Subgroups — C₄×D₄×C₃⋊(C₃⋊D₃) #13179671

Order 1728.

5964 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
3	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₃⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6312	C₂	1	2	yes	maximal, complemented
6	#11723934	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
8	#11723922	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₄×C₃⋊D₃	—	3	13	no	maximal
13	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	2	yes	complemented
16	C₂×#6312	C₂²	1	2	yes	—
17	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
18	D₄×C₃⋊(C₃⋊D₃)	C₄	1	8	yes	direct product factor
19	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	8	no	—
21	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
22	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
26	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
27	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃³×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
30	#88864	C₂²	1	2	yes	complemented
31	#88859	C₂²	1	2	yes	complemented
32	#88859	C₂²	1	2	yes	complemented
33	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
34	#88857	C₂²	1	2	yes	complemented
35	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×C₃⋊D₃	—	3	13	no	—
39	C₂²×C₄×C₃⋊D₃	—	3	26	no	—
40	C₃²×C₄×D₄	D₃	1	13	yes	complemented
41	D₄×C₃⋊Dic₃	—	3	13	no	—
42	C₄×#638	—	3	26	no	—
43	#64102	—	3	13	no	—
44	C₄⋊C₄×C₃⋊D₃	—	3	13	no	—
45	#64090	—	3	26	no	—
46	C₂²⋊C₄×C₃⋊D₃	—	3	26	no	—
47	C₄×C₄⋊(C₃⋊D₃)	—	3	13	no	—
48	C₄²×C₃⋊D₃	—	3	13	no	—
49	C₂³×C₃³	C₂³	1	2	yes	—
50	C₂²×C₃⋊(C₃⋊D₃)	—	2	4	no	—
51	C₂²×C₃⋊(C₃⋊D₃)	—	2	4	no	—
52	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	8	yes	complemented
53	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
54	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
55	C₃³×D₄	C₂×C₄	1	4	yes	complemented
56	C₂×C₃³×C₄	—	2	4	no	—
57	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
58	C₂×C₃³×C₄	C₂³	1	2	yes	—
59	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
60	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
61	#6312	C₂×C₄	1	8	yes	complemented
62	C₂×C₃⋊(C₃⋊Dic₃)	—	2	4	no	—
63	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
64	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
65	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
66	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₃⋊(C₃⋊D₃))	C₂×C₄	1	4	yes	complemented
68	C₄×C₃⋊(C₃⋊D₃)	—	2	4	no	—
69	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
70	C₄×C₃⋊(C₃⋊D₃)	—	2	4	no	—
71	C₄×C₃⋊(C₃⋊D₃)	—	2	4	no	—
72	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
73	C₄×C₃⋊(C₃⋊D₃)	D₄	1	4	yes	direct product factor
74	C₄×D₃×D₄	—	9	13	no	—
75	C₂³×C₃⋊D₃	—	3	26	no	—
76	C₂×C₃²×D₄	C₂×D₃	1	13	yes	—
77	C₂²×C₃²×C₄	C₂×D₃	1	26	yes	complemented
78	C₂×#638	—	3	26	no	—
79	C₂²×C₃⋊Dic₃	—	3	26	no	—
80	D₄×C₃⋊D₃	—	3	104	no	—
81	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
82	C₂×C₄×C₃⋊D₃	—	3	13	no	—
83	C₂×C₄×C₃⋊D₃	—	3	13	no	—
