⁴×C₃	—	2	6	no	—
116	C₂⁴×C₃	—	2	1	no	—
117	C₂⁴×C₃	—	3	6	no	—
118	C₂⁴×C₃	—	6	8	no	—
119	C₂⁴×C₃	—	6	4	no	—
120	C₂⁴×C₃	#67	1	8	yes	—
121	C₂⁴×C₃	C₃×D₄	1	8	yes	—
122	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
123	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
124	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
125	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
126	C₂³×D₃	—	2	4	no	—
127	C₂³×D₃	—	2	8	no	—
128	C₂³×D₃	C₂³×C₃	1	6	yes	—
129	C₂×C₃×D₄	—	3	16	no	—
130	C₂×C₃×D₄	—	6	48	no	—
131	C₂²×C₃×C₄	—	2	16	no	—
132	C₂²×C₃×C₄	—	2	96	no	—
133	C₂²×C₃×C₄	—	2	8	no	—
134	C₂²×C₃×C₄	—	2	48	no	—
135	C₂²×C₃×C₄	—	2	8	no	—
136	C₂²×C₃×C₄	—	2	48	no	—
137	C₂²×C₃×C₄	—	2	12	no	—
138	C₂²×C₃×C₄	—	2	16	no	—
139	C₂²×C₃×C₄	—	3	12	no	—
140	C₂²×C₃×C₄	—	3	6	no	—
141	C₂²×C₃×C₄	—	6	8	no	—
142	C₂²×C₃×C₄	—	6	4	no	—
143	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	—
144	C₂²×C₃×C₄	C₂²×D₃	1	16	yes	complemented
145	C₂²×C₃×C₄	C₂³×C₃	1	12	yes	—
146	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	complemented
147	C₂×#67	—	2	48	no	—
148	C₂×#67	C₂³×C₃	1	16	yes	—
149	C₂²×Dic₃	—	2	4	no	—
150	C₂²×Dic₃	—	2	8	no	—
151	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
152	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
153	C₃×C₄⋊C₄	—	3	32	no	—
154	C₃×C₂²⋊C₄	—	3	16	no	—
155	C₃×C₂²⋊C₄	—	3	32	no	—
156	#217	C₂³×C₃	1	16	yes	complemented
157	(C₂×D₃)⋊C₄	C₂³×C₃	1	32	yes	complemented
158	Dic₃⋊C₄	C₂³×C₃	1	32	yes	complemented
159	C₂²×C₃²	—	2	48	no	—
160	C₂²×C₃²	—	2	8	no	—
161	C₂²×C₃²	#123	1	16	yes	complemented
162	C₂²×C₃²	C₂²×D₄	1	8	yes	—
163	C₂²×C₃²	C₂²×D₄	1	6	yes	—
164	C₂²×C₃²	C₂×#41	1	12	yes	—
165	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
166	C₂×C₃×D₃	—	2	4	no	—
167	C₂×C₃×D₃	—	2	8	no	—
168	C₂×C₃×D₃	—	4	24	no	—
169	C₃²×C₄	—	2	8	no	—
170	C₃×Dic₃	—	2	4	no	—
171	C₃×Dic₃	—	2	8	no	—
172	C₂⁵	—	3	1	no	—
173	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
174	C₂²×D₄	—	3	12	no	—
175	C₂²×D₄	—	6	8	no	—
176	C₂³×C₄	—	2	8	no	—
177	C₂³×C₄	—	3	2	no	—
178	C₂³×C₄	—	3	1	no	—
179	C₂³×C₄	C₂×C₃×D₃	1	2	yes	—
180	C₂³×C₄	C₂×C₃×D₃	1	12	yes	complemented
181	#123	—	3	64	no	—
182	C₂×C₄⋊C₄	—	3	24	no	—
183	C₂×C₂²⋊C₄	—	3	12	no	—
184	C₂×C₂²⋊C₄	—	3	24	no	—
185	C₂³×C₃	—	2	64	no	—
186	C₂³×C₃	—	2	48	no	—
187	C₂³×C₃	—	2	32	no	—
188	C₂³×C₃	—	2	32	no	—
189	C₂³×C₃	—	2	24	no	—
190	C₂³×C₃	—	2	24	no	—
191	C₂³×C₃	—	2	4	no	—
192	C₂³×C₃	—	2	3	no	—
193	C₂³×C₃	—	2	8	no	—
194	C₂³×C₃	—	2	24	no	—
195	C₂³×C₃	—	2	4	no	—
196	C₂³×C₃	—	3	4	no	—
197	C₂³×C₃	—	6	24	no	—
198	C₂³×C₃	—	6	12	no	—
199	C₂³×C₃	—	12	16	no	—
200	C₂³×C₃	#235	1	8	yes	—
201	C₂³×C₃	C₂×#67	1	24	yes	—
202	C₂³×C₃	C₂×#67	1	4	yes	—
203	C₂³×C₃	C₂×C₃×D₄	1	24	yes	—
204	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
205	C₂³×C₃	C₃×#41	1	8	yes	—
206	C₂³×C₃	C₂³×D₃	1	4	yes	—
207	C₂³×C₃	C₂³×D₃	1	3	yes	—
208	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
209	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
210	C₂²×D₃	—	2	12	no	—
211	C₂²×D₃	—	2	24	no	—
212	C₂²×D₃	—	4	16	no	—
