Subgroups — C₂×C₃×#63508 #13153643

Order 1728.

1122 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₉	C₂	1	1	yes	maximal, characteristic
3	C₃×#63508	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×(C₂×D₉)⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₃×C₄⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×Dic₉⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#946	—	3	1	no	maximal
8	C₂×#63508	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
10	C₂×C₃×Q₈×C₉	—	2	4	no	—
11	C₂×C₃×Q₈×C₉	C₂²	1	4	yes	complemented
12	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×Dic₉	C₂²	1	2	yes	—
16	C₂×C₃×C₄×D₉	—	2	4	no	—
17	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
18	C₃×(C₂×D₉)⋊C₄	C₂²	1	8	yes	—
19	C₃×C₄⋊Dic₉	C₂²	1	4	yes	complemented
20	C₃×Dic₉⋊C₄	C₂²	1	8	yes	complemented
21	C₂²×C₃²×Q₈	D₃	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₃	—	3	1	no	—
23	C₃×#946	—	3	8	no	—
24	C₂×C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
25	C₂×C₃×C₄⋊Dic₃	—	3	1	no	—
26	C₂×C₃×Dic₃⋊C₄	—	3	2	no	—
27	C₂²×Q₈×C₉	—	2	1	no	—
28	C₂²×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₉	C₂×C₃	1	1	yes	characteristic
30	#63508	C₂×C₃	1	8	yes	direct product factor
31	C₂×(C₂×D₉)⋊C₄	C₂×C₃	1	2	yes	—
32	C₂×C₄⋊Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×Dic₉⋊C₄	C₂×C₃	1	2	yes	complemented
34	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
35	C₂²×C₃×D₉	—	2	2	no	—
36	C₂²×C₃×D₉	—	2	2	no	—
37	C₂²×C₃×D₉	Q₈	1	4	yes	complemented
38	C₂²×C₃×D₉	C₂³	1	2	yes	—
39	C₃×Q₈×C₉	—	2	8	no	—
40	C₂×C₃×C₄×C₉	—	2	4	no	—
41	C₂×C₃×C₄×C₉	D₄	1	4	yes	—
42	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
43	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
44	C₂×C₃×Dic₉	—	2	2	no	—
45	C₂×C₃×Dic₉	—	2	4	no	—
46	C₂×C₃×Dic₉	C₂³	1	2	yes	—
47	C₂×C₃×Dic₉	C₂³	1	4	yes	—
48	C₃×C₄×D₉	—	2	8	no	—
49	C₂×C₃×C₂²⋊Q₈	—	9	1	no	—
50	C₂×#946	—	3	1	no	—
51	C₂³×C₃×D₃	—	3	1	no	—
52	C₂×C₃²×Q₈	—	2	4	no	—
53	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
54	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
55	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
56	C₂²×C₃×Dic₃	—	3	1	no	—
57	C₂²×C₃×Dic₃	—	3	2	no	—
58	C₂×C₃×C₄×D₃	—	3	4	no	—
59	C₂×C₃×C₄×D₃	—	6	4	no	—
60	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
61	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
62	C₃×C₄⋊Dic₃	—	3	4	no	—
63	C₃×Dic₃⋊C₄	—	3	8	no	—
64	C₂×Q₈×C₉	—	2	8	no	—
65	C₂×Q₈×C₉	—	2	4	no	—
66	C₂×Q₈×C₉	—	2	4	no	—
67	C₂×Q₈×C₉	C₂²×C₃	1	4	yes	complemented
