Subgroups — C₂²×C₃×#3802 #13181539

Order 1728.

6210 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	C₂³×C₃×D₃²	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×D₁₂	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃×#625	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#3802	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃×D₃×D₄	—	3	2	no	maximal
7	C₂²×#3802	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
9	C₂³×C₃²×D₃	C₂²	1	4	yes	complemented
10	C₂²×C₃×D₃²	—	2	16	no	—
11	C₂²×C₃×D₃²	C₂²	1	24	yes	complemented
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	12	yes	complemented
15	C₂×C₃²×D₁₂	C₂²	1	24	yes	complemented
16	C₂×C₃×#625	C₂²	1	24	yes	complemented
17	C₃×#3802	C₂²	1	64	yes	direct product factor
18	C₂⁴×C₃×D₃	—	3	4	no	—
19	C₂³×D₃²	C₂×C₃	1	2	yes	complemented
20	C₂²×C₃²×D₄	—	3	2	no	—
21	C₂²×C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂²×C₃×#67	—	3	4	no	—
23	C₂×C₃×D₃×D₄	—	3	48	no	—
24	C₂²×C₃×D₁₂	—	2	2	no	—
25	C₂²×C₃×D₁₂	D₃	1	2	yes	complemented
26	C₂²×C₃×D₁₂	C₂×C₃	1	2	yes	complemented
27	C₂²×C₃×C₄×D₃	—	3	2	no	—
28	C₂²×C₃×C₄×D₃	—	6	1	no	—
29	C₂²×#625	C₂×C₃	1	2	yes	complemented
30	C₂×#3802	C₂×C₃	1	24	yes	direct product factor
31	C₂³×C₃³	C₂³	1	1	yes	characteristic
32	C₂²×C₃×C₃⋊D₃	D₄	1	8	yes	complemented
33	C₂²×C₃×C₃⋊D₃	C₂³	1	6	yes	—
34	C₂²×C₃²×D₃	—	2	16	no	—
35	C₂²×C₃²×D₃	C₂³	1	24	yes	complemented
36	C₂×C₃×D₃²	—	2	96	no	—
37	C₂×C₃×D₃²	C₂³	1	32	yes	complemented
38	C₂×C₃³×C₄	C₂³	1	6	yes	complemented
39	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	complemented
40	C₃×C₄×C₃⋊D₃	C₂³	1	16	yes	complemented
41	C₃²×D₁₂	C₂³	1	32	yes	complemented
42	C₃×#625	C₂³	1	32	yes	complemented
43	C₂³×C₃×D₄	—	9	1	no	—
44	C₂²×D₃×D₄	—	3	2	no	—
45	C₂⁴×C₃²	—	3	4	no	—
46	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
47	C₂³×C₃×D₃	—	2	4	no	—
48	C₂³×C₃×D₃	—	3	2	no	—
49	C₂³×C₃×D₃	—	3	48	no	—
50	C₂³×C₃×D₃	—	6	32	no	—
51	C₂³×C₃×D₃	—	6	1	no	—
52	C₂³×C₃×D₃	C₂×D₃	1	4	yes	complemented
53	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	complemented
54	C₂²×D₃²	—	2	16	no	—
55	C₂²×D₃²	C₂²×C₃	1	24	yes	complemented