84	C₂×C₄×C₃⋊D₃	—	3	13	no	—
85	C₂×C₄×C₃⋊D₃	—	3	26	no	—
86	C₂×C₄×C₃⋊D₃	—	3	26	no	—
87	C₂×C₄×C₃⋊D₃	—	3	26	no	—
88	C₂×C₄×C₃⋊D₃	—	6	104	no	—
89	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
90	C₃²×C₂²⋊C₄	C₂×D₃	1	26	yes	complemented
91	C₃²×C₄²	C₂×D₃	1	13	yes	complemented
92	#3757	—	3	26	no	—
93	#3752	—	3	26	no	—
94	#3752	—	3	26	no	—
95	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
96	#3750	—	3	26	no	—
97	C₄×C₃⋊Dic₃	—	3	13	no	—
98	C₄×C₃⋊Dic₃	—	3	13	no	—
99	C₄×C₃⋊Dic₃	—	3	13	no	—
100	C₂²×C₃³	—	2	2	no	—
101	C₂²×C₃³	—	2	2	no	—
102	C₂²×C₃³	C₂²×C₄	1	4	yes	complemented
103	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
104	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
105	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
106	C₂×C₃⋊(C₃⋊D₃)	—	2	16	no	—
107	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	2	yes	—
108	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	4	yes	complemented
109	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	2	yes	—
110	C₂×C₃⋊(C₃⋊D₃)	#41	1	2	yes	—
111	C₃³×C₄	—	2	2	no	—
112	C₃³×C₄	—	2	1	no	—
113	C₃³×C₄	C₂²×C₄	1	2	yes	complemented
114	C₃³×C₄	C₂×D₄	1	2	yes	complemented
115	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
116	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
117	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	2	yes	complemented
118	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	2	yes	complemented
119	C₂×D₃×D₄	—	9	13	no	—
120	C₂²×C₄×D₃	—	9	26	no	—
121	C₃×C₄×D₄	C₃⋊D₃	1	13	yes	complemented
122	D₄×Dic₃	—	9	13	no	—
123	C₄×#67	—	9	26	no	—
124	#893	—	9	13	no	—
125	D₃×C₄⋊C₄	—	9	13	no	—
126	#67⋊C₄	—	9	26	no	—
127	D₃×C₂²⋊C₄	—	9	26	no	—
128	C₄×D₁₂	—	9	13	no	—
129	C₄²×D₃	—	9	13	no	—
130	C₂³×C₃²	C₂²×D₃	1	26	yes	—
131	C₂²×C₃⋊D₃	—	3	13	no	—
132	C₂²×C₃⋊D₃	—	3	104	no	—
133	C₂²×C₃⋊D₃	—	3	26	no	—
134	C₂²×C₃⋊D₃	—	6	52	no	—
135	C₂²×C₃⋊D₃	—	6	52	no	—
136	C₃²×D₄	C₄×D₃	1	52	yes	complemented
137	C₂×C₃²×C₄	—	2	52	no	—
138	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
139	C₂×C₃²×C₄	C₂²×D₃	1	26	yes	—
140	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
141	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
142	#638	—	3	104	no	—
143	C₂×C₃⋊Dic₃	—	3	13	no	—
144	C₂×C₃⋊Dic₃	—	3	13	no	—
145	C₂×C₃⋊Dic₃	—	3	13	no	—
146	C₂×C₃⋊Dic₃	—	3	26	no	—
147	C₂×C₃⋊Dic₃	—	6	52	no	—
148	C₄⋊(C₃⋊D₃)	—	3	52	no	—
149	C₄×C₃⋊D₃	—	3	52	no	—
150	C₄×C₃⋊D₃	—	3	52	no	—
151	C₄×C₃⋊D₃	—	6	52	no	—
152	C₄×C₃⋊D₃	—	6	26	no	—
153	C₄×C₃⋊D₃	—	6	52	no	—
154	C₄×C₃⋊D₃	—	6	52	no	—
155	C₂×C₄×D₄	—	27	1	no	Sylow
156	C₂×C₃³	—	2	4	no	—
157	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₃³	C₂×#41	1	1	yes	characteristic
160	C₃⋊(C₃⋊D₃)	—	2	4	no	—
161	C₃⋊(C₃⋊D₃)	C₄×D₄	1	4	yes	direct product factor
162	C₂³×D₃	—	9	26	no	—
163	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	—
164	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	26	yes	complemented
165	C₂×#67	—	9	26	no	—
166	C₂²×Dic₃	—	9	26	no	—
167	D₃×D₄	—	9	104	no	—
