Subgroups — C₈×C₄⋊((C₃⋊D₃)⋊C₃) #13141452

Order 1728.

513 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×(C₃⋊D₃)⋊C₃	C₂	1	2	yes	maximal, complemented
2	C₄×C₄⋊((C₃⋊D₃)⋊C₃)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	#63647⋊C₃	C₂	1	2	yes	maximal, complemented
5	C₄⋊((C₃⋊(C₃⋊C₈))⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄⋊(C₃⋊D₃)	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×C₈×D₁₂	—	3	1	no	maximal
8	C₂×C₄⋊((C₃⋊D₃)⋊C₃)	C₄	1	1	yes	characteristic
9	C₂×C₄×(C₃⋊D₃)⋊C₃	C₂²	1	2	yes	—
10	C₂×C₈×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
11	C₂×C₈×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
12	C₄²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
13	#3752⋊C₃	C₄	1	2	yes	—
14	C₄⋊((C₃⋊Dic₃)⋊C₃)	C₄	1	1	yes	characteristic
15	C₂×(C₃⋊(C₃⋊C₈))⋊C₃	C₂²	1	2	yes	—
16	C₈×(C₃⋊D₃)⋊C₃	—	2	4	no	—
17	C₂×C₈×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
18	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×D₃×C₈	—	3	2	no	—
20	C₃×C₄×D₁₂	—	3	1	no	—
21	C₃²×C₄×C₈	—	2	1	no	—
22	C₃²×C₄×C₈	D₃	1	1	yes	characteristic, complemented
23	C₃²×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	#63647	C₂×C₃	1	2	yes	complemented
25	C₄⋊(C₃⋊(C₃⋊C₈))	C₂×C₃	1	1	yes	characteristic, complemented
26	C₃×(C₂×D₃)⋊C₈	—	3	2	no	—
27	C₃×C₄⋊(C₃⋊C₈)	—	3	1	no	—
28	C₂²×(C₃⋊D₃)⋊C₃	C₂×C₄	1	2	yes	—
29	C₂×C₄×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
32	C₂×(C₃⋊Dic₃)⋊C₃	C₂×C₄	1	2	yes	—
33	C₄⋊((C₃⋊D₃)⋊C₃)	C₈	1	4	yes	direct product factor
34	C₄×(C₃⋊D₃)⋊C₃	—	2	2	no	—
35	C₄×(C₃⋊D₃)⋊C₃	—	2	2	no	—
36	C₈×H(3,𝔽₃)	—	2	1	no	—
37	C₈×H(3,𝔽₃)	D₄	1	2	yes	complemented
38	(C₃⋊(C₃⋊C₈))⋊C₃	—	2	2	no	—
39	C₃×C₈×D₄	—	9	1	no	—
40	C₈×D₁₂	—	3	1	no	—
41	C₈×D₁₂	—	9	1	no	—
42	C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	1	1	yes	characteristic
43	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
44	C₂×C₃×D₁₂	—	3	1	no	—
45	C₂×C₃×C₄×D₃	—	3	2	no	—
46	C₂×C₃²×C₈	—	2	1	no	—
47	C₂×C₃²×C₈	—	2	1	no	—
48	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
49	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
50	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
52	C₃²×C₄²	—	2	1	no	—
53	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
54	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
