Subgroups — C₃⋊D₃×#405 #11857170

Order 1152.

1776 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₃⋊D₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	#10592821	C₂	1	1	yes	maximal, characteristic, complemented
6	#10592800	C₂	1	1	yes	maximal, characteristic, complemented
7	#10592696	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592407	C₂	1	2	yes	maximal, complemented
9	C₃⋊D₃×#97	C₂	1	2	yes	maximal, complemented
10	#10592388	C₂	1	2	yes	maximal, complemented
11	C₄×C₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
12	D₃×#405	—	3	4	no	maximal
13	C₂²×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₃²×#117	C₂²	1	1	yes	characteristic
17	#64135	C₂²	1	1	yes	characteristic
18	C₂×#3748	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
20	M₁₆×C₃⋊D₃	C₄	1	8	yes	complemented
21	C₂×#3743	C₂²	1	2	yes	—
22	C₂×C₈×C₃⋊D₃	C₄	1	8	yes	complemented
23	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
24	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
25	C₂×C₈×C₃⋊D₃	C₂²	1	2	yes	—
26	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
28	#64101	C₄	1	2	yes	—
29	C₄⋊C₄×C₃⋊D₃	C₄	1	2	yes	—
30	C₂²⋊C₄×C₃⋊D₃	C₄	1	2	yes	—
31	#64086	C₄	1	2	yes	—
32	#64081	C₂²	1	2	yes	—
33	C₄²×C₃⋊D₃	C₂²	1	2	yes	—
34	C₃²×#97	C₂²	1	2	yes	complemented
35	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
36	#63642	C₂²	1	2	yes	complemented
37	#63642	C₂²	1	2	yes	complemented
38	C₈×C₃⋊Dic₃	C₂²	1	2	yes	complemented
39	C₈×C₃⋊Dic₃	C₂²	1	2	yes	complemented
40	#63630	C₂²	1	2	yes	complemented
41	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
42	C₂×D₃×M₁₆	—	3	4	no	—
43	C₂²×D₃×C₈	—	3	4	no	—
44	D₃×#117	—	3	4	no	—
45	C₃×#405	D₃	1	4	yes	complemented
46	#5122	—	3	4	no	—
47	#5101	—	3	4	no	—
48	#4997	—	3	4	no	—
49	#4708	—	3	8	no	—
50	D₃×#97	—	3	8	no	—
51	#4689	—	3	8	no	—
52	C₄×D₃×C₈	—	3	8	no	—
53	C₂³×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
55	C₂²×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₃⋊D₃	C₂×C₄	1	4	yes	—
57	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₃⋊D₃	C₂×C₄	1	4	yes	—
60	C₂×C₄×C₃⋊D₃	C₂×C₄	1	4	yes	—
61	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
63	C₃²×M₁₆	C₂×C₄	1	4	yes	complemented
64	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
65	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃²×C₈	C₂³	1	2	yes	—
68	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
69	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₃²×C₄²	C₂³	1	2	yes	—
71	#3757	C₂×C₄	1	2	yes	—
72	#3752	C₂×C₄	1	4	yes	—
73	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	2	yes	—
74	#3750	C₂×C₄	1	4	yes	—
