Subgroups — C₂×C₃²×#832 #13162651

Order 1728.

2156 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#832	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃²×#102	—	3	1	no	maximal
6	C₂×C₃×#832	C₃	1	4	yes	maximal, direct product factor
7	C₂⁴×C₃³	—	2	1	no	—
8	C₂×C₃³×D₄	—	2	1	no	—
9	C₂×C₃³×D₄	—	2	2	no	—
10	C₂×C₃³×D₄	C₄	1	4	yes	complemented
11	C₂×C₃³×D₄	C₂²	1	2	yes	—
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×Dic₃	—	2	1	no	—
14	C₃²×C₄⋊Dic₃	—	2	1	no	—
15	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	complemented
16	C₂×C₃²×C₃⋊C₈	—	2	2	no	—
17	C₂×C₃²×C₃⋊C₈	C₂²	1	2	yes	complemented
18	C₂²×C₃²×D₄	—	2	4	no	—
19	C₂²×C₃²×D₄	D₃	1	1	yes	characteristic
20	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	—
21	C₂²×C₃²×C₈	—	3	1	no	—
22	C₂×C₃²×C₄⋊C₄	—	3	1	no	—
23	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	4	yes	complemented
24	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	4	yes	complemented
25	C₃²×#102	—	3	4	no	—
26	C₃×#832	C₂×C₃	1	16	yes	direct product factor
27	C₂³×C₃³	—	2	4	no	—
28	C₂³×C₃³	—	2	2	no	—
29	C₂³×C₃³	—	4	2	no	—
30	C₂³×C₃³	—	4	2	no	—
31	C₂³×C₃³	D₄	1	1	yes	characteristic
32	C₃³×D₄	—	2	4	no	—
33	C₃³×D₄	—	2	2	no	—
34	C₃³×D₄	C₂×C₄	1	4	yes	complemented
35	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
36	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃³×C₄	D₄	1	2	yes	—
38	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
39	C₂×C₃²×Dic₃	—	2	2	no	—
40	C₂×C₃²×Dic₃	—	4	2	no	—
41	C₃²×C₃⋊C₈	—	2	2	no	—
42	C₂×C₃×#102	—	3	4	no	—
43	C₂×#832	C₃²	1	1	yes	characteristic, direct product factor
44	C₂⁴×C₃²	—	2	8	no	—
45	C₂⁴×C₃²	—	2	1	no	—
46	C₂⁴×C₃²	—	2	4	no	—
47	C₂×C₃²×D₄	—	2	8	no	—
48	C₂×C₃²×D₄	—	2	16	no	—
49	C₂×C₃²×D₄	—	2	16	no	—
50	C₂×C₃²×D₄	—	2	8	no	—
51	C₂×C₃²×D₄	—	2	1	no	—
52	C₂×C₃²×D₄	—	2	2	no	—
53	C₂×C₃²×D₄	—	2	4	no	—
54	C₂×C₃²×D₄	—	2	8	no	—
55	C₂×C₃²×D₄	Dic₃	1	4	yes	complemented
56	C₂×C₃²×D₄	C₃×C₄	1	16	yes	complemented
57	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
58	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	—
59	C₂²×C₃²×C₄	—	2	4	no	—
60	C₂²×C₃²×C₄	—	6	1	no	—
61	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
63	C₂²×C₃×Dic₃	—	2	4	no	—
64	C₂×C₃²×C₈	—	3	2	no	—
65	C₂×C₃²×C₈	—	6	2	no	—
66	C₃²×C₄⋊C₄	—	3	2	no	—
67	C₃²×C₄⋊C₄	—	6	1	no	—
68	C₃×C₄⋊Dic₃	—	2	4	no	—
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	complemented
70	C₂×C₃×C₃⋊C₈	—	2	8	no	—
71	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	8	yes	complemented
72	C₂²×C₃³	—	2	4	no	—
73	C₂²×C₃³	—	4	8	no	—
74	C₂²×C₃³	—	4	2	no	—
75	C₂²×C₃³	—	4	2	no	—
76	C₂²×C₃³	C₂²⋊C₄	1	2	yes	—
77	C₂²×C₃³	D₈	1	2	yes	—
78	C₂²×C₃³	SD₁₆	1	2	yes	—