56	C₂×C₃²×D₄	—	3	24	no	—
57	C₂²×C₃²×C₄	—	2	1	no	—
58	C₂²×C₃²×C₄	—	2	2	no	—
59	C₂²×C₃²×C₄	—	4	1	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	complemented
61	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
62	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
63	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	12	yes	complemented
64	C₂×C₃×#67	—	3	48	no	—
65	C₂²×C₃×Dic₃	—	3	2	no	—
66	C₂²×C₃×Dic₃	—	6	1	no	—
67	C₃×D₃×D₄	—	3	128	no	—
68	C₂×C₃×D₁₂	—	2	24	no	—
69	C₂×C₃×D₁₂	C₂×D₃	1	24	yes	complemented
70	C₂×C₃×D₁₂	C₂²×C₃	1	24	yes	complemented
71	C₂×C₃×C₄×D₃	—	3	24	no	—
72	C₂×C₃×C₄×D₃	—	6	12	no	—
73	C₂×#625	C₂²×C₃	1	24	yes	complemented
74	#3802	C₂²×C₃	1	64	yes	direct product factor
75	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
76	C₂²×C₃³	C₂⁴	1	3	yes	—
77	C₂×C₃×C₃⋊D₃	C₂×D₄	1	24	yes	complemented
78	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
79	C₂×C₃²×D₃	—	2	48	no	—
80	C₂×C₃²×D₃	C₂⁴	1	16	yes	complemented
81	C₃×D₃²	—	2	64	no	—
82	C₃³×C₄	C₂⁴	1	4	yes	complemented
83	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	complemented
84	C₂⁵×C₃	—	9	2	no	—
85	C₂⁴×D₃	—	3	4	no	—
86	C₂²×C₃×D₄	—	3	2	no	—
87	C₂²×C₃×D₄	—	3	2	no	—
88	C₂²×C₃×D₄	—	6	2	no	—
89	C₂²×C₃×D₄	—	9	24	no	—
90	C₂²×C₃×D₄	—	9	2	no	—
91	C₂³×C₃×C₄	—	9	1	no	—
92	C₂²×#67	—	3	4	no	—
93	C₂×D₃×D₄	—	3	48	no	—
94	C₂²×D₁₂	C₃×D₃	1	2	yes	complemented
95	C₂²×C₄×D₃	—	3	2	no	—
96	C₂²×C₄×D₃	—	6	1	no	—
97	C₂³×C₃²	—	2	1	no	—
98	C₂³×C₃²	—	2	2	no	—
99	C₂³×C₃²	—	3	24	no	—
100	C₂³×C₃²	—	4	1	no	—
101	C₂³×C₃²	—	6	16	no	—
102	C₂³×C₃²	C₂²×D₃	1	2	yes	—
103	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
104	C₂²×C₃⋊D₃	C₃×D₄	1	8	yes	complemented
105	C₂²×C₃⋊D₃	C₂³×C₃	1	6	yes	—
106	C₂²×C₃×D₃	—	2	16	no	—
107	C₂²×C₃×D₃	—	2	16	no	—
108	C₂²×C₃×D₃	—	2	24	no	—
109	C₂²×C₃×D₃	—	3	16	no	—
110	C₂²×C₃×D₃	—	3	12	no	—
111	C₂²×C₃×D₃	—	3	64	no	—
112	C₂²×C₃×D₃	—	4	16	no	—
113	C₂²×C₃×D₃	—	6	8	no	—
114	C₂²×C₃×D₃	—	6	6	no	—
115	C₂²×C₃×D₃	—	6	192	no	—
116	C₂²×C₃×D₃	C₂²×D₃	1	24	yes	complemented
117	C₂²×C₃×D₃	C₂³×C₃	1	24	yes	complemented
118	C₂×D₃²	—	2	96	no	—
119	C₂×D₃²	C₂³×C₃	1	32	yes	complemented