75	C₄×C₃⋊Dic₃	C₂×C₄	1	4	yes	—
76	C₄×C₃⋊Dic₃	C₂³	1	2	yes	—
77	#3748	C₂×C₄	1	4	yes	complemented
78	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	complemented
79	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
80	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
81	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
82	#3743	C₂×C₄	1	8	yes	complemented
83	C₈×C₃⋊D₃	C₂×C₄	1	4	yes	—
84	C₈×C₃⋊D₃	C₂×C₄	1	4	yes	—
85	C₈×C₃⋊D₃	C₂×C₄	1	8	yes	—
86	C₈×C₃⋊D₃	C₂×C₄	1	4	yes	complemented
87	C₈×C₃⋊D₃	C₂×C₄	1	4	yes	complemented
88	C₂×#405	—	9	1	no	Sylow
89	C₂²×C₄×D₃	—	3	4	no	—
90	C₂×C₃×M₁₆	C₂×D₃	1	4	yes	—
91	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
92	C₃×#117	C₂×D₃	1	4	yes	—
93	#926	—	3	4	no	—
94	C₂×#208	—	3	4	no	—
95	C₂²×C₃⋊C₈	—	3	4	no	—
96	D₃×M₁₆	—	3	32	no	—
97	C₂×ΓL(1,𝔽₂₅)	—	3	8	no	—
98	C₂×D₃×C₈	—	3	32	no	—
99	C₂×D₃×C₈	—	3	4	no	—
100	C₂×D₃×C₈	—	3	8	no	—
101	C₂×D₃×C₈	—	3	4	no	—
102	C₂×D₃×C₈	—	3	4	no	—
103	C₂×D₃×C₈	—	3	4	no	—
104	#892	—	3	8	no	—
105	D₃×C₄⋊C₄	—	3	8	no	—
106	D₃×C₂²⋊C₄	—	3	8	no	—
107	#877	—	3	8	no	—
108	#872	—	3	8	no	—
109	C₄²×D₃	—	3	8	no	—
110	C₃×#97	C₂×D₃	1	8	yes	complemented
111	C₃×C₄×C₈	C₂×D₃	1	8	yes	complemented
112	#815	—	3	8	no	—
113	#815	—	3	8	no	—
114	C₈×Dic₃	—	3	8	no	—
115	C₈×Dic₃	—	3	8	no	—
116	#803	—	3	8	no	—
117	C₄×C₃⋊C₈	—	3	8	no	—
118	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₃⋊D₃	—	2	4	no	—
120	C₂²×C₃⋊D₃	C₄²	1	4	yes	—
121	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
124	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
126	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
127	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
128	C₂×C₃⋊Dic₃	C₄²	1	4	yes	—
129	C₂×C₃⋊Dic₃	C₂²×C₄	1	4	yes	—
130	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×C₃⋊D₃	—	2	8	no	—
133	C₄×C₃⋊D₃	C₄²	1	4	yes	—
134	C₄×C₃⋊D₃	C₄²	1	4	yes	—
135	C₄×C₃⋊D₃	C₂²×C₄	1	2	yes	—
136	C₄×C₃⋊D₃	C₂²×C₄	1	2	yes	—
137	C₄×C₃⋊D₃	C₂²×C₄	1	2	yes	—
138	C₄×C₃⋊D₃	C₂²×C₄	1	2	yes	—
139	C₃²×C₈	C₂²×C₄	1	2	yes	—
140	C₃²×C₈	C₂²×C₄	1	2	yes	—
141	C₃²×C₈	C₂²×C₄	1	4	yes	—
142	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	2	yes	—
143	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	2	yes	—
144	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	4	yes	—
145	C₂²×M₁₆	—	9	1	no	—
146	C₂³×C₈	—	9	1	no	—
147	C₂×#117	—	9	1	no	—
148	#405	—	9	1	no	—
149	#405	—	9	1	no	—
150	#405	—	9	1	no	—
151	#405	—	9	2	no	—
152	#405	—	9	2	no	—
153	#405	C₃⋊D₃	1	1	yes	characteristic, direct product factor
154	C₂×#97	—	9	2	no	—
155	C₂×C₄×C₈	—	9	2	no	—
156	C₂³×D₃	—	3	4	no	—