79	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
80	C₃³×C₄	C₂²⋊C₄	1	2	yes	—
81	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
82	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
83	C₃²×Dic₃	—	4	2	no	—
84	C₂²×C₃×D₄	—	2	4	no	—
85	C₂²×C₃×D₄	C₃×D₃	1	4	yes	—
86	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic
87	C₂²×C₃×C₈	—	3	4	no	—
88	C₂×C₃×C₄⋊C₄	—	3	4	no	—
89	C₂×C₄⋊Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
90	C₂²×C₃⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
91	C₃×#102	—	3	16	no	—
92	#832	C₂×C₃²	1	4	yes	direct product factor
93	C₂³×C₃²	—	2	32	no	—
94	C₂³×C₃²	—	2	16	no	—
95	C₂³×C₃²	—	2	4	no	—
96	C₂³×C₃²	—	2	16	no	—
97	C₂³×C₃²	—	2	2	no	—
98	C₂³×C₃²	—	2	8	no	—
99	C₂³×C₃²	—	2	4	no	—
100	C₂³×C₃²	—	4	16	no	—
101	C₂³×C₃²	—	4	16	no	—
102	C₂³×C₃²	—	4	2	no	—
103	C₂³×C₃²	—	4	2	no	—
104	C₂³×C₃²	—	4	8	no	—
105	C₂³×C₃²	—	4	8	no	—
106	C₂³×C₃²	#67	1	1	yes	characteristic
107	C₂³×C₃²	C₃×D₄	1	4	yes	—
108	C₃²×D₄	—	2	32	no	—
109	C₃²×D₄	—	2	16	no	—
110	C₃²×D₄	—	2	4	no	—
111	C₃²×D₄	—	2	16	no	—
112	C₃²×D₄	—	2	2	no	—
113	C₃²×D₄	—	2	8	no	—
114	C₃²×D₄	—	2	16	no	—
115	C₃²×D₄	C₂×Dic₃	1	4	yes	complemented
116	C₃²×D₄	C₂×C₃×C₄	1	16	yes	complemented
117	C₂×C₃²×C₄	—	2	8	no	—
118	C₂×C₃²×C₄	—	2	4	no	—
119	C₂×C₃²×C₄	—	2	8	no	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	—	6	2	no	—
122	C₂×C₃²×C₄	—	12	2	no	—
123	C₂×C₃²×C₄	C₂×Dic₃	1	2	yes	—
124	C₂×C₃²×C₄	#67	1	1	yes	characteristic
125	C₂×C₃²×C₄	#67	1	2	yes	—
126	C₂×C₃²×C₄	C₂×C₃×C₄	1	8	yes	—
127	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
128	C₂×C₃²×C₄	C₃×D₄	1	8	yes	—
129	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
131	C₂×C₃×Dic₃	—	2	8	no	—
132	C₂×C₃×Dic₃	—	4	8	no	—
133	C₃²×C₈	—	6	2	no	—
134	C₃×C₃⋊C₈	—	2	8	no	—
135	C₂×#102	—	3	1	no	Sylow
136	C₂×C₃³	—	4	4	no	—
137	C₂×C₃³	#102	1	4	yes	complemented
138	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₃³	C₂×D₈	1	1	yes	characteristic
140	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
141	C₂⁴×C₃	—	2	8	no	—
142	C₂⁴×C₃	—	2	4	no	—
143	C₂⁴×C₃	—	2	1	no	—
144	C₂×C₃×D₄	—	2	8	no	—
145	C₂×C₃×D₄	—	2	16	no	—
146	C₂×C₃×D₄	—	2	4	no	—
147	C₂×C₃×D₄	—	2	8	no	—
148	C₂×C₃×D₄	—	2	1	no	—
149	C₂×C₃×D₄	—	2	2	no	—
150	C₂×C₃×D₄	—	2	16	no	—
151	C₂×C₃×D₄	—	2	8	no	—
152	C₂×C₃×D₄	C₃×Dic₃	1	16	yes	complemented
153	C₂×C₃×D₄	C₃²×C₄	1	4	yes	complemented
154	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
155	C₂×C₃×D₄	C₂²×C₃²	1	2	yes	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	6	4	no	—
158	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
159	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
160	C₂²×Dic₃	—	2	1	no	—
161	C₂×C₃×C₈	—	3	8	no	—
162	C₂×C₃×C₈	—	6	8	no	—
