Subgroups — C₂×C₃×D₃×#97 #11857116

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×C₈	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#815	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#803	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₃×#97	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₃×#97	—	3	1	no	maximal
8	C₂×D₃×#97	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₄	1	2	yes	—
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₈	C₂²	1	2	yes	—
12	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₃	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃×D₃×C₈	C₄	1	16	yes	complemented
17	C₂×C₃×D₃×C₈	C₂²	1	8	yes	—
18	C₃×C₄²×D₃	C₄	1	4	yes	—
19	C₃×C₄²×D₃	C₂²	1	4	yes	—
20	C₃²×#97	C₂²	1	4	yes	complemented
21	C₃×#815	C₂²	1	8	yes	complemented
22	C₃×#803	C₂²	1	4	yes	complemented
23	C₂³×C₃×C₈	—	3	2	no	—
24	C₂²×C₃×C₄²	—	3	1	no	—
25	C₂²×D₃×C₈	C₂×C₃	1	2	yes	—
26	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#97	—	2	1	no	—
28	C₂×C₃×#97	—	3	2	no	—
29	C₂×C₃×#97	—	3	1	no	—
30	C₂×C₃×#97	—	3	8	no	—
31	C₂×C₃×#97	D₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#815	C₂×C₃	1	2	yes	complemented
34	C₂×#803	C₂×C₃	1	1	yes	characteristic, complemented
35	D₃×#97	C₂×C₃	1	8	yes	direct product factor
36	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
38	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
40	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₃	—	2	8	no	—
42	C₂×C₃×C₄×D₃	C₂×C₄	1	8	yes	—
43	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₃	C₂×C₄	1	8	yes	—
45	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
46	C₂×C₃²×C₈	C₂×C₄	1	8	yes	complemented
47	C₂×C₃²×C₈	C₂³	1	4	yes	—
48	C₃²×C₄²	C₂×C₄	1	2	yes	—
49	C₃²×C₄²	C₂³	1	2	yes	—
50	C₃×C₄×Dic₃	C₂×C₄	1	8	yes	—
51	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
52	C₃×C₄×Dic₃	C₂³	1	2	yes	—
53	C₂×C₃×C₃⋊C₈	C₂×C₄	1	8	yes	complemented
54	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
55	C₃×D₃×C₈	C₂×C₄	1	32	yes	complemented
56	C₂²×#97	—	3	1	no	Sylow
57	C₂³×C₃×C₄	—	3	1	no	—
58	C₂³×C₃×C₄	—	3	2	no	—
59	C₂²×C₄×D₃	C₃×C₄	1	2	yes	—
60	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₃×C₈	—	2	2	no	—
62	C₂²×C₃×C₈	—	3	2	no	—
63	C₂²×C₃×C₈	—	3	16	no	—
64	C₂²×C₃×C₈	—	3	8	no	—
65	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
66	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
67	C₂×C₃×C₄²	—	2	1	no	—
68	C₂×C₃×C₄²	—	3	2	no	—
69	C₂×C₃×C₄²	—	3	1	no	—
70	C₂×C₃×C₄²	—	3	4	no	—
71	C₂×C₃×C₄²	—	3	4	no	—
72	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
73	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄×Dic₃	C₃×C₄	1	2	yes	—
75	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
77	C₂×D₃×C₈	C₃×C₄	1	16	yes	complemented
78	C₂×D₃×C₈	C₂²×C₃	1	8	yes	—
79	C₄²×D₃	C₃×C₄	1	4	yes	—
80	C₄²×D₃	C₂²×C₃	1	4	yes	—
81	C₃×#97	—	2	4	no	—
82	C₃×#97	—	3	8	no	—
83	C₃×#97	—	3	4	no	—
84	C₃×#97	C₂×D₃	1	4	yes	direct product factor
85	C₃×#97	C₂²×C₃	1	4	yes	complemented
86	#815	C₂²×C₃	1	8	yes	complemented
87	#803	C₂²×C₃	1	4	yes	complemented
88	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₃×D₃	C₄²	1	4	yes	—
90	C₂²×C₃×D₃	M₁₆	1	8	yes	—
91	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
92	C₂×C₃²×C₄	—	2	4	no	—