68	C₂²×C₄×C₉	—	2	2	no	—
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	C₂²×C₃	1	2	yes	—
71	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
72	C₂²×Dic₉	C₂²×C₃	1	2	yes	—
73	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄×D₉	—	2	4	no	—
75	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
76	(C₂×D₉)⋊C₄	C₂²×C₃	1	8	yes	—
77	C₄⋊Dic₉	C₂²×C₃	1	4	yes	complemented
78	Dic₉⋊C₄	C₂²×C₃	1	8	yes	complemented
79	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
80	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
81	C₂²×C₃×C₉	#41	1	2	yes	—
82	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
83	C₂×C₃×D₉	—	2	8	no	—
84	C₂×C₃×D₉	—	2	2	no	—
85	C₂×C₃×D₉	—	2	2	no	—
86	C₂×C₃×D₉	C₂×Q₈	1	4	yes	complemented
87	C₃×C₄×C₉	—	2	4	no	—
88	C₃×C₄×C₉	C₂×D₄	1	4	yes	—
89	C₃×Dic₉	—	2	2	no	—
90	C₃×Dic₉	—	2	4	no	—
91	C₂²×C₃×Q₈	—	2	1	no	—
92	C₂²×C₃×Q₈	D₉	1	1	yes	characteristic, complemented
93	C₂²×C₃×Q₈	C₃×D₃	1	1	yes	characteristic
94	C₂³×C₃×C₄	—	9	1	no	—
95	C₂²×C₄×D₃	—	3	1	no	—
96	C₃×C₂²⋊Q₈	—	9	8	no	—
97	C₂×C₃×C₄⋊C₄	—	9	2	no	—
98	C₂×C₃×C₄⋊C₄	—	9	1	no	—
99	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
100	#946	—	3	8	no	—
101	C₂×(C₂×D₃)⋊C₄	—	3	2	no	—
102	C₂×C₄⋊Dic₃	—	3	1	no	—
103	C₂×Dic₃⋊C₄	—	3	2	no	—
104	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
105	C₂²×C₃×D₃	—	3	4	no	—
106	C₂²×C₃×D₃	—	3	2	no	—
107	C₂²×C₃×D₃	—	6	2	no	—
108	C₂²×C₃×D₃	—	6	2	no	—
109	C₃²×Q₈	—	2	8	no	—
110	C₂×C₃²×C₄	—	2	4	no	—
111	C₂×C₃²×C₄	#67	1	4	yes	—
112	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
113	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
114	C₂×C₃×Dic₃	—	3	2	no	—
115	C₂×C₃×Dic₃	—	3	4	no	—
116	C₂×C₃×Dic₃	—	6	4	no	—
117	C₂×C₃×Dic₃	—	6	2	no	—
118	C₃×C₄×D₃	—	6	8	no	—
119	C₂³×C₉	—	2	1	no	—
120	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
121	C₂²×D₉	—	2	2	no	—
122	C₂²×D₉	—	2	2	no	—
123	C₂²×D₉	C₃×Q₈	1	4	yes	complemented
124	C₂²×D₉	C₂³×C₃	1	2	yes	—
125	Q₈×C₉	—	2	16	no	—
126	Q₈×C₉	—	2	8	no	—
127	C₂×C₄×C₉	—	2	8	no	—
128	C₂×C₄×C₉	—	2	4	no	—
129	C₂×C₄×C₉	—	2	4	no	—
130	C₂×C₄×C₉	—	2	4	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	C₃×D₄	1	4	yes	—
133	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
134	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
135	C₂×Dic₉	—	2	2	no	—
136	C₂×Dic₉	—	2	4	no	—
137	C₂×Dic₉	C₂³×C₃	1	2	yes	—
138	C₂×Dic₉	C₂³×C₃	1	4	yes	—
139	C₄×D₉	—	2	8	no	—
140	C₂×C₂²⋊Q₈	—	9	1	no	Sylow
141	C₂×C₃×C₉	C₂²⋊Q₈	1	4	yes	complemented
142	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