120	C₃²×D₄	—	3	32	no	—
121	C₂×C₃²×C₄	—	2	6	no	—
122	C₂×C₃²×C₄	—	2	12	no	—
123	C₂×C₃²×C₄	—	4	6	no	—
124	C₂×C₃²×C₄	C₂²×D₃	1	12	yes	complemented
125	C₂×C₃²×C₄	C₂³×C₃	1	6	yes	complemented
126	C₂×C₃⋊Dic₃	C₂³×C₃	1	6	yes	complemented
127	C₄×C₃⋊D₃	C₂³×C₃	1	16	yes	complemented
128	C₃×#67	—	3	64	no	—
129	C₂×C₃×Dic₃	—	3	12	no	—
130	C₂×C₃×Dic₃	—	6	6	no	—
131	C₃×D₁₂	—	2	32	no	—
132	C₃×D₁₂	C₂²×D₃	1	32	yes	complemented
133	C₃×D₁₂	C₂³×C₃	1	32	yes	complemented
134	C₃×C₄×D₃	—	3	32	no	—
135	C₃×C₄×D₃	—	6	16	no	—
136	#625	C₂³×C₃	1	32	yes	complemented
137	C₂³×D₄	—	9	1	no	Sylow
138	C₂×C₃³	C₂²×D₄	1	6	yes	complemented
139	C₂×C₃³	C₂⁵	1	1	yes	characteristic
140	C₃×C₃⋊D₃	C₂²×D₄	1	8	yes	complemented
141	C₃²×D₃	—	2	16	no	—
142	C₂⁴×C₃	—	3	4	no	—
143	C₂⁴×C₃	—	3	4	no	—
144	C₂⁴×C₃	—	6	4	no	—
145	C₂⁴×C₃	—	9	24	no	—
146	C₂⁴×C₃	—	9	1	no	—
147	C₂⁴×C₃	—	18	16	no	—
148	C₂³×D₃	—	3	2	no	—
149	C₂³×D₃	—	3	48	no	—
150	C₂³×D₃	—	6	1	no	—
151	C₂³×D₃	—	6	32	no	—
152	C₂³×D₃	C₂×C₃×D₃	1	4	yes	complemented
153	C₂×C₃×D₄	—	3	24	no	—
154	C₂×C₃×D₄	—	3	24	no	—
155	C₂×C₃×D₄	—	6	24	no	—
156	C₂×C₃×D₄	—	9	64	no	—
157	C₂×C₃×D₄	—	9	24	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	—	4	1	no	—
161	C₂²×C₃×C₄	—	9	1	no	—
162	C₂²×C₃×C₄	—	9	12	no	—
163	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic, complemented
164	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	complemented
165	C₂×#67	—	3	48	no	—
166	C₂²×Dic₃	—	3	2	no	—
167	C₂²×Dic₃	—	6	1	no	—
168	D₃×D₄	—	3	128	no	—
169	C₂×D₁₂	C₂×C₃×D₃	1	24	yes	complemented
170	C₂×C₄×D₃	—	3	24	no	—
171	C₂×C₄×D₃	—	6	12	no	—
172	C₂²×C₃²	—	2	3	no	—
173	C₂²×C₃²	—	2	6	no	—
174	C₂²×C₃²	—	2	4	no	—
175	C₂²×C₃²	—	2	8	no	—
176	C₂²×C₃²	—	3	16	no	—
177	C₂²×C₃²	—	4	4	no	—
178	C₂²×C₃²	—	4	3	no	—
179	C₂²×C₃²	—	6	48	no	—
180	C₂²×C₃²	D₃×D₄	1	8	yes	complemented
181	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	complemented
182	C₂²×C₃²	C₂³×D₃	1	6	yes	—
183	C₂²×C₃²	C₂⁴×C₃	1	3	yes	—
184	C₂×C₃⋊D₃	C₂×C₃×D₄	1	24	yes	complemented
185	C₂×C₃⋊D₃	C₂⁴×C₃	1	4	yes	—
186	C₂×C₃×D₃	—	2	48	no	—
187	C₂×C₃×D₃	—	2	48	no	—
188	C₂×C₃×D₃	—	2	16	no	—
189	C₂×C₃×D₃	—	3	48	no	—