93	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
94	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
96	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
97	C₂×C₃×Dic₃	—	2	4	no	—
98	C₂×C₃×Dic₃	C₄²	1	4	yes	—
99	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
100	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
101	C₃×C₄×D₃	—	2	16	no	—
102	C₃×C₄×D₃	C₄²	1	8	yes	—
103	C₃×C₄×D₃	C₂²×C₄	1	8	yes	—
104	C₃²×C₈	C₂²×C₄	1	8	yes	complemented
105	C₃×C₃⋊C₈	C₂²×C₄	1	8	yes	complemented
106	C₂³×C₈	—	3	2	no	—
107	C₂²×C₄²	—	3	1	no	—
108	C₂×#97	—	3	2	no	—
109	C₂×#97	—	3	1	no	—
110	C₂×#97	—	3	8	no	—
111	C₂×#97	C₃×D₃	1	1	yes	characteristic, direct product factor
112	C₂⁴×C₃	—	3	1	no	—
113	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
114	C₂²×C₃×C₄	—	2	2	no	—
115	C₂²×C₃×C₄	—	2	1	no	—
116	C₂²×C₃×C₄	—	3	1	no	—
117	C₂²×C₃×C₄	—	3	2	no	—
118	C₂²×C₃×C₄	—	3	8	no	—
119	C₂²×C₃×C₄	—	3	2	no	—
120	C₂²×C₃×C₄	—	3	2	no	—
121	C₂²×C₃×C₄	—	3	8	no	—
122	C₂²×C₃×C₄	—	6	8	no	—
123	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
124	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
125	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
127	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
128	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂×C₄×D₃	—	2	8	no	—
130	C₂×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
131	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
132	C₂×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
133	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
134	C₂×C₃×C₈	—	2	8	no	—
135	C₂×C₃×C₈	—	2	4	no	—
136	C₂×C₃×C₈	—	3	8	no	—
137	C₂×C₃×C₈	—	3	4	no	—
138	C₂×C₃×C₈	—	3	32	no	—
139	C₂×C₃×C₈	C₄×D₃	1	8	yes	complemented
140	C₂×C₃×C₈	C₂×C₃×C₄	1	8	yes	complemented
141	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
142	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
143	C₃×C₄²	—	2	2	no	—
144	C₃×C₄²	—	2	2	no	—
145	C₃×C₄²	—	3	8	no	—
146	C₃×C₄²	—	3	2	no	—
147	C₃×C₄²	—	3	2	no	—
148	C₃×C₄²	C₄×D₃	1	2	yes	—
149	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
150	C₃×C₄²	C₂²×D₃	1	2	yes	—
151	C₃×C₄²	C₂³×C₃	1	2	yes	—
152	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
153	C₄×Dic₃	C₂×C₃×C₄	1	8	yes	—
154	C₄×Dic₃	C₂³×C₃	1	2	yes	—
155	C₂×C₃⋊C₈	C₂×C₃×C₄	1	8	yes	complemented
156	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
157	D₃×C₈	C₂×C₃×C₄	1	32	yes	complemented
158	C₂²×C₃²	C₂×C₄²	1	2	yes	—
159	C₂²×C₃²	C₂×M₁₆	1	4	yes	—
160	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₃×D₃	#97	1	16	yes	direct product factor
162	C₂×C₃×D₃	C₂×C₄²	1	4	yes	—
163	C₂×C₃×D₃	C₂×M₁₆	1	8	yes	—
164	C₃²×C₄	—	2	4	no	—
165	C₃²×C₄	C₂×C₄²	1	2	yes	—
166	C₃²×C₄	C₂³×C₄	1	2	yes	—
167	C₃×Dic₃	—	2	4	no	—
168	C₃×Dic₃	C₂×C₄²	1	4	yes	—
169	C₂³×C₄	—	3	1	no	—
170	C₂³×C₄	—	3	2	no	—
171	C₂²×C₈	—	3	2	no	—
172	C₂²×C₈	—	3	16	no	—
173	C₂²×C₈	—	3	8	no	—
174	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
175	C₂×C₄²	—	3	2	no	—
176	C₂×C₄²	—	3	1	no	—
177	C₂×C₄²	—	3	4	no	—
178	C₂×C₄²	—	3	4	no	—
179	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
180	#97	—	3	8	no	—
181	#97	—	3	4	no	—
182	#97	C₂×C₃×D₃	1	4	yes	direct product factor
183	C₂³×C₃	—	2	1	no	—
184	C₂³×C₃	—	3	4	no	—
185	C₂³×C₃	—	3	8	no	—
186	C₂³×C₃	—	3	2	no	—