55	#3752	C₃×C₄	1	2	yes	—
56	C₄⋊(C₃⋊Dic₃)	C₃×C₄	1	1	yes	characteristic
57	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
58	C₈×C₃⋊D₃	—	2	4	no	—
59	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
60	C₃×C₄⋊Dic₃	—	3	1	no	—
61	C₂×C₃×C₃⋊C₈	—	3	2	no	—
62	C₃×D₃×C₈	—	6	4	no	—
63	C₂²×H(3,𝔽₃)	C₂²×C₄	1	1	yes	characteristic
64	C₂×(C₃⋊D₃)⋊C₃	—	2	2	no	—
65	C₂×(C₃⋊D₃)⋊C₃	—	2	2	no	—
66	C₂×(C₃⋊D₃)⋊C₃	C₂×C₈	1	4	yes	complemented
67	C₄×H(3,𝔽₃)	—	2	1	no	—
68	C₄×H(3,𝔽₃)	C₂×C₈	1	2	yes	complemented
69	C₄×H(3,𝔽₃)	C₂×D₄	1	1	yes	characteristic
70	C₄×H(3,𝔽₃)	#41	1	1	yes	characteristic
71	(C₃⋊Dic₃)⋊C₃	—	2	2	no	—
72	C₂²×C₃×C₈	—	9	2	no	—
73	C₃×C₄×D₄	—	9	1	no	—
74	C₂×D₃×C₈	—	3	2	no	—
75	C₂×D₃×C₈	—	9	2	no	—
76	C₄×D₁₂	—	3	1	no	—
77	C₄×D₁₂	—	9	1	no	—
78	C₃×C₄⋊C₈	—	9	1	no	—
79	C₃×C₂²⋊C₈	—	9	2	no	—
80	C₃×C₄×C₈	—	3	1	no	—
81	C₃×C₄×C₈	—	3	1	no	—
82	C₃×C₄×C₈	—	6	1	no	—
83	C₃×C₄×C₈	C₃×D₃	1	1	yes	characteristic
84	(C₂×D₃)⋊C₈	—	3	2	no	—
85	(C₂×D₃)⋊C₈	—	9	2	no	—
86	C₄⋊(C₃⋊C₈)	—	3	1	no	—
87	C₄⋊(C₃⋊C₈)	—	9	1	no	—
88	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	2	yes	—
89	C₂²×C₃×D₃	—	3	2	no	—
90	C₂×C₃²×C₄	—	2	1	no	—
91	C₂×C₃²×C₄	—	2	1	no	—
92	C₂×C₃²×C₄	—	2	1	no	—
93	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
99	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
100	C₄⋊(C₃⋊D₃)	C₃×C₈	1	4	yes	complemented
101	C₄×C₃⋊D₃	—	2	2	no	—
102	C₄×C₃⋊D₃	—	2	2	no	—
103	C₂×C₃×Dic₃	—	3	2	no	—
104	C₃×D₁₂	—	3	4	no	—
105	C₃×C₄×D₃	—	6	2	no	—
106	C₃×C₄×D₃	—	6	2	no	—
107	C₃²×C₈	—	2	2	no	—
108	C₃²×C₈	—	2	1	no	—
109	C₃²×C₈	—	2	1	no	—
110	C₃²×C₈	—	2	2	no	—
111	C₃²×C₈	D₁₂	1	2	yes	complemented
112	C₃²×C₈	C₃×D₄	1	2	yes	complemented
113	C₃⋊(C₃⋊C₈)	—	2	2	no	—
114	C₃×C₃⋊C₈	—	6	2	no	—
115	C₈×D₄	—	9	1	no	Sylow
116	C₂×H(3,𝔽₃)	C₄×D₄	1	1	yes	characteristic
117	C₂×H(3,𝔽₃)	C₂²×C₈	1	1	yes	characteristic
118	C₂×H(3,𝔽₃)	#131	1	1	yes	characteristic
119	(C₃⋊D₃)⋊C₃	—	2	4	no	—
120	C₂×C₃×D₄	—	9	1	no	—
121	C₂²×C₃×C₄	—	9	2	no	—
122	C₂×D₁₂	—	3	1	no	—
123	C₂×D₁₂	—	9	1	no	—
124	C₂×C₄×D₃	—	3	2	no	—
125	C₂×C₄×D₃	—	9	2	no	—
126	C₂×C₃×C₈	—	3	1	no	—
127	C₂×C₃×C₈	—	3	1	no	—
128	C₂×C₃×C₈	—	3	1	no	—
129	C₂×C₃×C₈	—	3	1	no	—
130	C₂×C₃×C₈	—	6	1	no	—
131	C₂×C₃×C₈	—	6	1	no	—
132	C₂×C₃×C₈	—	9	2	no	—
133	C₂×C₃×C₈	—	18	4	no	—
134	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