190	C₂×C₃×D₃	—	3	8	no	—
191	C₂×C₃×D₃	—	4	48	no	—
192	C₂×C₃×D₃	—	6	24	no	—
193	C₂×C₃×D₃	—	6	4	no	—
194	C₂×C₃×D₃	—	6	128	no	—
195	C₂×C₃×D₃	C₂³×D₃	1	16	yes	complemented
196	C₂×C₃×D₃	C₂⁴×C₃	1	16	yes	complemented
197	D₃²	—	2	64	no	—
198	C₃²×C₄	—	2	4	no	—
199	C₃²×C₄	—	2	8	no	—
200	C₃²×C₄	—	4	4	no	—
201	C₃²×C₄	C₂³×D₃	1	8	yes	complemented
202	C₃²×C₄	C₂⁴×C₃	1	4	yes	complemented
203	C₃⋊Dic₃	C₂⁴×C₃	1	4	yes	complemented
204	C₃×Dic₃	—	3	8	no	—
205	C₃×Dic₃	—	6	4	no	—
206	C₂⁵	—	9	2	no	—
207	C₂²×D₄	—	3	2	no	—
208	C₂²×D₄	—	9	24	no	—
209	C₂²×D₄	—	9	2	no	—
210	C₂³×C₄	—	9	1	no	—
211	C₃³	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₃	—	2	2	no	—
213	C₂³×C₃	—	2	1	no	—
214	C₂³×C₃	—	3	24	no	—
215	C₂³×C₃	—	3	24	no	—
216	C₂³×C₃	—	4	1	no	—
217	C₂³×C₃	—	6	24	no	—
218	C₂³×C₃	—	6	16	no	—
219	C₂³×C₃	—	6	16	no	—
220	C₂³×C₃	—	9	32	no	—
221	C₂³×C₃	—	9	6	no	—
222	C₂³×C₃	—	9	8	no	—
223	C₂³×C₃	—	12	16	no	—
224	C₂³×C₃	—	18	96	no	—
225	C₂³×C₃	C₂×D₃²	1	1	yes	characteristic
226	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
227	C₂²×D₃	—	2	16	no	—
228	C₂²×D₃	—	3	12	no	—
229	C₂²×D₃	—	3	16	no	—
230	C₂²×D₃	—	3	64	no	—
231	C₂²×D₃	—	6	8	no	—
232	C₂²×D₃	—	6	6	no	—
233	C₂²×D₃	—	6	192	no	—
234	C₂²×D₃	C₂²×C₃×D₃	1	24	yes	complemented
235	C₃×D₄	—	3	32	no	—
236	C₃×D₄	—	3	32	no	—
237	C₃×D₄	—	6	32	no	—
238	C₃×D₄	—	9	32	no	—
239	C₂×C₃×C₄	—	2	12	no	—
240	C₂×C₃×C₄	—	2	6	no	—
241	C₂×C₃×C₄	—	4	6	no	—
242	C₂×C₃×C₄	—	9	6	no	—
243	C₂×C₃×C₄	—	9	16	no	—
244	C₂×C₃×C₄	C₂×D₃²	1	6	yes	complemented
245	C₂×C₃×C₄	C₂²×C₃×D₃	1	12	yes	complemented
246	#67	—	3	64	no	—
247	C₂×Dic₃	—	3	12	no	—
248	C₂×Dic₃	—	6	6	no	—
249	D₁₂	C₂²×C₃×D₃	1	32	yes	complemented
250	C₄×D₃	—	3	32	no	—
251	C₄×D₃	—	6	16	no	—
252	C₂×C₃²	—	2	6	no	—
253	C₂×C₃²	—	2	12	no	—
254	C₂×C₃²	—	2	1	no	—
255	C₂×C₃²	—	2	2	no	—
256	C₂×C₃²	—	4	6	no	—
257	C₂×C₃²	—	4	1	no	—
258	C₂×C₃²	—	6	16	no	—
259	C₂×C₃²	C₂×D₃×D₄	1	12	yes	complemented
260	C₂×C₃²	C₂²×C₃×D₄	1	6	yes	complemented
261	C₂×C₃²	C₂⁴×D₃	1	2	yes	—
262	C₂×C₃²	C₂⁵×C₃	1	1	yes	characteristic
263	C₃⋊D₃	C₂²×C₃×D₄	1	8	yes	complemented
264	C₃×D₃	—	2	16	no	—
265	C₃×D₃	—	2	16	no	—
266	C₃×D₃	—	3	16	no	—
