Subgroups — C₂²×C₃×#821 #11857723

Order 1152.

2313 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#821	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₃×#102	—	3	1	no	maximal
6	C₂²×#821	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂⁴×C₃×D₃	—	2	1	no	—
8	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₂³×C₃×Dic₃	—	2	1	no	—
10	C₂²×C₃×D₁₂	—	2	4	no	—
11	C₂²×C₃×D₁₂	—	2	3	no	—
12	C₂²×C₃×D₁₂	C₄	1	8	yes	complemented
13	C₂²×C₃×D₁₂	C₂²	1	6	yes	—
14	C₂²×C₃²×C₈	—	2	4	no	—
15	C₂²×C₃²×C₈	C₂²	1	6	yes	complemented
16	C₂×C₃×C₄⋊Dic₃	—	2	3	no	—
17	C₂×C₃×C₄⋊Dic₃	C₂²	1	6	yes	complemented
18	C₃×#821	C₂²	1	16	yes	direct product factor
19	C₂³×C₃×D₄	—	3	1	no	—
20	C₂³×D₁₂	C₂×C₃	1	1	yes	characteristic
21	C₂³×C₃×C₈	—	2	1	no	—
22	C₂³×C₃×C₈	D₃	1	1	yes	characteristic, complemented
23	C₂³×C₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
25	C₂²×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×#102	—	3	12	no	—
27	C₂×#821	C₂×C₃	1	12	yes	direct product factor
28	C₂⁴×C₃²	D₄	1	1	yes	characteristic
29	C₂³×C₃×D₃	—	2	8	no	—
30	C₂³×C₃×D₃	—	2	6	no	—
31	C₂³×C₃×D₃	—	4	4	no	—
32	C₂³×C₃×D₃	—	4	4	no	—
33	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
34	C₂²×C₃²×C₄	D₄	1	3	yes	—
35	C₂²×C₃²×C₄	D₄	1	4	yes	—
36	C₂²×C₃²×C₄	C₂³	1	3	yes	—
37	C₂²×C₃×Dic₃	—	2	6	no	—
38	C₂²×C₃×Dic₃	—	4	4	no	—
39	C₂×C₃×D₁₂	—	2	24	no	—
40	C₂×C₃×D₁₂	—	2	6	no	—
41	C₂×C₃×D₁₂	—	2	12	no	—
42	C₂×C₃×D₁₂	C₂×C₄	1	24	yes	complemented
43	C₂×C₃×D₁₂	C₂³	1	4	yes	—
44	C₂×C₃²×C₈	—	2	12	no	—
45	C₂×C₃²×C₈	C₂³	1	4	yes	complemented
46	C₃×C₄⋊Dic₃	—	2	6	no	—
47	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
48	C₂²×#102	—	3	1	no	Sylow
49	C₂⁵×C₃	—	6	1	no	—
50	C₂⁴×D₃	—	2	1	no	—
51	C₂²×C₃×D₄	—	3	8	no	—
52	C₂²×C₃×D₄	—	3	6	no	—
53	C₂²×C₃×D₄	—	6	3	no	—
54	C₂²×C₃×D₄	—	6	4	no	—
55	C₂³×C₃×C₄	—	2	1	no	—
56	C₂³×C₃×C₄	—	6	1	no	—
57	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
58	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
59	C₂³×Dic₃	—	2	1	no	—
60	C₂²×D₁₂	—	2	3	no	—
61	C₂²×D₁₂	—	2	4	no	—
62	C₂²×D₁₂	C₃×C₄	1	8	yes	complemented
63	C₂²×D₁₂	C₂²×C₃	1	6	yes	—
64	C₂²×C₃×C₈	—	2	8	no	—
65	C₂²×C₃×C₈	—	2	4	no	—
66	C₂²×C₃×C₈	—	2	4	no	—
67	C₂²×C₃×C₈	—	2	6	no	—
68	C₂²×C₃×C₈	C₂×D₃	1	6	yes	complemented
69	C₂²×C₃×C₈	C₂²×C₃	1	6	yes	complemented
70	C₂×C₃×C₄⋊C₄	—	3	6	no	—
71	C₂×C₃×C₄⋊C₄	—	6	3	no	—
72	C₂×C₄⋊Dic₃	—	2	3	no	—
73	C₂×C₄⋊Dic₃	C₂²×C₃	1	6	yes	complemented
74	C₃×#102	—	3	16	no	—
75	#821	C₂²×C₃	1	16	yes	direct product factor
76	C₂³×C₃²	C₂²⋊C₄	1	4	yes	—
77	C₂³×C₃²	D₈	1	4	yes	—
78	C₂³×C₃²	SD₁₆	1	4	yes	—