135	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
136	C₃×C₄⋊C₄	—	9	1	no	—
137	C₃×C₂²⋊C₄	—	9	2	no	—
138	C₃×C₄²	—	3	1	no	—
139	C₃×C₄²	—	3	1	no	—
140	C₃×C₄²	—	6	1	no	—
141	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
142	(C₂×D₃)⋊C₄	—	3	2	no	—
143	(C₂×D₃)⋊C₄	—	9	2	no	—
144	C₄⋊Dic₃	—	3	1	no	—
145	C₄⋊Dic₃	—	9	1	no	—
146	C₂×C₃⋊C₈	—	3	2	no	—
147	C₂×C₃⋊C₈	—	9	2	no	—
148	D₃×C₈	—	6	4	no	—
149	D₃×C₈	—	18	4	no	—
150	C₂²×C₃²	—	2	1	no	—
151	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
152	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
153	C₂×C₃⋊D₃	—	2	2	no	—
154	C₂×C₃⋊D₃	—	2	2	no	—
155	C₂×C₃⋊D₃	C₂×C₃×C₈	1	4	yes	complemented
156	C₂×C₃×D₃	—	3	4	no	—
157	C₂×C₃×D₃	—	6	2	no	—
158	C₂×C₃×D₃	—	6	2	no	—
159	C₃²×C₄	—	2	2	no	—
160	C₃²×C₄	—	2	1	no	—
161	C₃²×C₄	—	2	1	no	—
162	C₃²×C₄	—	2	2	no	—
163	C₃²×C₄	—	2	1	no	—
164	C₃²×C₄	—	2	1	no	—
165	C₃²×C₄	D₃×C₈	1	2	yes	complemented
166	C₃²×C₄	C₂×C₃×C₈	1	2	yes	complemented
167	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
168	C₃²×C₄	#235	1	1	yes	characteristic
169	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
170	C₃²×C₄	C₃×#41	1	1	yes	characteristic
171	C₃⋊Dic₃	—	2	2	no	—
172	C₃×Dic₃	—	6	2	no	—
173	C₂²×C₈	—	9	2	no	—
174	C₄×D₄	—	9	1	no	—
175	C₄⋊C₈	—	9	1	no	—
176	C₂²⋊C₈	—	9	2	no	—
177	C₄×C₈	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
178	H(3,𝔽₃)	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
179	C₂³×C₃	—	9	2	no	—
180	C₂²×D₃	—	3	2	no	—
181	C₂²×D₃	—	9	2	no	—
182	C₃×D₄	—	9	4	no	—
183	C₂×C₃×C₄	—	3	1	no	—
184	C₂×C₃×C₄	—	3	1	no	—
185	C₂×C₃×C₄	—	3	1	no	—
186	C₂×C₃×C₄	—	3	1	no	—
187	C₂×C₃×C₄	—	3	1	no	—
188	C₂×C₃×C₄	—	3	1	no	—
189	C₂×C₃×C₄	—	6	1	no	—
190	C₂×C₃×C₄	—	6	1	no	—
191	C₂×C₃×C₄	—	6	1	no	—
192	C₂×C₃×C₄	—	9	2	no	—
193	C₂×C₃×C₄	—	18	2	no	—
194	C₂×C₃×C₄	—	18	2	no	—
195	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
196	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
198	C₂×Dic₃	—	3	2	no	—
199	C₂×Dic₃	—	9	2	no	—
200	D₁₂	—	3	4	no	—
201	D₁₂	—	9	4	no	—
202	C₄×D₃	—	6	2	no	—
203	C₄×D₃	—	6	2	no	—
204	C₄×D₃	—	18	2	no	—
205	C₄×D₃	—	18	2	no	—
206	C₃×C₈	—	2	1	no	—
207	C₃×C₈	—	3	2	no	—
208	C₃×C₈	—	3	2	no	—
209	C₃×C₈	—	6	1	no	—
210	C₃×C₈	—	6	1	no	—
211	C₃×C₈	—	6	2	no	—
212	C₃×C₈	—	6	2	no	—
213	C₃×C₈	—	18	2	no	—
214	C₃×C₈	C₃×D₁₂	1	2	yes	—