145	C₃×D₉	—	2	4	no	—
146	C₂⁴×C₃	—	9	1	no	—
147	C₂³×D₃	—	3	1	no	—
148	C₂×C₃×Q₈	—	2	8	no	—
149	C₂×C₃×Q₈	—	2	4	no	—
150	C₂×C₃×Q₈	—	2	4	no	—
151	C₂×C₃×Q₈	—	2	4	no	—
152	C₂×C₃×Q₈	C₂×D₉	1	4	yes	complemented
153	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	1	no	—
156	C₂²×C₃×C₄	—	9	2	no	—
157	C₂²×C₃×C₄	—	9	1	no	—
158	C₂²×C₃×C₄	—	9	4	no	—
159	C₂²×C₃×C₄	—	18	4	no	—
160	C₂²×C₃×C₄	C₂×D₉	1	2	yes	—
161	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
163	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
164	C₂²×Dic₃	—	3	1	no	—
165	C₂²×Dic₃	—	3	2	no	—
166	C₂×C₄×D₃	—	3	4	no	—
167	C₂×C₄×D₃	—	6	4	no	—
168	C₃×C₄⋊C₄	—	9	8	no	—
169	C₃×C₄⋊C₄	—	9	4	no	—
170	C₃×C₂²⋊C₄	—	9	8	no	—
171	(C₂×D₃)⋊C₄	—	3	8	no	—
172	C₄⋊Dic₃	—	3	4	no	—
173	Dic₃⋊C₄	—	3	8	no	—
174	C₂²×C₃²	D₃×Q₈	1	2	yes	—
175	C₂²×C₃²	#239	1	2	yes	—
176	C₂²×C₃²	C₂×#67	1	2	yes	—
177	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
178	C₂×C₃×D₃	—	3	4	no	—
179	C₂×C₃×D₃	—	6	8	no	—
180	C₂×C₃×D₃	—	6	2	no	—
181	C₂×C₃×D₃	—	6	2	no	—
182	C₃²×C₄	—	2	4	no	—
183	C₃²×C₄	C₂×#67	1	4	yes	—
184	C₃×Dic₃	—	6	4	no	—
185	C₃×Dic₃	—	6	2	no	—
186	C₂²×C₉	—	2	1	no	—
187	C₂²×C₉	—	2	2	no	—
188	C₂²×C₉	—	2	2	no	—
189	C₂²×C₉	—	2	2	no	—
190	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
191	C₂²×C₉	C₂×C₃×Q₈	1	2	yes	—
192	C₂²×C₉	C₃×#41	1	2	yes	—
193	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
194	C₂×D₉	—	2	8	no	—
195	C₂×D₉	—	2	2	no	—
196	C₂×D₉	—	2	2	no	—
197	C₂×D₉	C₂×C₃×Q₈	1	4	yes	complemented
198	C₄×C₉	—	2	8	no	—
199	C₄×C₉	—	2	4	no	—
200	C₄×C₉	—	2	4	no	—
201	C₄×C₉	C₂×C₃×D₄	1	4	yes	—
202	Dic₉	—	2	2	no	—
203	Dic₉	—	2	4	no	—
204	C₂²×Q₈	C₃×D₉	1	1	yes	characteristic, complemented
205	C₂³×C₄	—	9	1	no	—
206	C₂²⋊Q₈	—	9	8	no	—
207	C₂×C₄⋊C₄	—	9	2	no	—
208	C₂×C₄⋊C₄	—	9	1	no	—
209	C₂×C₂²⋊C₄	—	9	2	no	—
210	C₃×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
211	C₂³×C₃	—	2	1	no	—
212	C₂³×C₃	—	9	4	no	—
213	C₂³×C₃	—	9	2	no	—
214	C₂³×C₃	—	18	2	no	—
215	C₂³×C₃	—	18	2	no	—
216	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
217	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
218	C₂²×D₃	—	3	2	no	—
219	C₂²×D₃	—	3	4	no	—
220	C₂²×D₃	—	6	2	no	—
221	C₂²×D₃	—	6	2	no	—
222	C₃×Q₈	—	2	16	no	—
223	C₃×Q₈	—	2	8	no	—
224	C₃×Q₈	—	2	8	no	—
225	C₂×C₃×C₄	—	2	8	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	9	4	no	—
232	C₂×C₃×C₄	—	9	2	no	—
233	C₂×C₃×C₄	—	18	4	no	—
234	C₂×C₃×C₄	—	18	2	no	—
235	C₂×C₃×C₄	—	18	8	no	—
236	C₂×C₃×C₄	#611	1	4	yes	—
237	C₂×C₃×C₄	C₂²×D₉	1	4	yes	—
238	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