79	C₂³×C₃²	C₂×D₄	1	3	yes	—
80	C₂²×C₃×D₃	—	2	24	no	—
81	C₂²×C₃×D₃	—	2	4	no	—
82	C₂²×C₃×D₃	—	4	32	no	—
83	C₂²×C₃×D₃	—	4	12	no	—
84	C₂²×C₃×D₃	—	4	12	no	—
85	C₂×C₃²×C₄	C₂²⋊C₄	1	12	yes	—
86	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
87	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
88	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
89	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
90	C₂×C₃×Dic₃	—	2	4	no	—
91	C₂×C₃×Dic₃	—	4	12	no	—
92	C₃×D₁₂	—	2	24	no	—
93	C₃×D₁₂	—	2	4	no	—
94	C₃×D₁₂	C₂²×C₄	1	8	yes	complemented
95	C₃²×C₈	—	2	4	no	—
96	C₂³×D₄	—	3	1	no	—
97	C₂³×C₈	C₃×D₃	1	1	yes	characteristic, complemented
98	C₂²×C₄⋊C₄	—	3	1	no	—
99	C₂×#102	—	3	12	no	—
100	C₂⁴×C₃	—	2	1	no	—
101	C₂⁴×C₃	—	6	8	no	—
102	C₂⁴×C₃	—	6	6	no	—
103	C₂⁴×C₃	—	12	4	no	—
104	C₂⁴×C₃	—	12	4	no	—
105	C₂⁴×C₃	D₁₂	1	1	yes	characteristic
106	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
107	C₂³×D₃	—	2	8	no	—
108	C₂³×D₃	—	2	6	no	—
109	C₂³×D₃	—	4	4	no	—
110	C₂³×D₃	—	4	4	no	—
111	C₂×C₃×D₄	—	3	24	no	—
112	C₂×C₃×D₄	—	3	4	no	—
113	C₂×C₃×D₄	—	6	24	no	—
114	C₂×C₃×D₄	—	6	6	no	—
115	C₂×C₃×D₄	—	6	12	no	—
116	C₂²×C₃×C₄	—	2	4	no	—
117	C₂²×C₃×C₄	—	2	3	no	—
118	C₂²×C₃×C₄	—	2	4	no	—
119	C₂²×C₃×C₄	—	2	3	no	—
120	C₂²×C₃×C₄	—	6	6	no	—
121	C₂²×C₃×C₄	—	12	4	no	—
122	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
123	C₂²×C₃×C₄	D₁₂	1	3	yes	—
124	C₂²×C₃×C₄	#67	1	4	yes	—
125	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
126	C₂²×C₃×C₄	C₃×D₄	1	3	yes	—
127	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
128	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
129	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
130	C₂²×Dic₃	—	2	6	no	—
131	C₂²×Dic₃	—	4	4	no	—
132	C₂×D₁₂	—	2	24	no	—
133	C₂×D₁₂	—	2	6	no	—
134	C₂×D₁₂	—	2	12	no	—
135	C₂×D₁₂	C₂×C₃×C₄	1	24	yes	complemented
136	C₂×D₁₂	C₂³×C₃	1	4	yes	—
137	C₂×C₃×C₈	—	2	24	no	—
138	C₂×C₃×C₈	—	2	12	no	—
139	C₂×C₃×C₈	—	2	12	no	—
140	C₂×C₃×C₈	—	2	4	no	—
141	C₂×C₃×C₈	C₂²×D₃	1	4	yes	complemented
142	C₂×C₃×C₈	C₂³×C₃	1	4	yes	complemented
143	C₃×C₄⋊C₄	—	3	4	no	—
144	C₃×C₄⋊C₄	—	6	6	no	—
145	C₄⋊Dic₃	—	2	6	no	—
146	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
147	C₂²×C₃²	#102	1	16	yes	complemented
148	C₂²×C₃²	C₂×C₂²⋊C₄	1	6	yes	—
149	C₂²×C₃²	C₂×D₈	1	6	yes	—
150	C₂²×C₃²	C₂×SD₁₆	1	6	yes	—
151	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₃×D₃	—	2	8	no	—
153	C₂×C₃×D₃	—	4	4	no	—
154	C₂×C₃×D₃	—	4	4	no	—
155	C₂×C₃×D₃	—	4	48	no	—
156	C₃²×C₄	C₂×C₂²⋊C₄	1	6	yes	—
157	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