215	C₃⋊C₈	—	6	2	no	—
216	C₃⋊C₈	—	18	2	no	—
217	C₂×C₃²	—	2	1	no	—
218	C₂×C₃²	—	2	1	no	—
219	C₂×C₃²	—	2	1	no	—
220	C₂×C₃²	C₄×D₁₂	1	1	yes	characteristic
221	C₂×C₃²	C₂×D₃×C₈	1	1	yes	characteristic
222	C₂×C₃²	#901	1	1	yes	characteristic
223	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
224	C₂×C₃²	C₂²×C₃×C₈	1	1	yes	characteristic
225	C₂×C₃²	C₃×#131	1	1	yes	characteristic
226	C₃⋊D₃	—	2	4	no	—
227	C₃×D₃	—	6	4	no	—
228	C₂×D₄	—	9	1	no	—
229	C₂²×C₄	—	9	2	no	—
230	C₂×C₈	—	9	2	no	—
231	C₂×C₈	—	18	4	no	—
232	C₂×C₈	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
233	C₂×C₈	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
234	C₄⋊C₄	—	9	1	no	—
235	C₂²⋊C₄	—	9	2	no	—
236	C₄²	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
237	C₂²×C₃	—	3	1	no	—
238	C₂²×C₃	—	3	1	no	—
239	C₂²×C₃	—	6	1	no	—
240	C₂²×C₃	—	9	4	no	—
241	C₂²×C₃	—	18	2	no	—
242	C₂²×C₃	—	18	2	no	—
243	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
244	C₂×D₃	—	3	4	no	—
245	C₂×D₃	—	6	2	no	—
246	C₂×D₃	—	6	2	no	—
247	C₂×D₃	—	9	4	no	—
248	C₂×D₃	—	18	2	no	—
249	C₂×D₃	—	18	2	no	—
250	C₃×C₄	—	2	1	no	—
251	C₃×C₄	—	3	1	no	—
252	C₃×C₄	—	3	1	no	—
253	C₃×C₄	—	3	1	no	—
254	C₃×C₄	—	3	1	no	—
255	C₃×C₄	—	3	2	no	—
256	C₃×C₄	—	3	2	no	—
257	C₃×C₄	—	6	1	no	—
258	C₃×C₄	—	6	1	no	—
259	C₃×C₄	—	6	2	no	—
260	C₃×C₄	—	6	1	no	—
261	C₃×C₄	—	6	1	no	—
262	C₃×C₄	—	6	2	no	—
263	C₃×C₄	—	18	2	no	—
264	C₃×C₄	C₃×D₃×C₈	1	2	yes	—
265	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
266	C₃×C₄	C₃×#235	1	1	yes	characteristic
267	Dic₃	—	6	2	no	—
268	Dic₃	—	18	2	no	—
269	C₃²	—	2	1	no	—
270	C₃²	C₈×D₁₂	1	1	yes	characteristic, complemented
271	C₃²	C₃×C₈×D₄	1	1	yes	characteristic, complemented
272	C₂³	—	9	2	no	—
273	D₄	—	9	4	no	—
274	C₂×C₄	—	9	2	no	—
275	C₂×C₄	—	18	2	no	—
276	C₂×C₄	—	18	2	no	—
277	C₂×C₄	C₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
278	C₂×C₄	C₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
279	C₂×C₄	C₂²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
280	C₈	—	2	1	no	—
281	C₈	—	18	2	no	—
282	C₈	C₄⋊((C₃⋊D₃)⋊C₃)	1	2	yes	direct product factor
283	C₂×C₃	—	3	1	no	—
284	C₂×C₃	—	3	1	no	—
285	C₂×C₃	—	3	1	no	—
286	C₂×C₃	—	3	1	no	—
287	C₂×C₃	—	3	1	no	—
288	C₂×C₃	—	3	1	no	—
289	C₂×C₃	—	6	1	no	—
290	C₂×C₃	—	6	1	no	—
291	C₂×C₃	—	6	1	no	—
292	C₂×C₃	—	18	4	no	—