157	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
158	C₂²×Dic₃	—	3	4	no	—
159	C₂×C₄×D₃	—	3	4	no	—
160	C₂×C₄×D₃	—	3	4	no	—
161	C₂×C₄×D₃	—	3	16	no	—
162	C₂×C₄×D₃	—	3	16	no	—
163	C₂×C₄×D₃	—	3	4	no	—
164	C₂×C₄×D₃	—	3	4	no	—
165	C₂×C₄×D₃	—	3	16	no	—
166	C₃×M₁₆	C₄×D₃	1	16	yes	complemented
167	C₂×C₃×C₈	C₄×D₃	1	16	yes	complemented
168	C₂×C₃×C₈	C₂²×D₃	1	8	yes	—
169	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
170	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
171	C₃×C₄⋊C₄	C₄×D₃	1	8	yes	—
172	C₃×C₂²⋊C₄	C₄×D₃	1	8	yes	—
173	C₃×C₄²	C₂²×D₃	1	8	yes	—
174	#217	—	3	8	no	—
175	(C₂×D₃)⋊C₄	—	3	16	no	—
176	C₄⋊Dic₃	—	3	8	no	—
177	Dic₃⋊C₄	—	3	16	no	—
178	C₄×Dic₃	—	3	16	no	—
179	C₄×Dic₃	—	3	8	no	—
180	#208	—	3	16	no	—
181	C₂×C₃⋊C₈	—	3	16	no	—
182	C₂×C₃⋊C₈	—	3	4	no	—
183	C₂×C₃⋊C₈	—	3	8	no	—
184	C₂×C₃⋊C₈	—	3	4	no	—
185	ΓL(1,𝔽₂₅)	—	3	32	no	—
186	D₃×C₈	—	3	16	no	—
187	D₃×C₈	—	3	16	no	—
188	D₃×C₈	—	3	16	no	—
189	D₃×C₈	—	3	16	no	—
190	D₃×C₈	—	3	32	no	—
191	C₂²×C₃²	—	2	2	no	—
192	C₂²×C₃²	C₂×C₄²	1	2	yes	—
193	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₃⋊D₃	—	2	2	no	—
195	C₂×C₃⋊D₃	—	2	8	no	—
196	C₂×C₃⋊D₃	C₂×C₄²	1	2	yes	—
197	C₂×C₃⋊D₃	C₂×C₄²	1	2	yes	—
198	C₂×C₃⋊D₃	#131	1	4	yes	—
199	C₃²×C₄	—	2	4	no	—
200	C₃²×C₄	C₂×C₄²	1	2	yes	—
201	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
202	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
203	C₃⋊Dic₃	—	2	4	no	—
204	C₃⋊Dic₃	C₂×C₄²	1	2	yes	—
205	C₃⋊Dic₃	C₂×C₄²	1	2	yes	—
206	C₂³×C₄	—	9	1	no	—
207	C₂×M₁₆	—	9	1	no	—
208	C₂×M₁₆	—	9	8	no	—
209	C₂×M₁₆	—	9	2	no	—
210	C₂×M₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
211	C₂²×C₈	—	9	1	no	—
212	C₂²×C₈	—	9	8	no	—
213	C₂²×C₈	—	9	1	no	—
214	C₂²×C₈	—	9	1	no	—
215	C₂²×C₈	—	9	2	no	—
216	C₂²×C₈	—	9	1	no	—
217	C₂²×C₈	—	9	1	no	—
218	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
219	#117	—	9	1	no	—
220	#117	—	9	2	no	—
221	#117	—	9	2	no	—
222	#117	—	9	2	no	—
223	#117	C₂×C₃⋊D₃	1	1	yes	characteristic
224	C₂×C₄⋊C₄	—	9	2	no	—
225	C₂×C₂²⋊C₄	—	9	2	no	—
226	C₂×C₄²	—	9	2	no	—
227	#97	—	9	2	no	—
228	#97	—	9	2	no	—
229	#97	—	9	2	no	—
230	#97	C₂×C₃⋊D₃	1	2	yes	complemented
231	C₄×C₈	—	9	2	no	—
232	C₄×C₈	—	9	2	no	—
233	C₄×C₈	—	9	2	no	—
234	C₄×C₈	C₂×C₃⋊D₃	1	2	yes	complemented
235	C₂³×C₃	C₂×C₄×D₃	1	4	yes	—
236	C₂²×D₃	—	3	4	no	—
237	C₂²×D₃	—	3	16	no	—
238	C₂²×D₃	—	3	4	no	—
239	C₂²×D₃	—	6	16	no	—
240	C₂×C₃×C₄	C₂×C₄×D₃	1	16	yes	—
241	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
242	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
243	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
244	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