158	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
159	C₃×Dic₃	—	4	4	no	—
160	C₂⁵	—	6	1	no	—
161	C₂²×D₄	—	3	8	no	—
162	C₂²×D₄	—	3	6	no	—
163	C₂²×D₄	—	6	3	no	—
164	C₂²×D₄	—	6	4	no	—
165	C₂³×C₄	—	6	1	no	—
166	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
167	C₂²×C₈	—	2	4	no	—
168	C₂²×C₈	C₂×C₃×D₃	1	6	yes	complemented
169	C₂×C₄⋊C₄	—	3	6	no	—
170	C₂×C₄⋊C₄	—	6	3	no	—
171	#102	—	3	16	no	—
172	C₂³×C₃	—	2	4	no	—
173	C₂³×C₃	—	2	4	no	—
174	C₂³×C₃	—	2	4	no	—
175	C₂³×C₃	—	2	3	no	—
176	C₂³×C₃	—	6	24	no	—
177	C₂³×C₃	—	6	4	no	—
178	C₂³×C₃	—	12	32	no	—
179	C₂³×C₃	—	12	12	no	—
180	C₂³×C₃	—	12	12	no	—
181	C₂³×C₃	#204	1	4	yes	—
182	C₂³×C₃	D₂₄	1	4	yes	—
183	C₂³×C₃	(C₂×D₃)⋊C₄	1	4	yes	—
184	C₂³×C₃	C₃×C₂²⋊C₄	1	4	yes	—
185	C₂³×C₃	C₃×D₈	1	4	yes	—
186	C₂³×C₃	C₃×SD₁₆	1	4	yes	—
187	C₂³×C₃	C₂×D₁₂	1	3	yes	—
188	C₂³×C₃	C₂×C₃×D₄	1	3	yes	—
189	C₂²×D₃	—	2	24	no	—
190	C₂²×D₃	—	2	4	no	—
191	C₂²×D₃	—	4	32	no	—
192	C₂²×D₃	—	4	12	no	—
193	C₂²×D₃	—	4	12	no	—
194	C₃×D₄	—	3	8	no	—
195	C₃×D₄	—	6	24	no	—
196	C₃×D₄	—	6	4	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	2	12	no	—
199	C₂×C₃×C₄	—	2	6	no	—
200	C₂×C₃×C₄	—	2	3	no	—
201	C₂×C₃×C₄	—	2	6	no	—
202	C₂×C₃×C₄	—	6	4	no	—
203	C₂×C₃×C₄	—	12	12	no	—
204	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	12	yes	—
205	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	12	yes	—
206	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
207	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
208	C₂×C₃×C₄	C₂×#67	1	6	yes	—
209	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
210	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
211	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
212	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
214	C₂×Dic₃	—	2	4	no	—
215	C₂×Dic₃	—	4	12	no	—
216	D₁₂	—	2	24	no	—
217	D₁₂	—	2	4	no	—
218	D₁₂	C₂²×C₃×C₄	1	8	yes	complemented
219	C₃×C₈	—	2	8	no	—
220	C₃×C₈	—	2	4	no	—
221	C₃×C₈	—	2	4	no	—
222	C₂×C₃²	C₂×#102	1	12	yes	complemented
223	C₂×C₃²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
225	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
226	C₃×D₃	—	4	8	no	—
227	C₂⁴	—	6	8	no	—
228	C₂⁴	—	6	6	no	—
229	C₂⁴	—	12	4	no	—
230	C₂⁴	—	12	4	no	—
231	C₂⁴	C₃×D₁₂	1	1	yes	characteristic
232	C₂×D₄	—	3	4	no	—
233	C₂×D₄	—	3	24	no	—
234	C₂×D₄	—	6	24	no	—
235	C₂×D₄	—	6	6	no	—
236	C₂×D₄	—	6	12	no	—
237	C₂²×C₄	—	6	6	no	—
238	C₂²×C₄	—	12	4	no	—
239	C₂²×C₄	C₃×C₄×D₃	1	4	yes	—
240	C₂²×C₄	C₃×D₁₂	1	3	yes	—
241	C₂²×C₄	C₃×#67	1	4	yes	—
242	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