239	C₂×C₃×C₄	C₃×#67	1	4	yes	—
240	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
241	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
242	C₂×Dic₃	—	3	2	no	—
243	C₂×Dic₃	—	3	4	no	—
244	C₂×Dic₃	—	6	4	no	—
245	C₂×Dic₃	—	6	2	no	—
246	C₄×D₃	—	6	8	no	—
247	C₂×C₃²	#946	1	4	yes	—
248	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
249	C₂×C₃²	C₂×#239	1	1	yes	characteristic
250	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
251	C₃×D₃	—	6	4	no	—
252	C₂×C₉	—	2	4	no	—
253	C₂×C₉	—	2	1	no	—
254	C₂×C₉	—	2	1	no	—
255	C₂×C₉	—	2	1	no	—
256	C₂×C₉	C₃×C₂²⋊Q₈	1	4	yes	complemented
257	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
258	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
259	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
260	D₉	—	2	4	no	—
261	C₂⁴	—	9	1	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	C₂×C₃×D₉	1	4	yes	complemented
264	C₂²×C₄	—	9	2	no	—
265	C₂²×C₄	—	9	1	no	—
266	C₂²×C₄	—	9	4	no	—
267	C₂²×C₄	—	18	4	no	—
268	C₂²×C₄	C₂×C₃×D₉	1	2	yes	—
269	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
270	C₄⋊C₄	—	9	8	no	—
271	C₄⋊C₄	—	9	4	no	—
272	C₂²⋊C₄	—	9	8	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	—	9	4	no	—
278	C₂²×C₃	—	18	8	no	—
279	C₂²×C₃	—	18	2	no	—
280	C₂²×C₃	—	18	2	no	—
281	C₂²×C₃	Q₈×D₉	1	2	yes	—
282	C₂²×C₃	#3701	1	2	yes	—
283	C₂²×C₃	C₂×#611	1	2	yes	—
284	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
285	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
286	C₂²×C₃	C₃×#239	1	2	yes	—
287	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
288	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
289	C₂×D₃	—	3	4	no	—
290	C₂×D₃	—	6	8	no	—
291	C₂×D₃	—	6	2	no	—
292	C₂×D₃	—	6	2	no	—
293	C₃×C₄	—	2	8	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	18	4	no	—
298	C₃×C₄	—	18	2	no	—
299	C₃×C₄	C₂×#611	1	4	yes	—
300	C₃×C₄	C₂×C₃×#67	1	4	yes	—
301	Dic₃	—	6	4	no	—
302	Dic₃	—	6	2	no	—
303	C₃²	C₂×#946	1	1	yes	characteristic
304	C₉	—	2	1	no	—
305	C₉	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented
306	C₂³	—	9	2	no	—
307	C₂³	—	9	4	no	—
308	C₂³	—	18	2	no	—
309	C₂³	—	18	2	no	—
310	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
311	Q₈	—	2	8	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	9	4	no	—
314	C₂×C₄	—	9	2	no	—
315	C₂×C₄	—	18	4	no	—
316	C₂×C₄	—	18	2	no	—
317	C₂×C₄	—	18	8	no	—
318	C₂×C₄	C₃×#611	1	4	yes	—
319	C₂×C₄	C₂²×C₃×D₉	1	4	yes	—
320	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
321	C₂×C₃	—	2	1	no	—