168	C₂×D₁₂	—	9	13	no	—
169	C₂×C₄×D₃	—	9	13	no	—
170	C₂×C₄×D₃	—	9	13	no	—
171	C₂×C₄×D₃	—	9	13	no	—
172	C₂×C₄×D₃	—	9	26	no	—
173	C₂×C₄×D₃	—	9	26	no	—
174	C₂×C₄×D₃	—	9	26	no	—
175	C₂×C₄×D₃	—	18	104	no	—
176	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
177	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	26	yes	complemented
178	C₃×C₄²	C₂×C₃⋊D₃	1	13	yes	complemented
179	#217	—	9	26	no	—
180	(C₂×D₃)⋊C₄	—	9	26	no	—
181	(C₂×D₃)⋊C₄	—	9	26	no	—
182	C₄⋊Dic₃	—	9	13	no	—
183	Dic₃⋊C₄	—	9	26	no	—
184	C₄×Dic₃	—	9	13	no	—
185	C₄×Dic₃	—	9	13	no	—
186	C₄×Dic₃	—	9	13	no	—
187	C₂²×C₃²	—	2	26	no	—
188	C₂²×C₃²	—	2	26	no	—
189	C₂²×C₃²	C₂×C₄×D₃	1	52	yes	complemented
190	C₂²×C₃²	C₂³×D₃	1	13	yes	—
191	C₂×C₃⋊D₃	—	3	26	no	—
192	C₂×C₃⋊D₃	—	3	26	no	—
193	C₂×C₃⋊D₃	—	3	26	no	—
194	C₂×C₃⋊D₃	—	3	52	no	—
195	C₂×C₃⋊D₃	—	6	208	no	—
196	C₂×C₃⋊D₃	—	6	26	no	—
197	C₂×C₃⋊D₃	—	6	26	no	—
198	C₃²×C₄	—	2	26	no	—
199	C₃²×C₄	—	2	13	no	—
200	C₃²×C₄	C₂×C₄×D₃	1	26	yes	complemented
201	C₃²×C₄	D₃×D₄	1	26	yes	complemented
202	C₃⋊Dic₃	—	3	26	no	—
203	C₃⋊Dic₃	—	3	26	no	—
204	C₃⋊Dic₃	—	6	26	no	—
205	C₃⋊Dic₃	—	6	13	no	—
206	C₂²×D₄	—	27	1	no	—
207	C₂³×C₄	—	27	2	no	—
208	C₄×D₄	—	27	1	no	—
209	C₄×D₄	—	27	2	no	—
210	C₄×D₄	—	27	1	no	—
211	C₄×D₄	—	27	2	no	—
212	C₄×D₄	—	27	1	no	—
213	C₄×D₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
214	C₂×C₄⋊C₄	—	27	1	no	—
215	C₂×C₂²⋊C₄	—	27	2	no	—
216	C₂×C₄²	—	27	1	no	—
217	C₃³	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
218	C₂³×C₃	C₂²×C₃⋊D₃	1	26	yes	—
219	C₂²×D₃	—	9	13	no	—
220	C₂²×D₃	—	9	26	no	—
221	C₂²×D₃	—	9	104	no	—
222	C₂²×D₃	—	18	52	no	—
223	C₂²×D₃	—	18	52	no	—
224	C₃×D₄	C₄×C₃⋊D₃	1	52	yes	complemented
225	C₂×C₃×C₄	—	2	52	no	—
226	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
227	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	26	yes	—
228	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
229	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
230	#67	—	9	104	no	—
231	C₂×Dic₃	—	9	13	no	—
232	C₂×Dic₃	—	9	13	no	—
233	C₂×Dic₃	—	9	13	no	—
234	C₂×Dic₃	—	9	26	no	—
235	C₂×Dic₃	—	18	52	no	—
236	D₁₂	—	9	52	no	—
237	C₄×D₃	—	9	52	no	—
238	C₄×D₃	—	9	52	no	—
239	C₄×D₃	—	18	52	no	—
240	C₄×D₃	—	18	26	no	—
241	C₄×D₃	—	18	52	no	—
242	C₄×D₃	—	18	52	no	—
243	C₂×C₃²	—	2	52	no	—
244	C₂×C₃²	C₂²×C₄×D₃	1	13	yes	—
245	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
246	C₂×C₃²	D₃×#41	1	13	yes	—
247	C₃⋊D₃	—	3	52	no	—
248	C₃⋊D₃	—	6	52	no	—
249	C₂⁴	—	27	2	no	—
250	C₂×D₄	—	27	2	no	—
251	C₂×D₄	—	27	8	no	—
252	C₂×D₄	—	27	1	no	—
253	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
254	C₂²×C₄	—	27	1	no	—
255	C₂²×C₄	—	27	1	no	—
256	C₂²×C₄	—	27	2	no	—
257	C₂²×C₄	—	27	1	no	—
258	C₂²×C₄	—	27	2	no	—
259	C₂²×C₄	—	27	2	no	—
260	C₂²×C₄	—	27	2	no	—
261	C₂²×C₄	—	54	8	no	—
262	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
263	C₄⋊C₄	—	27	2	no	—
264	C₄⋊C₄	—	27	1	no	—
265	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
266	C₂²⋊C₄	—	27	2	no	—
267	C₂²⋊C₄	—	27	2	no	—
268	C₂²⋊C₄	—	27	2	no	—