213	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
214	C₃×D₄	—	6	32	no	—
215	C₂×C₃×C₄	—	2	48	no	—
216	C₂×C₃×C₄	—	2	64	no	—
217	C₂×C₃×C₄	—	2	24	no	—
218	C₂×C₃×C₄	—	2	32	no	—
219	C₂×C₃×C₄	—	2	24	no	—
220	C₂×C₃×C₄	—	2	32	no	—
221	C₂×C₃×C₄	—	2	8	no	—
222	C₂×C₃×C₄	—	3	8	no	—
223	C₂×C₃×C₄	—	3	4	no	—
224	C₂×C₃×C₄	—	6	24	no	—
225	C₂×C₃×C₄	—	6	12	no	—
226	C₂×C₃×C₄	C₂³×D₃	1	8	yes	—
227	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
228	#67	—	2	32	no	—
229	C₂×Dic₃	—	2	12	no	—
230	C₂×Dic₃	—	2	24	no	—
231	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
232	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
233	C₂×C₃²	—	2	8	no	—
234	C₂×C₃²	C₂×#123	1	12	yes	complemented
235	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
236	C₂×C₃²	C₂²×#41	1	2	yes	—
237	C₃×D₃	—	4	4	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	3	6	no	—
240	C₂⁴	—	6	8	no	—
241	C₂⁴	—	6	4	no	—
242	C₂⁴	C₃×#67	1	8	yes	—
243	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
244	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
245	C₂×D₄	—	3	16	no	—
246	C₂×D₄	—	6	48	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	48	no	—
249	C₂²×C₄	—	3	12	no	—
250	C₂²×C₄	—	3	6	no	—
251	C₂²×C₄	—	6	8	no	—
252	C₂²×C₄	—	6	4	no	—
253	C₂²×C₄	C₂²×C₃×D₃	1	12	yes	—
254	C₂²×C₄	C₂²×C₃×D₃	1	16	yes	complemented
255	C₄⋊C₄	—	3	32	no	—
256	C₂²⋊C₄	—	3	16	no	—
257	C₂²⋊C₄	—	3	32	no	—
258	C₂²×C₃	—	2	96	no	—
259	C₂²×C₃	—	2	16	no	—
260	C₂²×C₃	—	2	8	no	—
261	C₂²×C₃	—	2	8	no	—
262	C₂²×C₃	—	2	48	no	—
263	C₂²×C₃	—	2	48	no	—
264	C₂²×C₃	—	2	16	no	—
265	C₂²×C₃	—	2	12	no	—
266	C₂²×C₃	—	2	8	no	—
267	C₂²×C₃	—	2	6	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	6	8	no	—
270	C₂²×C₃	—	6	4	no	—
271	C₂²×C₃	—	12	24	no	—
272	C₂²×C₃	#929	1	16	yes	direct product factor
273	C₂²×C₃	C₃×#123	1	16	yes	complemented
274	C₂²×C₃	C₂×#235	1	12	yes	—
275	C₂²×C₃	C₂²×#67	1	8	yes	—
276	C₂²×C₃	C₂²×#67	1	6	yes	—
277	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
278	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
279	C₂²×C₃	C₂×C₃×#41	1	12	yes	—
280	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
281	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
282	C₂×D₃	—	2	4	no	—
283	C₂×D₃	—	2	8	no	—
284	C₂×D₃	—	4	24	no	—
285	C₃×C₄	—	2	16	no	—
286	C₃×C₄	—	2	8	no	—
287	C₃×C₄	—	2	8	no	—
288	C₃×C₄	—	6	8	no	—
289	C₃×C₄	—	6	4	no	—
290	Dic₃	—	2	4	no	—
291	Dic₃	—	2	8	no	—
292	C₃²	C₂²×#123	1	1	yes	characteristic, complemented, Sylow
293	C₂³	—	2	32	no	—
294	C₂³	—	2	24	no	—
295	C₂³	—	3	4	no	—
296	C₂³	—	6	24	no	—
297	C₂³	—	6	12	no	—
298	C₂³	—	12	16	no	—
299	C₂³	C₃×#235	1	8	yes	—
300	C₂³	C₂×C₃×#67	1	24	yes	—
301	C₂³	C₂×C₃×#67	1	4	yes	—
302	C₂³	C₂³×C₃×D₃	1	4	yes	—
303	C₂³	C₂³×C₃×D₃	1	3	yes	—
304	D₄	—	6	32	no	—
305	C₂×C₄	—	2	24	no	—
306	C₂×C₄	—	2	32	no	—
307	C₂×C₄	—	3	8	no	—
308	C₂×C₄	—	3	4	no	—
309	C₂×C₄	—	6	24	no	—
310	C₂×C₄	—	6	12	no	—
311	C₂×C₄	C₂³×C₃×D₃	1	8	yes	—
312	C₂×C₃	—	2	16	no	—
313	C₂×C₃	—	2	8	no	—
314	C₂×C₃	—	2	8	no	—
315	C₂×C₃	—	2	12	no	—
316	C₂×C₃	—	2	2	no	—
317	C₂×C₃	—	2	1	no	—
318	C₂×C₃	—	12	4	no	—