267	C₃×D₃	—	4	16	no	—
268	C₃×D₃	—	6	8	no	—
269	C₂⁴	—	3	4	no	—
270	C₂⁴	—	9	24	no	—
271	C₂⁴	—	9	1	no	—
272	C₂⁴	—	18	16	no	—
273	C₂×D₄	—	3	24	no	—
274	C₂×D₄	—	9	64	no	—
275	C₂×D₄	—	9	24	no	—
276	C₂²×C₄	—	9	1	no	—
277	C₂²×C₄	—	9	12	no	—
278	C₂²×C₄	C₃×D₃²	1	1	yes	characteristic, complemented
279	C₂²×C₃	—	2	3	no	—
280	C₂²×C₃	—	2	6	no	—
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	—	2	8	no	—
283	C₂²×C₃	—	3	16	no	—
284	C₂²×C₃	—	3	16	no	—
285	C₂²×C₃	—	4	3	no	—
286	C₂²×C₃	—	4	4	no	—
287	C₂²×C₃	—	6	16	no	—
288	C₂²×C₃	—	6	48	no	—
289	C₂²×C₃	—	6	48	no	—
290	C₂²×C₃	—	9	24	no	—
291	C₂²×C₃	—	9	4	no	—
292	C₂²×C₃	—	12	48	no	—
293	C₂²×C₃	—	18	64	no	—
294	C₂²×C₃	#3802	1	4	yes	direct product factor
295	C₂²×C₃	C₃×D₃×D₄	1	8	yes	complemented
296	C₂²×C₃	C₂²×D₃²	1	3	yes	—
297	C₂²×C₃	C₂³×C₃×D₃	1	6	yes	—
298	C₂×D₃	—	2	48	no	—
299	C₂×D₃	—	3	48	no	—
300	C₂×D₃	—	3	8	no	—
301	C₂×D₃	—	6	4	no	—
302	C₂×D₃	—	6	24	no	—
303	C₂×D₃	—	6	128	no	—
304	C₂×D₃	C₂³×C₃×D₃	1	16	yes	complemented
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	2	8	no	—
307	C₃×C₄	—	4	4	no	—
308	C₃×C₄	—	9	4	no	—
309	C₃×C₄	C₂²×D₃²	1	4	yes	complemented
310	C₃×C₄	C₂³×C₃×D₃	1	8	yes	complemented
311	Dic₃	—	3	8	no	—
312	Dic₃	—	6	4	no	—
313	C₃²	—	2	1	no	—
314	C₃²	—	2	2	no	—
315	C₃²	—	4	1	no	—
316	C₃²	C₂²×D₃×D₄	1	2	yes	complemented
317	C₃²	C₂³×C₃×D₄	1	1	yes	characteristic, complemented
318	C₂³	—	3	24	no	—
319	C₂³	—	6	16	no	—
320	C₂³	—	9	32	no	—
321	C₂³	—	9	6	no	—
322	C₂³	—	9	8	no	—
323	C₂³	—	18	96	no	—
324	C₂³	C₂×C₃×D₃²	1	1	yes	characteristic
325	D₄	—	3	32	no	—
326	D₄	—	9	32	no	—
327	C₂×C₄	—	9	6	no	—
328	C₂×C₄	—	9	16	no	—
329	C₂×C₄	C₂×C₃×D₃²	1	6	yes	complemented
330	C₂×C₃	—	2	1	no	—
331	C₂×C₃	—	2	2	no	—
332	C₂×C₃	—	2	6	no	—
333	C₂×C₃	—	2	12	no	—
334	C₂×C₃	—	4	1	no	—
335	C₂×C₃	—	4	6	no	—
336	C₂×C₃	—	6	16	no	—
337	C₂×C₃	—	6	16	no	—
338	C₂×C₃	—	9	8	no	—
339	C₂×C₃	—	12	16	no	—
340	C₂×C₃	C₂×#3802	1	6	yes	direct product factor
341	C₂×C₃	C₂×C₃×D₃×D₄	1	12	yes	complemented
342	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
343	C₂×C₃	C₂⁴×C₃×D₃	1	2	yes	—
344	D₃	—	2	16	no	—
345	D₃	—	3	16	no	—