163	C₃×C₄⋊C₄	—	3	8	no	—
164	C₃×C₄⋊C₄	—	6	4	no	—
165	C₄⋊Dic₃	—	2	1	no	—
166	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	complemented
167	C₂×C₃⋊C₈	—	2	2	no	—
168	C₂×C₃⋊C₈	C₂²×C₃²	1	2	yes	complemented
169	C₂²×C₃²	—	2	32	no	—
170	C₂²×C₃²	—	2	4	no	—
171	C₂²×C₃²	—	2	16	no	—
172	C₂²×C₃²	—	2	8	no	—
173	C₂²×C₃²	—	2	8	no	—
174	C₂²×C₃²	—	2	8	no	—
175	C₂²×C₃²	—	2	4	no	—
176	C₂²×C₃²	—	4	16	no	—
177	C₂²×C₃²	—	4	16	no	—
178	C₂²×C₃²	—	4	64	no	—
179	C₂²×C₃²	—	4	8	no	—
180	C₂²×C₃²	—	4	32	no	—
181	C₂²×C₃²	—	4	2	no	—
182	C₂²×C₃²	—	4	2	no	—
183	C₂²×C₃²	—	4	8	no	—
184	C₂²×C₃²	—	4	8	no	—
185	C₂²×C₃²	#213	1	2	yes	—
186	C₂²×C₃²	#214	1	2	yes	—
187	C₂²×C₃²	#217	1	2	yes	—
188	C₂²×C₃²	C₃×C₂²⋊C₄	1	8	yes	—
189	C₂²×C₃²	C₃×D₈	1	8	yes	—
190	C₂²×C₃²	C₃×SD₁₆	1	8	yes	—
191	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
192	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
193	C₃²×C₄	—	2	8	no	—
194	C₃²×C₄	—	2	4	no	—
195	C₃²×C₄	—	2	4	no	—
196	C₃²×C₄	—	12	2	no	—
197	C₃²×C₄	#217	1	2	yes	—
198	C₃²×C₄	C₃×C₂²⋊C₄	1	8	yes	—
199	C₃²×C₄	C₂²×Dic₃	1	1	yes	characteristic
200	C₃²×C₄	C₂×#67	1	1	yes	characteristic
201	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
202	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
203	C₃×Dic₃	—	4	8	no	—
204	C₂²×D₄	C₃²×D₃	1	1	yes	characteristic
205	C₂²×C₈	—	3	1	no	—
206	C₂×C₄⋊C₄	—	3	1	no	—
207	#102	—	3	4	no	—
208	C₃³	C₂×#102	1	1	yes	characteristic, complemented, Sylow
209	C₂³×C₃	—	2	32	no	—
210	C₂³×C₃	—	2	16	no	—
211	C₂³×C₃	—	2	16	no	—
212	C₂³×C₃	—	2	4	no	—
213	C₂³×C₃	—	2	8	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	4	16	no	—
217	C₂³×C₃	—	4	16	no	—
218	C₂³×C₃	—	4	8	no	—
219	C₂³×C₃	—	4	8	no	—
220	C₂³×C₃	—	4	2	no	—
221	C₂³×C₃	—	4	2	no	—
222	C₂³×C₃	C₃×#67	1	4	yes	—
223	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
224	C₃×D₄	—	2	32	no	—
225	C₃×D₄	—	2	16	no	—
226	C₃×D₄	—	2	16	no	—
227	C₃×D₄	—	2	4	no	—
228	C₃×D₄	—	2	8	no	—
229	C₃×D₄	—	2	2	no	—
230	C₃×D₄	—	2	16	no	—
231	C₃×D₄	C₂×C₃×Dic₃	1	16	yes	complemented
232	C₃×D₄	C₂×C₃²×C₄	1	4	yes	complemented
233	C₂×C₃×C₄	—	2	8	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	6	8	no	—
238	C₂×C₃×C₄	—	12	8	no	—
239	C₂×C₃×C₄	C₂×C₃×Dic₃	1	8	yes	—
240	C₂×C₃×C₄	C₃×#67	1	4	yes	—
241	C₂×C₃×C₄	C₃×#67	1	8	yes	—
242	C₂×C₃×C₄	C₂×C₃²×C₄	1	2	yes	—
243	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₃²×D₄	1	2	yes	—
245	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
246	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
247	C₂×Dic₃	—	2	2	no	—
248	C₂×Dic₃	—	4	2	no	—
249	C₃×C₈	—	6	8	no	—
250	C₃⋊C₈	—	2	2	no	—
251	C₂×C₃²	—	2	4	no	—
252	C₂×C₃²	—	2	4	no	—
253	C₂×C₃²	—	2	4	no	—
254	C₂×C₃²	—	2	16	no	—