243	C₂×C₈	—	2	12	no	—
244	C₂×C₈	C₂²×C₃×D₃	1	4	yes	complemented
245	C₄⋊C₄	—	3	4	no	—
246	C₄⋊C₄	—	6	6	no	—
247	C₂²×C₃	—	2	6	no	—
248	C₂²×C₃	—	2	6	no	—
249	C₂²×C₃	—	2	6	no	—
250	C₂²×C₃	—	2	1	no	—
251	C₂²×C₃	—	2	16	no	—
252	C₂²×C₃	—	6	8	no	—
253	C₂²×C₃	—	12	4	no	—
254	C₂²×C₃	—	12	4	no	—
255	C₂²×C₃	—	12	48	no	—
256	C₂²×C₃	#821	1	16	yes	direct product factor
257	C₂²×C₃	C₃×#102	1	16	yes	complemented
258	C₂²×C₃	C₂×#204	1	6	yes	—
259	C₂²×C₃	C₂×D₂₄	1	6	yes	—
260	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	6	yes	—
261	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	6	yes	—
262	C₂²×C₃	C₂×C₃×D₈	1	6	yes	—
263	C₂²×C₃	C₂×C₃×SD₁₆	1	6	yes	—
264	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
265	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
266	C₂×D₃	—	2	8	no	—
267	C₂×D₃	—	4	4	no	—
268	C₂×D₃	—	4	4	no	—
269	C₂×D₃	—	4	48	no	—
270	C₃×C₄	—	2	6	no	—
271	C₃×C₄	—	2	1	no	—
272	C₃×C₄	—	2	1	no	—
273	C₃×C₄	—	12	4	no	—
274	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	6	yes	—
275	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	6	yes	—
276	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
277	C₃×C₄	C₂²×#67	1	1	yes	characteristic
278	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
279	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
280	Dic₃	—	4	4	no	—
281	C₃²	C₂²×#102	1	1	yes	characteristic, complemented, Sylow
282	C₂³	—	6	24	no	—
283	C₂³	—	6	4	no	—
284	C₂³	—	12	12	no	—
285	C₂³	—	12	12	no	—
286	C₂³	—	12	32	no	—
287	C₂³	C₃×#204	1	4	yes	—
288	C₂³	C₃×D₂₄	1	4	yes	—
289	C₂³	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
290	C₂³	C₂×C₃×D₁₂	1	3	yes	—
291	D₄	—	3	8	no	—
292	D₄	—	6	24	no	—
293	D₄	—	6	4	no	—
294	C₂×C₄	—	6	4	no	—
295	C₂×C₄	—	12	12	no	—
296	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	12	yes	—
297	C₂×C₄	C₂×C₃×C₄×D₃	1	6	yes	—
298	C₂×C₄	C₂×C₃×D₁₂	1	3	yes	—
299	C₂×C₄	C₂×C₃×#67	1	6	yes	—
300	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
301	C₈	—	2	4	no	—
302	C₂×C₃	—	2	1	no	—
303	C₂×C₃	—	2	12	no	—
304	C₂×C₃	—	2	1	no	—
305	C₂×C₃	—	2	1	no	—
306	C₂×C₃	—	12	8	no	—
307	C₂×C₃	C₂×#821	1	12	yes	direct product factor
308	C₂×C₃	C₂×C₃×#102	1	12	yes	complemented
309	C₂×C₃	C₂²×#204	1	1	yes	characteristic
310	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
311	C₂×C₃	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
312	C₂×C₃	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
314	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
315	D₃	—	4	8	no	—
316	C₂²	—	6	8	no	—
317	C₂²	—	12	48	no	—