269	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
270	C₄²	—	27	1	no	—
271	C₄²	—	27	1	no	—
272	C₄²	—	27	1	no	—
273	C₄²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
274	C₂²×C₃	—	2	26	no	—
275	C₂²×C₃	—	2	26	no	—
276	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	52	yes	complemented
277	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
278	C₂×D₃	—	9	26	no	—
279	C₂×D₃	—	9	26	no	—
280	C₂×D₃	—	9	26	no	—
281	C₂×D₃	—	9	52	no	—
282	C₂×D₃	—	18	208	no	—
283	C₂×D₃	—	18	26	no	—
284	C₂×D₃	—	18	26	no	—
285	C₃×C₄	—	2	26	no	—
286	C₃×C₄	—	2	13	no	—
287	C₃×C₄	C₂×C₄×C₃⋊D₃	1	26	yes	complemented
288	C₃×C₄	D₄×C₃⋊D₃	1	26	yes	complemented
289	Dic₃	—	9	26	no	—
290	Dic₃	—	9	26	no	—
291	Dic₃	—	18	26	no	—
292	Dic₃	—	18	13	no	—
293	C₃²	C₄×D₃×D₄	1	13	yes	complemented
294	C₂³	—	27	1	no	—
295	C₂³	—	27	2	no	—
296	C₂³	—	27	8	no	—
297	C₂³	—	54	4	no	—
298	C₂³	—	54	4	no	—
299	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
300	D₄	—	27	8	no	—
301	D₄	—	27	4	no	—
302	D₄	C₄×C₃⋊(C₃⋊D₃)	1	4	yes	direct product factor
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	27	1	no	—
305	C₂×C₄	—	27	1	no	—
306	C₂×C₄	—	27	4	no	—
307	C₂×C₄	—	27	4	no	—
308	C₂×C₄	—	27	1	no	—
309	C₂×C₄	—	27	2	no	—
310	C₂×C₄	—	54	4	no	—
311	C₂×C₄	—	54	4	no	—
312	C₂×C₄	—	54	2	no	—
313	C₂×C₄	—	54	4	no	—
314	C₂×C₄	—	54	4	no	—
315	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
316	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
317	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
318	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
319	C₂×C₃	—	2	52	no	—
320	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	13	yes	—
321	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
322	C₂×C₃	#41×C₃⋊D₃	1	13	yes	—
323	D₃	—	9	52	no	—
324	D₃	—	18	52	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	27	2	no	—
328	C₂²	—	27	2	no	—
329	C₂²	—	27	2	no	—
330	C₂²	—	27	4	no	—
331	C₂²	—	54	16	no	—
332	C₂²	—	54	2	no	—
333	C₂²	—	54	2	no	—
334	C₂²	C₂×C₄×C₃⋊(C₃⋊D₃)	1	4	yes	complemented
335	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	1	no	—
338	C₄	—	27	2	no	—
339	C₄	—	27	2	no	—
340	C₄	—	54	2	no	—
341	C₄	—	54	1	no	—
342	C₄	C₂×C₄×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
343	C₄	D₄×C₃⋊(C₃⋊D₃)	1	2	yes	direct product factor
344	C₃	C₄×D₄×C₃⋊D₃	1	13	yes	complemented
345	C₂	—	2	4	no	—
346	C₂	—	27	4	no	—
347	C₂	—	54	4	no	—
348	C₂	C₂²×C₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
349	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
350	C₂	#41×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)
commutator	C₂×C₃³	C₂³×C₄
Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
Fitting	C₃³×C₄×D₄	C₂
socle, cosocle	C₂²×C₃³	C₂⁴
prime radical	C₂×D₄×C₃⋊(C₃⋊D₃)	C₂
hypercenter	C₄×D₄	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	C₂×C₄×D₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₃³×C₄×D₄	C₂	semidirect
4. D₄×C₃⋊(C₃⋊Dic₃)	C₂	semidirect
5. C₄×#6312	C₂	semidirect
6. #11723934	C₂	semidirect