346	D₃	—	6	8	no	—
347	C₂²	—	3	16	no	—
348	C₂²	—	6	48	no	—
349	C₂²	—	9	4	no	—
350	C₂²	—	9	24	no	—
351	C₂²	—	18	64	no	—
352	C₂²	C₃×#3802	1	4	yes	direct product factor
353	C₂²	C₂²×C₃×D₃²	1	3	yes	—
354	C₄	—	9	4	no	—
355	C₄	C₂²×C₃×D₃²	1	4	yes	complemented
356	C₃	—	2	1	no	—
357	C₃	—	2	2	no	—
358	C₃	—	4	1	no	—
359	C₃	C₂²×#3802	1	1	yes	characteristic, direct product factor
360	C₃	C₂²×C₃×D₃×D₄	1	2	yes	complemented
361	C₂	—	6	16	no	—
362	C₂	—	9	8	no	—
363	C₂	C₂×C₃×#3802	1	6	yes	direct product factor
364	C₂	C₂³×C₃×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₃²
commutator, cosocle	C₂×C₃²	C₂⁵×C₃
Frattini	C₂	C₂³×C₃×D₃²
Fitting	C₂²×C₃³×C₄	C₂²
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₃×C₄	D₃²
hypocenter	C₃²	C₂³×C₃×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×D₃²	C₂	semidirect
2. C₂²×C₃×C₄×C₃⋊D₃	C₂	semidirect
3. C₂²×C₃²×D₁₂	C₂	semidirect
4. C₂²×C₃×#625	C₂	semidirect
5. C₂×C₃×#3802	C₂	direct (N × H)
7. C₂²×#3802	C₃	direct (N × H)
9. C₂³×C₃²×D₃	C₂²	semidirect
11. C₂²×C₃×D₃²	C₂²	semidirect
12. C₂²×C₃³×C₄	C₂²	semidirect
13. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
14. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
15. C₂×C₃²×D₁₂	C₂²	semidirect
16. C₂×C₃×#625	C₂²	semidirect
17. C₃×#3802	C₂²	direct (N × H)
19. C₂³×D₃²	C₂×C₃	semidirect
21. C₂²×C₄×C₃⋊D₃	C₂×C₃	semidirect
25. C₂²×C₃×D₁₂	D₃	semidirect
26. C₂²×C₃×D₁₂	C₂×C₃	semidirect
29. C₂²×#625	C₂×C₃	semidirect
30. C₂×#3802	C₂×C₃	direct (N × H)
32. C₂²×C₃×C₃⋊D₃	D₄	semidirect
35. C₂²×C₃²×D₃	C₂³	semidirect
37. C₂×C₃×D₃²	C₂³	semidirect
38. C₂×C₃³×C₄	C₂³	semidirect
39. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
40. C₃×C₄×C₃⋊D₃	C₂³	semidirect
41. C₃²×D₁₂	C₂³	semidirect
42. C₃×#625	C₂³	semidirect
52. C₂³×C₃×D₃	C₂×D₃	semidirect
53. C₂³×C₃×D₃	C₂²×C₃	semidirect
55. C₂²×D₃²	C₂²×C₃	semidirect
60. C₂²×C₃²×C₄	C₂×D₃	semidirect
61. C₂²×C₃²×C₄	C₂²×C₃	semidirect
62. C₂²×C₃⋊Dic₃	C₂²×C₃	semidirect
63. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
69. C₂×C₃×D₁₂	C₂×D₃	semidirect
70. C₂×C₃×D₁₂	C₂²×C₃	semidirect
73. C₂×#625	C₂²×C₃	semidirect
74. #3802	C₂²×C₃	direct (N × H)