293	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
294	C₂×C₃	C₂×C₃×D₃×C₈	1	1	yes	characteristic
295	C₂×C₃	C₃×#901	1	1	yes	characteristic
296	D₃	—	6	4	no	—
297	D₃	—	18	4	no	—
298	C₂²	—	9	4	no	—
299	C₂²	—	18	2	no	—
300	C₂²	—	18	2	no	—
301	C₂²	C₂×C₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
302	C₄	—	2	1	no	—
303	C₄	—	18	2	no	—
304	C₄	C₈×(C₃⋊D₃)⋊C₃	1	2	yes	complemented
305	C₄	C₂×C₄⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
306	C₄	#3828⋊C₃	1	1	yes	characteristic
307	C₃	—	3	1	no	—
308	C₃	—	3	1	no	—
309	C₃	—	6	1	no	—
310	C₃	C₃×C₈×D₁₂	1	1	yes	characteristic
311	C₂	—	18	4	no	—
312	C₂	C₄×C₄⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
313	C₂	C₂×C₈×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
314	C₂	#64110⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×(C₃⋊D₃)⋊C₃
commutator	C₂×C₃²	C₂²×C₃×C₈
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₄×C₈×H(3,𝔽₃)	C₂
socle	C₂²×C₃	C₂×C₃×C₄×D₃
prime radical	C₂×C₄⋊((C₃⋊D₃)⋊C₃)	C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₄×C₈	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₃×C₈×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×(C₃⋊D₃)⋊C₃	C₂	semidirect
3. C₄×C₈×H(3,𝔽₃)	C₂	semidirect
4. #63647⋊C₃	C₂	semidirect
5. C₄⋊((C₃⋊(C₃⋊C₈))⋊C₃)	C₂	semidirect
6. C₈×C₄⋊(C₃⋊D₃)	C₃	semidirect
17. C₂×C₈×C₃⋊D₃	C₂×C₃	semidirect
22. C₃²×C₄×C₈	D₃	semidirect
23. C₃²×C₄×C₈	C₂×C₃	semidirect
24. #63647	C₂×C₃	semidirect
25. C₄⋊(C₃⋊(C₃⋊C₈))	C₂×C₃	semidirect
33. C₄⋊((C₃⋊D₃)⋊C₃)	C₈	direct (N × H)
37. C₈×H(3,𝔽₃)	D₄	semidirect
66. C₂×(C₃⋊D₃)⋊C₃	C₂×C₈	semidirect
68. C₄×H(3,𝔽₃)	C₂×C₈	semidirect
100. C₄⋊(C₃⋊D₃)	C₃×C₈	semidirect
111. C₃²×C₈	D₁₂	semidirect
112. C₃²×C₈	C₃×D₄	semidirect
155. C₂×C₃⋊D₃	C₂×C₃×C₈	semidirect
165. C₃²×C₄	D₃×C₈	semidirect
166. C₃²×C₄	C₂×C₃×C₈	semidirect
177. C₄×C₈	(C₃⋊D₃)⋊C₃	semidirect
178. H(3,𝔽₃)	C₈×D₄	semidirect
270. C₃²	C₈×D₁₂	semidirect
271. C₃²	C₃×C₈×D₄	semidirect
282. C₈	C₄⋊((C₃⋊D₃)⋊C₃)	direct (N × H)
304. C₄	C₈×(C₃⋊D₃)⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×(C₃⋊D₃)⋊C₃	2
C₄×C₄⋊((C₃⋊D₃)⋊C₃)	2
C₄×C₈×H(3,𝔽₃)	2
#63647⋊C₃	2
C₄⋊((C₃⋊(C₃⋊C₈))⋊C₃)	2
C₈×C₄⋊(C₃⋊D₃)	3
C₃×C₈×D₁₂	3

Subgroups — C8×C4⋊((C3⋊D3)⋊C3) #13141452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₄⋊((C₃⋊D₃)⋊C₃) #13141452