245	C₂×Dic₃	—	3	16	no	—
246	C₂×Dic₃	—	3	4	no	—
247	C₂×Dic₃	—	3	4	no	—
248	C₂×Dic₃	—	3	16	no	—
249	C₄×D₃	—	3	16	no	—
250	C₄×D₃	—	3	16	no	—
251	C₄×D₃	—	3	8	no	—
252	C₄×D₃	—	3	8	no	—
253	C₄×D₃	—	3	8	no	—
254	C₄×D₃	—	3	8	no	—
255	C₄×D₃	—	6	32	no	—
256	C₃×C₈	C₂×C₄×D₃	1	8	yes	—
257	C₃×C₈	C₂×C₄×D₃	1	8	yes	—
258	C₃×C₈	C₂×C₄×D₃	1	16	yes	—
259	C₃⋊C₈	—	3	8	no	—
260	C₃⋊C₈	—	3	8	no	—
261	C₃⋊C₈	—	3	16	no	—
262	C₂×C₃²	—	2	2	no	—
263	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
264	C₂×C₃²	C₂×#131	1	2	yes	—
265	C₃⋊D₃	—	2	2	no	—
266	C₃⋊D₃	#405	1	4	yes	direct product factor
267	C₂⁴	—	9	1	no	—
268	C₂²×C₄	—	9	1	no	—
269	C₂²×C₄	—	9	1	no	—
270	C₂²×C₄	—	9	1	no	—
271	C₂²×C₄	—	9	1	no	—
272	C₂²×C₄	—	9	1	no	—
273	C₂²×C₄	—	9	4	no	—
274	C₂²×C₄	—	9	4	no	—
275	C₂²×C₄	—	9	4	no	—
276	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
277	M₁₆	—	9	4	no	—
278	M₁₆	—	9	8	no	—
279	M₁₆	C₄×C₃⋊D₃	1	4	yes	complemented
280	C₂×C₈	—	9	1	no	—
281	C₂×C₈	—	9	2	no	—
282	C₂×C₈	—	9	1	no	—
283	C₂×C₈	—	9	4	no	—
284	C₂×C₈	—	9	4	no	—
285	C₂×C₈	—	9	4	no	—
286	C₂×C₈	—	9	4	no	—
287	C₂×C₈	—	9	4	no	—
288	C₂×C₈	—	9	8	no	—
289	C₂×C₈	C₄×C₃⋊D₃	1	4	yes	complemented
290	C₂×C₈	C₂²×C₃⋊D₃	1	2	yes	—
291	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
292	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
293	C₄⋊C₄	—	9	4	no	—
294	C₄⋊C₄	—	9	2	no	—
295	C₄⋊C₄	C₄×C₃⋊D₃	1	2	yes	—
296	C₂²⋊C₄	—	9	2	no	—
297	C₂²⋊C₄	—	9	4	no	—
298	C₂²⋊C₄	C₄×C₃⋊D₃	1	2	yes	—
299	C₄²	—	9	2	no	—
300	C₄²	—	9	4	no	—
301	C₄²	C₂²×C₃⋊D₃	1	2	yes	—
302	C₂²×C₃	—	2	8	no	—
303	C₂²×C₃	C₄²×D₃	1	8	yes	—
304	C₂²×C₃	C₂²×C₄×D₃	1	4	yes	—
305	C₂×D₃	—	3	8	no	—
306	C₂×D₃	—	3	16	no	—
307	C₂×D₃	—	3	8	no	—
308	C₂×D₃	—	6	32	no	—
309	C₂×D₃	—	6	8	no	—
310	C₃×C₄	—	2	16	no	—
311	C₃×C₄	C₄²×D₃	1	8	yes	—
312	C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
313	C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
314	Dic₃	—	3	8	no	—
315	Dic₃	—	3	8	no	—
316	Dic₃	—	6	16	no	—
317	C₃²	C₂×#405	1	1	yes	characteristic, complemented, Sylow
318	C₂³	—	9	1	no	—
319	C₂³	—	9	4	no	—
320	C₂³	—	9	1	no	—
321	C₂³	—	18	4	no	—
322	C₂³	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
323	C₂×C₄	—	9	4	no	—
324	C₂×C₄	—	9	1	no	—
325	C₂×C₄	—	9	1	no	—
326	C₂×C₄	—	9	4	no	—
327	C₂×C₄	—	9	4	no	—
328	C₂×C₄	—	9	2	no	—
329	C₂×C₄	—	9	2	no	—
330	C₂×C₄	—	9	2	no	—
331	C₂×C₄	—	9	2	no	—
332	C₂×C₄	—	9	4	no	—
333	C₂×C₄	—	18	8	no	—
334	C₂×C₄	C₂×C₄×C₃⋊D₃	1	4	yes	—
335	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
337	C₂×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
338	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