319	C₂×C₃	C₂×#929	1	12	yes	direct product factor
320	C₂×C₃	C₂×C₃×#123	1	12	yes	complemented
321	C₂×C₃	C₂²×#235	1	2	yes	—
322	C₂×C₃	C₂³×#67	1	1	yes	characteristic
323	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
324	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
325	D₃	—	4	4	no	—
326	C₂²	—	2	48	no	—
327	C₂²	—	2	8	no	—
328	C₂²	—	6	8	no	—
329	C₂²	—	6	4	no	—
330	C₂²	—	12	24	no	—
331	C₂²	C₃×#929	1	16	yes	direct product factor
332	C₂²	C₂×C₃×#235	1	12	yes	—
333	C₂²	C₂²×C₃×#67	1	8	yes	—
334	C₂²	C₂²×C₃×#67	1	6	yes	—
335	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
336	C₄	—	2	8	no	—
337	C₄	—	6	8	no	—
338	C₄	—	6	4	no	—
339	C₃	—	2	1	no	—
340	C₃	C₂²×#929	1	1	yes	characteristic, direct product factor
341	C₃	C₂²×C₃×#123	1	1	yes	characteristic, complemented
342	C₂	—	2	8	no	—
343	C₂	—	12	4	no	—
344	C₂	C₂×C₃×#929	1	12	yes	direct product factor
345	C₂	C₂²×C₃×#235	1	2	yes	—
346	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	C₂⁴×C₃²×C₄	C₂
socle	C₂⁴×C₃²	C₂³
prime radical	C₂³×C₃×#67	C₂
hypercenter	C₂⁴×C₃×C₄	D₃
hypocenter	C₃	C₂²×C₃×#123
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂⁴×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃²×C₄	C₂	semidirect
3. C₂²×C₃×#217	C₂	semidirect
4. C₂×C₃×#929	C₂	direct (N × H)
5. C₂²×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
8. C₂²×#929	C₃	direct (N × H)
13. C₂³×C₃²×C₄	C₂²	semidirect
18. C₂×C₃×#217	C₂²	semidirect
19. C₃×#929	C₂²	direct (N × H)
20. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
24. C₂⁴×C₃×C₄	D₃	semidirect
25. C₂⁴×C₃×C₄	C₂×C₃	semidirect
31. C₂²×#217	C₂×C₃	semidirect
32. C₂×#929	C₂×C₃	direct (N × H)
33. C₂²×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
34. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
45. C₂²×C₃²×C₄	C₂³	semidirect
52. C₃×#217	C₂³	semidirect
53. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
54. C₃×Dic₃⋊C₄	C₂³	semidirect
71. C₂³×C₃×C₄	C₂×D₃	semidirect
73. C₂³×C₃×C₄	C₂²×C₃	semidirect
82. C₂×#217	C₂²×C₃	semidirect
83. #929	C₂²×C₃	direct (N × H)
84. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
85. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
106. C₂⁴×C₄	C₃×D₃	semidirect
144. C₂²×C₃×C₄	C₂²×D₃	semidirect
146. C₂²×C₃×C₄	C₂³×C₃	semidirect
156. #217	C₂³×C₃	semidirect
157. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
158. Dic₃⋊C₄	C₂³×C₃	semidirect
161. C₂²×C₃²	#123	semidirect
180. C₂³×C₄	C₂×C₃×D₃	semidirect
234. C₂×C₃²	C₂×#123	semidirect
254. C₂²×C₄	C₂²×C₃×D₃	semidirect
272. C₂²×C₃	#929	direct (N × H)
273. C₂²×C₃	C₃×#123	semidirect
292. C₃²	C₂²×#123	semidirect
319. C₂×C₃	C₂×#929	direct (N × H)
320. C₂×C₃	C₂×C₃×#123	semidirect
331. C₂²	C₃×#929	direct (N × H)
340. C₃	C₂²×#929	direct (N × H)
341. C₃	C₂²×C₃×#123	semidirect
344. C₂	C₂×C₃×#929	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²×C₄	2
C₂³×C₃×#67	2
C₂²×C₃×#217	2
C₂×C₃×#929	2
C₂²×C₃×(C₂×D₃)⋊C₄	2
C₂²×C₃×Dic₃⋊C₄	2
C₂²×C₃×#123	3
C₂²×#929	3

Subgroups — C22×C3×#929 #11900363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#929 #11900363