255	C₂×C₃²	—	4	32	no	—
256	C₂×C₃²	—	4	4	no	—
257	C₂×C₃²	—	4	16	no	—
258	C₂×C₃²	#832	1	4	yes	direct product factor
259	C₂×C₃²	C₃×#102	1	16	yes	complemented
260	C₂×C₃²	C₂×#213	1	1	yes	characteristic
261	C₂×C₃²	C₂×#214	1	1	yes	characteristic
262	C₂×C₃²	C₂×#217	1	1	yes	characteristic
263	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
264	C₂×C₃²	C₂×C₃×D₈	1	4	yes	—
265	C₂×C₃²	C₂×C₃×SD₁₆	1	4	yes	—
266	C₂⁴	—	2	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	C₃²×Dic₃	1	4	yes	complemented
270	C₂×D₄	C₂×C₃²×D₃	1	2	yes	—
271	C₂²×C₄	—	6	1	no	—
272	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
273	C₂×C₈	—	3	2	no	—
274	C₂×C₈	—	6	2	no	—
275	C₄⋊C₄	—	3	2	no	—
276	C₄⋊C₄	—	6	1	no	—
277	C₂²×C₃	—	2	32	no	—
278	C₂²×C₃	—	2	16	no	—
279	C₂²×C₃	—	2	4	no	—
280	C₂²×C₃	—	2	8	no	—
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	—	2	8	no	—
283	C₂²×C₃	—	2	8	no	—
284	C₂²×C₃	—	4	16	no	—
285	C₂²×C₃	—	4	16	no	—
286	C₂²×C₃	—	4	64	no	—
287	C₂²×C₃	—	4	8	no	—
288	C₂²×C₃	—	4	8	no	—
289	C₂²×C₃	—	4	32	no	—
290	C₂²×C₃	—	4	2	no	—
291	C₂²×C₃	—	4	2	no	—
292	C₂²×C₃	—	4	8	no	—
293	C₂²×C₃	C₃×#213	1	8	yes	—
294	C₂²×C₃	C₃×#214	1	8	yes	—
295	C₂²×C₃	C₃×#217	1	8	yes	—
296	C₂²×C₃	C₃²×C₂²⋊C₄	1	2	yes	—
297	C₂²×C₃	C₃²×D₈	1	2	yes	—
298	C₂²×C₃	C₃²×SD₁₆	1	2	yes	—
299	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
300	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
301	C₃×C₄	—	2	8	no	—
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	12	8	no	—
305	C₃×C₄	C₃×#217	1	8	yes	—
306	C₃×C₄	C₃²×C₂²⋊C₄	1	2	yes	—
307	C₃×C₄	C₂²×C₃×Dic₃	1	4	yes	—
308	C₃×C₄	C₂×C₃×#67	1	4	yes	—
309	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
310	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
311	Dic₃	—	4	2	no	—
312	C₃²	—	2	4	no	—
313	C₃²	C₂×#832	1	1	yes	characteristic, direct product factor
314	C₃²	C₂×C₃×#102	1	4	yes	complemented
315	C₂³	—	2	4	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	C₃²×#67	1	1	yes	characteristic
320	D₄	—	2	4	no	—
321	D₄	—	2	2	no	—
322	D₄	C₂×C₃²×Dic₃	1	4	yes	complemented
323	C₂×C₄	—	6	2	no	—
324	C₂×C₄	—	12	2	no	—
325	C₂×C₄	C₂×C₃²×Dic₃	1	2	yes	—
326	C₂×C₄	C₃²×#67	1	1	yes	characteristic
327	C₂×C₄	C₃²×#67	1	2	yes	—
328	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
329	C₈	—	6	2	no	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	2	4	no	—
332	C₂×C₃	—	2	4	no	—
333	C₂×C₃	—	2	16	no	—
334	C₂×C₃	—	4	32	no	—
335	C₂×C₃	—	4	16	no	—
336	C₂×C₃	—	4	4	no	—
337	C₂×C₃	C₃×#832	1	16	yes	direct product factor
338	C₂×C₃	C₃²×#102	1	4	yes	complemented
339	C₂×C₃	C₂×C₃×#213	1	4	yes	—
340	C₂×C₃	C₂×C₃×#214	1	4	yes	—
341	C₂×C₃	C₂×C₃×#217	1	4	yes	—
342	C₂×C₃	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₃	C₂×C₃²×D₈	1	1	yes	characteristic