187	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
188	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
189	C₂²×D₃	C₃×C₄²	1	4	yes	—
190	C₂²×D₃	C₃×M₁₆	1	8	yes	—
191	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
192	C₂×C₃×C₄	—	2	4	no	—
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	—	2	1	no	—
195	C₂×C₃×C₄	—	2	1	no	—
196	C₂×C₃×C₄	—	2	4	no	—
197	C₂×C₃×C₄	—	2	4	no	—
198	C₂×C₃×C₄	—	3	4	no	—
199	C₂×C₃×C₄	—	3	2	no	—
200	C₂×C₃×C₄	—	3	8	no	—
201	C₂×C₃×C₄	—	3	8	no	—
202	C₂×C₃×C₄	—	3	4	no	—
203	C₂×C₃×C₄	—	4	4	no	—
204	C₂×C₃×C₄	—	6	16	no	—
205	C₂×C₃×C₄	—	6	4	no	—
206	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
207	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
208	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
209	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
210	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	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	C₃×C₄²	1	4	yes	—
216	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
217	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
218	C₄×D₃	—	2	16	no	—
219	C₄×D₃	C₃×C₄²	1	8	yes	—
220	C₄×D₃	C₂²×C₃×C₄	1	8	yes	—
221	C₃×C₈	—	2	8	no	—
222	C₃×C₈	—	3	8	no	—
223	C₃×C₈	C₂×C₄×D₃	1	8	yes	complemented
224	C₃×C₈	C₂²×C₃×C₄	1	8	yes	complemented
225	C₃⋊C₈	C₂²×C₃×C₄	1	8	yes	complemented
226	C₂×C₃²	C₂×#97	1	4	yes	complemented
227	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
228	C₂×C₃²	C₂²×M₁₆	1	2	yes	—
229	C₃×D₃	C₂×#97	1	8	yes	direct product factor
230	C₂⁴	—	3	1	no	—
231	C₂²×C₄	—	3	1	no	—
232	C₂²×C₄	—	3	2	no	—
233	C₂²×C₄	—	3	2	no	—
234	C₂²×C₄	—	3	8	no	—
235	C₂²×C₄	—	3	2	no	—
236	C₂²×C₄	—	3	8	no	—
237	C₂²×C₄	—	6	8	no	—
238	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
239	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
240	C₂×C₈	—	3	4	no	—
241	C₂×C₈	—	3	8	no	—
242	C₂×C₈	—	3	32	no	—
243	C₂×C₈	C₃×C₄×D₃	1	8	yes	complemented
244	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
245	C₄²	—	3	2	no	—
246	C₄²	—	3	8	no	—
247	C₄²	—	3	2	no	—
248	C₄²	C₃×C₄×D₃	1	2	yes	—
249	C₄²	C₂²×C₃×D₃	1	2	yes	—
250	C₂²×C₃	—	2	4	no	—
251	C₂²×C₃	—	2	1	no	—
252	C₂²×C₃	—	2	2	no	—
253	C₂²×C₃	—	3	4	no	—
254	C₂²×C₃	—	3	16	no	—
255	C₂²×C₃	—	3	8	no	—
256	C₂²×C₃	C₄²×D₃	1	2	yes	—
257	C₂²×C₃	D₃×M₁₆	1	4	yes	—
258	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
259	C₂²×C₃	C₂×C₃×M₁₆	1	4	yes	—
260	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
261	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
262	C₂×D₃	C₃×#97	1	16	yes	direct product factor
263	C₂×D₃	C₂×C₃×C₄²	1	4	yes	—
264	C₂×D₃	C₂×C₃×M₁₆	1	8	yes	—
265	C₃×C₄	—	2	4	no	—
266	C₃×C₄	—	2	4	no	—
267	C₃×C₄	—	2	2	no	—
268	C₃×C₄	—	2	2	no	—
269	C₃×C₄	—	3	4	no	—
270	C₃×C₄	—	4	4	no	—
271	C₃×C₄	—	6	4	no	—
272	C₃×C₄	C₄²×D₃	1	2	yes	—
273	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
274	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
275	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
276	Dic₃	—	2	4	no	—
277	Dic₃	C₂×C₃×C₄²	1	4	yes	—
278	C₃²	C₂²×#97	1	1	yes	characteristic, complemented, Sylow
279	C₂³	—	3	8	no	—
280	C₂³	—	3	2	no	—
281	C₂³	—	3	4	no	—
282	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	3	2	no	—
285	C₂×C₄	—	3	4	no	—
286	C₂×C₄	—	3	8	no	—
287	C₂×C₄	—	3	8	no	—
