Subgroups — C₂²×C₃²×(C₂×D₃)⋊C₄ #13179164

Order 1728.

4988 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂⁴×C₃²	C₂×D₃
commutator	C₂×C₃	C₂³×C₃²×C₄
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂³×C₃³×C₄	C₂
socle	C₂⁴×C₃³	C₂²
prime radical	C₂⁴×C₃²×D₃	C₂
cosocle	C₂²×C₃	C₂⁴×C₃²
hypercenter	C₂³×C₃²×C₄	D₃
hypocenter	C₃	C₂²×C₃²×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃² ◁ C₂³×C₃²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃³×C₄	C₂	semidirect
3. C₂³×C₃²×Dic₃	C₂	semidirect
4. C₂×C₃²×(C₂×D₃)⋊C₄	C₂	direct (N × H)
6. C₂²×C₃×(C₂×D₃)⋊C₄	C₃	direct (N × H)
10. C₂³×C₃²×D₃	C₄	semidirect
13. C₂²×C₃³×C₄	C₂²	semidirect
15. C₂²×C₃²×Dic₃	C₂²	semidirect
16. C₃²×(C₂×D₃)⋊C₄	C₂²	direct (N × H)
21. C₂³×C₃²×C₄	D₃	semidirect
22. C₂³×C₃²×C₄	C₂×C₃	semidirect
23. C₂³×C₃×Dic₃	C₂×C₃	semidirect
25. C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	direct (N × H)
33. C₂²×C₃²×D₃	C₂×C₄	semidirect
36. C₂×C₃³×C₄	C₂³	semidirect
38. C₂×C₃²×Dic₃	C₂³	semidirect
40. C₂²×(C₂×D₃)⋊C₄	C₃²	direct (N × H)
50. C₂³×C₃×D₃	C₃×C₄	semidirect
58. C₂²×C₃²×C₄	C₂×D₃	semidirect
59. C₂²×C₃²×C₄	C₂²×C₃	semidirect
61. C₂²×C₃×Dic₃	C₂²×C₃	semidirect
63. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	direct (N × H)
64. C₂²×C₃³	C₂²⋊C₄	semidirect
72. C₂×C₃²×D₃	C₂²×C₄	semidirect
79. C₂³×C₃×C₄	C₃×D₃	semidirect
80. C₂³×C₃×C₄	C₂×C₃²	semidirect
81. C₂³×Dic₃	C₂×C₃²	semidirect
83. C₂×(C₂×D₃)⋊C₄	C₂×C₃²	direct (N × H)
104. C₂²×C₃×D₃	C₂×C₃×C₄	semidirect
112. C₂×C₃²×C₄	C₂²×D₃	semidirect
113. C₂×C₃²×C₄	C₂³×C₃	semidirect
115. C₂×C₃×Dic₃	C₂³×C₃	semidirect
117. C₂×C₃³	C₂×C₂²⋊C₄	semidirect
131. C₂³×D₃	C₃²×C₄	semidirect
139. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
140. C₂²×C₃×C₄	C₂²×C₃²	semidirect
142. C₂²×Dic₃	C₂²×C₃²	semidirect
144. (C₂×D₃)⋊C₄	C₂²×C₃²	direct (N × H)
154. C₂²×C₃²	(C₂×D₃)⋊C₄	direct (N × H)
155. C₂²×C₃²	C₃×C₂²⋊C₄	semidirect
167. C₂×C₃×D₃	C₂²×C₃×C₄	semidirect
175. C₂³×C₄	C₃²×D₃	semidirect
177. C₃³	C₂²×C₂²⋊C₄	semidirect
198. C₂²×D₃	C₂×C₃²×C₄	semidirect
206. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
207. C₂×C₃×C₄	C₂³×C₃²	semidirect
209. C₂×Dic₃	C₂³×C₃²	semidirect
215. C₂×C₃²	C₂×(C₂×D₃)⋊C₄	direct (N × H)
216. C₂×C₃²	C₂×C₃×C₂²⋊C₄	semidirect
232. C₂²×C₄	C₂×C₃²×D₃	semidirect
243. C₂²×C₃	C₃×(C₂×D₃)⋊C₄	direct (N × H)
244. C₂²×C₃	C₃²×C₂²⋊C₄	semidirect
256. C₂×D₃	C₂²×C₃²×C₄	semidirect
263. C₃²	C₂²×(C₂×D₃)⋊C₄	direct (N × H)
264. C₃²	C₂²×C₃×C₂²⋊C₄	semidirect
277. C₂×C₄	C₂²×C₃²×D₃	semidirect
283. C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	direct (N × H)
284. C₂×C₃	C₂×C₃²×C₂²⋊C₄	semidirect
296. C₂²	C₃²×(C₂×D₃)⋊C₄	direct (N × H)
304. C₃	C₂²×C₃×(C₂×D₃)⋊C₄	direct (N × H)
305. C₃	C₂²×C₃²×C₂²⋊C₄	semidirect
307. C₂	C₂×C₃²×(C₂×D₃)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²×D₃	2
C₂³×C₃³×C₄	2
C₂³×C₃²×Dic₃	2
C₂×C₃²×(C₂×D₃)⋊C₄	2
C₂²×C₃²×C₂²⋊C₄	3
C₂²×C₃×(C₂×D₃)⋊C₄	3

Subgroups — C22×C32×(C2×D3)⋊C4 #13179164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×(C₂×D₃)⋊C₄ #13179164