322	C₂×C₃	—	2	1	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	2	4	no	—
325	C₂×C₃	—	18	4	no	—
326	C₂×C₃	#63508	1	4	yes	direct product factor
327	C₂×C₃	C₂×Q₈×D₉	1	1	yes	characteristic
328	C₂×C₃	C₂×#3701	1	1	yes	characteristic
329	C₂×C₃	C₂²×#611	1	1	yes	characteristic
330	C₂×C₃	C₃×#946	1	4	yes	—
331	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
332	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
333	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
334	D₃	—	6	4	no	—
335	C₂²	—	9	4	no	—
336	C₂²	—	18	2	no	—
337	C₂²	—	18	2	no	—
338	C₂²	—	18	8	no	—
339	C₂²	C₃×Q₈×D₉	1	2	yes	—
340	C₂²	C₃×#3701	1	2	yes	—
341	C₂²	C₂×C₃×#611	1	2	yes	—
342	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
343	C₄	—	2	4	no	—
344	C₄	—	18	4	no	—
345	C₄	—	18	2	no	—
346	C₄	C₂×C₃×#611	1	4	yes	—
347	C₃	—	2	1	no	—
348	C₃	C₂×#63508	1	1	yes	characteristic, direct product factor
349	C₃	C₂×C₃×#946	1	1	yes	characteristic
350	C₂	—	18	4	no	—
351	C₂	C₃×#63508	1	4	yes	direct product factor
352	C₂	C₂×C₃×Q₈×D₉	1	1	yes	characteristic
353	C₂	C₂×C₃×#3701	1	1	yes	characteristic
354	C₂	C₂²×C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂²×C₃×Q₈×C₉	C₂
socle	C₂³×C₃²	C₂²×D₃
prime radical	C₂³×C₃×D₉	C₂²
hypercenter	C₂²×C₃×Q₈	D₉
hypocenter	C₉	C₂×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×C₉	C₂	semidirect
3. C₃×#63508	C₂	direct (N × H)
5. C₂×C₃×C₄⋊Dic₉	C₂	semidirect
6. C₂×C₃×Dic₉⋊C₄	C₂	semidirect
8. C₂×#63508	C₃	direct (N × H)
11. C₂×C₃×Q₈×C₉	C₂²	semidirect
19. C₃×C₄⋊Dic₉	C₂²	semidirect
20. C₃×Dic₉⋊C₄	C₂²	semidirect
28. C₂²×Q₈×C₉	C₂×C₃	semidirect
30. #63508	C₂×C₃	direct (N × H)
32. C₂×C₄⋊Dic₉	C₂×C₃	semidirect
33. C₂×Dic₉⋊C₄	C₂×C₃	semidirect
37. C₂²×C₃×D₉	Q₈	semidirect
67. C₂×Q₈×C₉	C₂²×C₃	semidirect
77. C₄⋊Dic₉	C₂²×C₃	semidirect
78. Dic₉⋊C₄	C₂²×C₃	semidirect
86. C₂×C₃×D₉	C₂×Q₈	semidirect
92. C₂²×C₃×Q₈	D₉	semidirect
123. C₂²×D₉	C₃×Q₈	semidirect
141. C₂×C₃×C₉	C₂²⋊Q₈	semidirect
152. C₂×C₃×Q₈	C₂×D₉	semidirect
197. C₂×D₉	C₂×C₃×Q₈	semidirect
204. C₂²×Q₈	C₃×D₉	semidirect
210. C₃×C₉	C₂×C₂²⋊Q₈	semidirect
256. C₂×C₉	C₃×C₂²⋊Q₈	semidirect
263. C₂×Q₈	C₂×C₃×D₉	semidirect
305. C₉	C₂×C₃×C₂²⋊Q₈	semidirect
326. C₂×C₃	#63508	direct (N × H)
348. C₃	C₂×#63508	direct (N × H)
351. C₂	C₃×#63508	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×Q₈×C₉	2
C₂²×C₃×C₄×D₉	2
C₃×#63508	2
C₂×C₃×(C₂×D₉)⋊C₄	2
C₂×C₃×C₄⋊Dic₉	2
C₂×C₃×Dic₉⋊C₄	2
C₂×C₃×#946	3
C₂×#63508	3

Subgroups — C2×C3×#63508 #13153643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63508 #13153643