318	C₂²	—	12	4	no	—
319	C₂²	—	12	4	no	—
320	C₂²	C₃×#821	1	16	yes	direct product factor
321	C₂²	C₂×C₃×#204	1	6	yes	—
322	C₂²	C₂×C₃×D₂₄	1	6	yes	—
323	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	6	yes	—
324	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
325	C₄	—	12	4	no	—
326	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	6	yes	—
327	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
328	C₄	C₂²×C₃×#67	1	1	yes	characteristic
329	C₃	—	2	1	no	—
330	C₃	C₂²×#821	1	1	yes	characteristic, direct product factor
331	C₃	C₂²×C₃×#102	1	1	yes	characteristic, complemented
332	C₂	—	12	8	no	—
333	C₂	C₂×C₃×#821	1	12	yes	direct product factor
334	C₂	C₂²×C₃×#204	1	1	yes	characteristic
335	C₂	C₂²×C₃×D₂₄	1	1	yes	characteristic
336	C₂	C₂²×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂³×C₃²×C₈	C₂
socle	C₂⁴×C₃²	D₄
prime radical	C₂³×C₃×D₁₂	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂³×C₃×C₈	D₃
hypocenter	C₃	C₂²×C₃×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃²×C₈	C₂	semidirect
3. C₂²×C₃×C₄⋊Dic₃	C₂	semidirect
4. C₂×C₃×#821	C₂	direct (N × H)
6. C₂²×#821	C₃	direct (N × H)
12. C₂²×C₃×D₁₂	C₄	semidirect
15. C₂²×C₃²×C₈	C₂²	semidirect
17. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
18. C₃×#821	C₂²	direct (N × H)
22. C₂³×C₃×C₈	D₃	semidirect
23. C₂³×C₃×C₈	C₂×C₃	semidirect
25. C₂²×C₄⋊Dic₃	C₂×C₃	semidirect
27. C₂×#821	C₂×C₃	direct (N × H)
42. C₂×C₃×D₁₂	C₂×C₄	semidirect
45. C₂×C₃²×C₈	C₂³	semidirect
47. C₃×C₄⋊Dic₃	C₂³	semidirect
62. C₂²×D₁₂	C₃×C₄	semidirect
68. C₂²×C₃×C₈	C₂×D₃	semidirect
69. C₂²×C₃×C₈	C₂²×C₃	semidirect
73. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
75. #821	C₂²×C₃	direct (N × H)
94. C₃×D₁₂	C₂²×C₄	semidirect
97. C₂³×C₈	C₃×D₃	semidirect
135. C₂×D₁₂	C₂×C₃×C₄	semidirect
141. C₂×C₃×C₈	C₂²×D₃	semidirect
142. C₂×C₃×C₈	C₂³×C₃	semidirect
146. C₄⋊Dic₃	C₂³×C₃	semidirect
147. C₂²×C₃²	#102	semidirect
168. C₂²×C₈	C₂×C₃×D₃	semidirect
218. D₁₂	C₂²×C₃×C₄	semidirect
222. C₂×C₃²	C₂×#102	semidirect
244. C₂×C₈	C₂²×C₃×D₃	semidirect
256. C₂²×C₃	#821	direct (N × H)
257. C₂²×C₃	C₃×#102	semidirect
281. C₃²	C₂²×#102	semidirect
307. C₂×C₃	C₂×#821	direct (N × H)
308. C₂×C₃	C₂×C₃×#102	semidirect
320. C₂²	C₃×#821	direct (N × H)
330. C₃	C₂²×#821	direct (N × H)
331. C₃	C₂²×C₃×#102	semidirect
333. C₂	C₂×C₃×#821	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×C₃×D₁₂	2
C₂³×C₃²×C₈	2
C₂²×C₃×C₄⋊Dic₃	2
C₂×C₃×#821	2
C₂²×C₃×#102	3
C₂²×#821	3

Subgroups — C22×C3×#821 #11857723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#821 #11857723