288	C₂×C₄	—	3	4	no	—
289	C₂×C₄	—	6	16	no	—
290	C₂×C₄	—	6	4	no	—
291	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
292	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
293	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
294	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
295	C₈	—	3	8	no	—
296	C₈	C₂×C₃×C₄×D₃	1	8	yes	complemented
297	C₂×C₃	—	2	2	no	—
298	C₂×C₃	—	2	4	no	—
299	C₂×C₃	—	2	1	no	—
300	C₂×C₃	—	3	8	no	—
301	C₂×C₃	D₃×#97	1	4	yes	direct product factor
302	C₂×C₃	C₂×C₃×#97	1	4	yes	complemented
303	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
304	C₂×C₃	C₂×D₃×M₁₆	1	2	yes	—
305	C₂×C₃	C₂²×C₃×C₄²	1	1	yes	characteristic
306	C₂×C₃	C₂²×C₃×M₁₆	1	2	yes	—
307	D₃	C₂×C₃×#97	1	8	yes	direct product factor
308	C₂²	—	3	8	no	—
309	C₂²	—	3	16	no	—
310	C₂²	—	3	4	no	—
311	C₂²	C₃×C₄²×D₃	1	2	yes	—
312	C₂²	C₃×D₃×M₁₆	1	4	yes	—
313	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
314	C₄	—	2	4	no	—
315	C₄	—	3	4	no	—
316	C₄	—	6	4	no	—
317	C₄	C₃×C₄²×D₃	1	2	yes	—
318	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
319	C₃	—	2	1	no	—
320	C₃	C₂×D₃×#97	1	1	yes	characteristic, direct product factor
321	C₃	C₂²×C₃×#97	1	1	yes	characteristic, complemented
322	C₂	—	3	8	no	—
323	C₂	C₃×D₃×#97	1	4	yes	direct product factor
324	C₂	C₂×C₃×C₄²×D₃	1	1	yes	characteristic
325	C₂	C₂×C₃×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂×C₃	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₂²×C₃×#97
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
3. C₂×C₃²×#97	C₂	semidirect
4. C₂×C₃×#815	C₂	semidirect
5. C₂×C₃×#803	C₂	semidirect
6. C₃×D₃×#97	C₂	direct (N × H)
8. C₂×D₃×#97	C₃	direct (N × H)
16. C₂×C₃×D₃×C₈	C₄	semidirect
20. C₃²×#97	C₂²	semidirect
21. C₃×#815	C₂²	semidirect
22. C₃×#803	C₂²	semidirect
31. C₂×C₃×#97	D₃	direct (N × H)
32. C₂×C₃×#97	C₂×C₃	semidirect
33. C₂×#815	C₂×C₃	semidirect
34. C₂×#803	C₂×C₃	semidirect
35. D₃×#97	C₂×C₃	direct (N × H)
46. C₂×C₃²×C₈	C₂×C₄	semidirect
53. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
55. C₃×D₃×C₈	C₂×C₄	semidirect
77. C₂×D₃×C₈	C₃×C₄	semidirect
84. C₃×#97	C₂×D₃	direct (N × H)
85. C₃×#97	C₂²×C₃	semidirect
86. #815	C₂²×C₃	semidirect
87. #803	C₂²×C₃	semidirect
104. C₃²×C₈	C₂²×C₄	semidirect
105. C₃×C₃⋊C₈	C₂²×C₄	semidirect
111. C₂×#97	C₃×D₃	direct (N × H)
139. C₂×C₃×C₈	C₄×D₃	semidirect
140. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
155. C₂×C₃⋊C₈	C₂×C₃×C₄	semidirect
157. D₃×C₈	C₂×C₃×C₄	semidirect
161. C₂×C₃×D₃	#97	direct (N × H)
182. #97	C₂×C₃×D₃	direct (N × H)
223. C₃×C₈	C₂×C₄×D₃	semidirect
224. C₃×C₈	C₂²×C₃×C₄	semidirect
225. C₃⋊C₈	C₂²×C₃×C₄	semidirect
226. C₂×C₃²	C₂×#97	semidirect
229. C₃×D₃	C₂×#97	direct (N × H)
243. C₂×C₈	C₃×C₄×D₃	semidirect
262. C₂×D₃	C₃×#97	direct (N × H)
278. C₃²	C₂²×#97	semidirect
296. C₈	C₂×C₃×C₄×D₃	semidirect
301. C₂×C₃	D₃×#97	direct (N × H)
302. C₂×C₃	C₂×C₃×#97	semidirect
307. D₃	C₂×C₃×#97	direct (N × H)
320. C₃	C₂×D₃×#97	direct (N × H)
321. C₃	C₂²×C₃×#97	semidirect
323. C₂	C₃×D₃×#97	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×D₃×C₈	2
C₂×C₃×C₄²×D₃	2
C₂×C₃²×#97	2
C₂×C₃×#815	2
C₂×C₃×#803	2
C₃×D₃×#97	2
C₂²×C₃×#97	3
C₂×D₃×#97	3

Subgroups — C2×C3×D3×#97 #11857116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×#97 #11857116