75. C₂²×C₃³	C₂×D₄	semidirect
77. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
80. C₂×C₃²×D₃	C₂⁴	semidirect
82. C₃³×C₄	C₂⁴	semidirect
83. C₃×C₃⋊Dic₃	C₂⁴	semidirect
94. C₂²×D₁₂	C₃×D₃	semidirect
104. C₂²×C₃⋊D₃	C₃×D₄	semidirect
116. C₂²×C₃×D₃	C₂²×D₃	semidirect
117. C₂²×C₃×D₃	C₂³×C₃	semidirect
119. C₂×D₃²	C₂³×C₃	semidirect
124. C₂×C₃²×C₄	C₂²×D₃	semidirect
125. C₂×C₃²×C₄	C₂³×C₃	semidirect
126. C₂×C₃⋊Dic₃	C₂³×C₃	semidirect
127. C₄×C₃⋊D₃	C₂³×C₃	semidirect
132. C₃×D₁₂	C₂²×D₃	semidirect
133. C₃×D₁₂	C₂³×C₃	semidirect
136. #625	C₂³×C₃	semidirect
138. C₂×C₃³	C₂²×D₄	semidirect
140. C₃×C₃⋊D₃	C₂²×D₄	semidirect
152. C₂³×D₃	C₂×C₃×D₃	semidirect
163. C₂²×C₃×C₄	D₃²	semidirect
164. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
169. C₂×D₁₂	C₂×C₃×D₃	semidirect
180. C₂²×C₃²	D₃×D₄	semidirect
181. C₂²×C₃²	C₂×C₃×D₄	semidirect
184. C₂×C₃⋊D₃	C₂×C₃×D₄	semidirect
195. C₂×C₃×D₃	C₂³×D₃	semidirect
196. C₂×C₃×D₃	C₂⁴×C₃	semidirect
201. C₃²×C₄	C₂³×D₃	semidirect
202. C₃²×C₄	C₂⁴×C₃	semidirect
203. C₃⋊Dic₃	C₂⁴×C₃	semidirect
211. C₃³	C₂³×D₄	semidirect
234. C₂²×D₃	C₂²×C₃×D₃	semidirect
244. C₂×C₃×C₄	C₂×D₃²	semidirect
245. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
249. D₁₂	C₂²×C₃×D₃	semidirect
259. C₂×C₃²	C₂×D₃×D₄	semidirect
260. C₂×C₃²	C₂²×C₃×D₄	semidirect
263. C₃⋊D₃	C₂²×C₃×D₄	semidirect
278. C₂²×C₄	C₃×D₃²	semidirect
294. C₂²×C₃	#3802	direct (N × H)
295. C₂²×C₃	C₃×D₃×D₄	semidirect
304. C₂×D₃	C₂³×C₃×D₃	semidirect
309. C₃×C₄	C₂²×D₃²	semidirect
310. C₃×C₄	C₂³×C₃×D₃	semidirect
316. C₃²	C₂²×D₃×D₄	semidirect
317. C₃²	C₂³×C₃×D₄	semidirect
329. C₂×C₄	C₂×C₃×D₃²	semidirect
340. C₂×C₃	C₂×#3802	direct (N × H)
341. C₂×C₃	C₂×C₃×D₃×D₄	semidirect
352. C₂²	C₃×#3802	direct (N × H)
355. C₄	C₂²×C₃×D₃²	semidirect
359. C₃	C₂²×#3802	direct (N × H)
360. C₃	C₂²×C₃×D₃×D₄	semidirect
363. C₂	C₂×C₃×#3802	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×D₃²	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₂²×C₃²×D₁₂	2
C₂²×C₃×#625	2
C₂×C₃×#3802	2
C₂²×C₃×D₃×D₄	3
C₂²×#3802	3

Subgroups — C22×C3×#3802 #13181539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#3802 #13181539