344	C₂×C₃	C₂×C₃²×SD₁₆	1	1	yes	characteristic
345	C₂²	—	2	4	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	8	no	—
349	C₂²	C₃²×#213	1	2	yes	—
350	C₂²	C₃²×#214	1	2	yes	—
351	C₂²	C₃²×#217	1	2	yes	—
352	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
353	C₄	—	12	2	no	—
354	C₄	C₃²×#217	1	2	yes	—
355	C₄	C₂²×C₃²×Dic₃	1	1	yes	characteristic
356	C₄	C₂×C₃²×#67	1	1	yes	characteristic
357	C₃	—	2	4	no	—
358	C₃	C₂×C₃×#832	1	4	yes	direct product factor
359	C₃	C₂×C₃²×#102	1	1	yes	characteristic, complemented
360	C₂	—	4	4	no	—
361	C₂	C₃²×#832	1	4	yes	direct product factor
362	C₂	C₂×C₃²×#213	1	1	yes	characteristic
363	C₂	C₂×C₃²×#214	1	1	yes	characteristic
364	C₂	C₂×C₃²×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃²	#67
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting, prime radical	C₂²×C₃³×D₄	C₂
socle	C₂³×C₃³	D₄
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₂²×C₃²×D₄	D₃
hypocenter	C₃	C₂×C₃²×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃² ◁ C₂²×C₃²×C₄ ◁ C₂²×C₃²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄⋊Dic₃	C₂	semidirect
3. C₂²×C₃²×C₃⋊C₈	C₂	semidirect
4. C₃²×#832	C₂	direct (N × H)
6. C₂×C₃×#832	C₃	direct (N × H)
10. C₂×C₃³×D₄	C₄	semidirect
15. C₃²×C₄⋊Dic₃	C₂²	semidirect
17. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
23. C₂×C₃×C₄⋊Dic₃	C₂×C₃	semidirect
24. C₂²×C₃×C₃⋊C₈	C₂×C₃	semidirect
26. C₃×#832	C₂×C₃	direct (N × H)
34. C₃³×D₄	C₂×C₄	semidirect
43. C₂×#832	C₃²	direct (N × H)
55. C₂×C₃²×D₄	Dic₃	semidirect
56. C₂×C₃²×D₄	C₃×C₄	semidirect
69. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
71. C₂×C₃×C₃⋊C₈	C₂²×C₃	semidirect
89. C₂×C₄⋊Dic₃	C₂×C₃²	semidirect
90. C₂²×C₃⋊C₈	C₂×C₃²	semidirect
92. #832	C₂×C₃²	direct (N × H)
115. C₃²×D₄	C₂×Dic₃	semidirect
116. C₃²×D₄	C₂×C₃×C₄	semidirect
137. C₂×C₃³	#102	semidirect
152. C₂×C₃×D₄	C₃×Dic₃	semidirect
153. C₂×C₃×D₄	C₃²×C₄	semidirect
166. C₄⋊Dic₃	C₂²×C₃²	semidirect
168. C₂×C₃⋊C₈	C₂²×C₃²	semidirect
208. C₃³	C₂×#102	semidirect
231. C₃×D₄	C₂×C₃×Dic₃	semidirect
232. C₃×D₄	C₂×C₃²×C₄	semidirect
258. C₂×C₃²	#832	direct (N × H)
259. C₂×C₃²	C₃×#102	semidirect
269. C₂×D₄	C₃²×Dic₃	semidirect
313. C₃²	C₂×#832	direct (N × H)
314. C₃²	C₂×C₃×#102	semidirect
322. D₄	C₂×C₃²×Dic₃	semidirect
337. C₂×C₃	C₃×#832	direct (N × H)
338. C₂×C₃	C₃²×#102	semidirect
358. C₃	C₂×C₃×#832	direct (N × H)
359. C₃	C₂×C₃²×#102	semidirect
361. C₂	C₃²×#832	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×C₃³×D₄	2
C₂×C₃²×C₄⋊Dic₃	2
C₂²×C₃²×C₃⋊C₈	2
C₃²×#832	2
C₂×C₃²×#102	3
C₂×C₃×#832	3

Subgroups — C2×C32×#832 #13162651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#832 #13162651