339	C₈	—	9	2	no	—
340	C₈	—	9	2	no	—
341	C₈	—	9	4	no	—
342	C₈	C₂×C₄×C₃⋊D₃	1	2	yes	—
343	C₈	C₂×C₄×C₃⋊D₃	1	2	yes	—
344	C₈	C₂×C₄×C₃⋊D₃	1	4	yes	—
345	C₂×C₃	—	2	8	no	—
346	C₂×C₃	C₂×C₄²×D₃	1	4	yes	—
347	C₂×C₃	D₃×#131	1	8	yes	—
348	D₃	—	3	16	no	—
349	D₃	—	6	8	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	9	2	no	—
352	C₂²	—	9	4	no	—
353	C₂²	—	9	2	no	—
354	C₂²	—	18	8	no	—
355	C₂²	—	18	2	no	—
356	C₂²	C₄²×C₃⋊D₃	1	2	yes	—
357	C₂²	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
358	C₄	—	2	4	no	—
359	C₄	—	9	2	no	—
360	C₄	—	9	2	no	—
361	C₄	—	18	4	no	—
362	C₄	C₄²×C₃⋊D₃	1	2	yes	—
363	C₄	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
364	C₄	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
365	C₃	D₃×#405	1	4	yes	complemented
366	C₂	—	2	2	no	—
367	C₂	—	9	4	no	—
368	C₂	—	18	2	no	—
369	C₂	C₂×C₄²×C₃⋊D₃	1	1	yes	characteristic
370	C₂	C₃⋊D₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₄²
Frattini	C₂×C₄	C₂³×C₃⋊D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃⋊D₃	C₂×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#405	C₃⋊D₃
hypocenter	C₃²	C₂×#405
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
4. C₃²×#405	C₂	semidirect
5. #10592821	C₂	semidirect
6. #10592800	C₂	semidirect
7. #10592696	C₂	semidirect
8. #10592407	C₂	semidirect
9. C₃⋊D₃×#97	C₂	semidirect
10. #10592388	C₂	semidirect
11. C₄×C₈×C₃⋊D₃	C₂	semidirect
20. M₁₆×C₃⋊D₃	C₄	semidirect
22. C₂×C₈×C₃⋊D₃	C₄	semidirect
34. C₃²×#97	C₂²	semidirect
35. C₃²×C₄×C₈	C₂²	semidirect
36. #63642	C₂²	semidirect
37. #63642	C₂²	semidirect
38. C₈×C₃⋊Dic₃	C₂²	semidirect
39. C₈×C₃⋊Dic₃	C₂²	semidirect
40. #63630	C₂²	semidirect
41. C₄×C₃⋊(C₃⋊C₈)	C₂²	semidirect
45. C₃×#405	D₃	semidirect
63. C₃²×M₁₆	C₂×C₄	semidirect
64. C₂×C₃²×C₈	C₂×C₄	semidirect
77. #3748	C₂×C₄	semidirect
78. C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	semidirect
82. #3743	C₂×C₄	semidirect
86. C₈×C₃⋊D₃	C₂×C₄	semidirect
87. C₈×C₃⋊D₃	C₂×C₄	semidirect
110. C₃×#97	C₂×D₃	semidirect
111. C₃×C₄×C₈	C₂×D₃	semidirect
153. #405	C₃⋊D₃	direct (N × H)
166. C₃×M₁₆	C₄×D₃	semidirect
167. C₂×C₃×C₈	C₄×D₃	semidirect
230. #97	C₂×C₃⋊D₃	semidirect
234. C₄×C₈	C₂×C₃⋊D₃	semidirect
266. C₃⋊D₃	#405	direct (N × H)
279. M₁₆	C₄×C₃⋊D₃	semidirect
289. C₂×C₈	C₄×C₃⋊D₃	semidirect
317. C₃²	C₂×#405	semidirect
365. C₃	D₃×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₃⋊D₃	2
C₂²×C₈×C₃⋊D₃	2
C₃⋊D₃×#117	2
C₃²×#405	2
#10592821	2
#10592800	2
#10592696	2
#10592407	2
C₃⋊D₃×#97	2
#10592388	2
C₄×C₈×C₃⋊D₃	2
D₃×#405	3

Subgroups — C3⋊D3×#405 #11857170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#405 #11857170