7. C₄⋊C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
8. #11723922	C₂	semidirect
9. C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
10. C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	semidirect
11. C₄²×C₃⋊(C₃⋊D₃)	C₂	semidirect
15. C₂²×C₃³×C₄	C₂²	semidirect
17. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
18. D₄×C₃⋊(C₃⋊D₃)	C₄	direct (N × H)
25. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
26. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
27. C₃³×C₄⋊C₄	C₂²	semidirect
28. C₃³×C₂²⋊C₄	C₂²	semidirect
29. C₃³×C₄²	C₂²	semidirect
30. #88864	C₂²	semidirect
31. #88859	C₂²	semidirect
32. #88859	C₂²	semidirect
33. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
34. #88857	C₂²	semidirect
35. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
36. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
37. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
40. C₃²×C₄×D₄	D₃	semidirect
52. C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
55. C₃³×D₄	C₂×C₄	semidirect
61. #6312	C₂×C₄	semidirect
67. C₄⋊(C₃⋊(C₃⋊D₃))	C₂×C₄	semidirect
72. C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
73. C₄×C₃⋊(C₃⋊D₃)	D₄	direct (N × H)
77. C₂²×C₃²×C₄	C₂×D₃	semidirect
89. C₃²×C₄⋊C₄	C₂×D₃	semidirect
90. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
91. C₃²×C₄²	C₂×D₃	semidirect
102. C₂²×C₃³	C₂²×C₄	semidirect
108. C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	semidirect
113. C₃³×C₄	C₂²×C₄	semidirect
114. C₃³×C₄	C₂×D₄	semidirect
117. C₃⋊(C₃⋊Dic₃)	C₂²×C₄	semidirect
118. C₃⋊(C₃⋊Dic₃)	C₂×D₄	semidirect
121. C₃×C₄×D₄	C₃⋊D₃	semidirect
136. C₃²×D₄	C₄×D₃	semidirect
161. C₃⋊(C₃⋊D₃)	C₄×D₄	direct (N × H)
164. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
176. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
177. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
178. C₃×C₄²	C₂×C₃⋊D₃	semidirect
189. C₂²×C₃²	C₂×C₄×D₃	semidirect
200. C₃²×C₄	C₂×C₄×D₃	semidirect
201. C₃²×C₄	D₃×D₄	semidirect
213. C₄×D₄	C₃⋊(C₃⋊D₃)	direct (N × H)
217. C₃³	C₂×C₄×D₄	semidirect
224. C₃×D₄	C₄×C₃⋊D₃	semidirect
262. C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
265. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
269. C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
273. C₄²	C₂×C₃⋊(C₃⋊D₃)	semidirect
276. C₂²×C₃	C₂×C₄×C₃⋊D₃	semidirect
287. C₃×C₄	C₂×C₄×C₃⋊D₃	semidirect
288. C₃×C₄	D₄×C₃⋊D₃	semidirect
293. C₃²	C₄×D₃×D₄	semidirect
302. D₄	C₄×C₃⋊(C₃⋊D₃)	direct (N × H)
334. C₂²	C₂×C₄×C₃⋊(C₃⋊D₃)	semidirect
342. C₄	C₂×C₄×C₃⋊(C₃⋊D₃)	semidirect
343. C₄	D₄×C₃⋊(C₃⋊D₃)	direct (N × H)
344. C₃	C₄×D₄×C₃⋊D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₃⋊(C₃⋊D₃)	2
C₂²×C₄×C₃⋊(C₃⋊D₃)	2
C₃³×C₄×D₄	2
D₄×C₃⋊(C₃⋊Dic₃)	2
C₄×#6312	2
#11723934	2
C₄⋊C₄×C₃⋊(C₃⋊D₃)	2
#11723922	2
C₂²⋊C₄×C₃⋊(C₃⋊D₃)	2
C₄×C₄⋊(C₃⋊(C₃⋊D₃))	2
C₄²×C₃⋊(C₃⋊D₃)	2
C₄×D₄×C₃⋊D₃	3

Subgroups — C4×D4×C3⋊(C3⋊D3) #13179671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₄×C₃⋊(C₃⋊D₃) #13179671