Subgroups — #611⋊(C₃⋊C₈) #13139485

Order 1728.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×#611	C₂	1	1	yes	maximal, characteristic
3	C₂×D₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₉)⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₉⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃⋊C₈×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#67⋊(C₃⋊C₈)	—	3	1	no	maximal
9	#611⋊C₈	—	3	1	no	maximal
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×#611	C₄	1	1	yes	characteristic
12	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
13	C₂×C₃⋊(C₉⋊C₈)	—	2	2	no	—
14	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₃×#3676	C₄	1	1	yes	characteristic
17	C₃×(C₂×D₉)⋊C₄	C₄	1	1	yes	characteristic
18	C₃×Dic₉⋊C₄	C₄	1	1	yes	characteristic
19	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	D₉×C₃⋊C₈	—	2	2	no	—
23	C₂²×C₃⋊(C₃⋊C₈)	—	3	1	no	—
24	C₃×C₄×#67	—	3	1	no	—
25	C₂×D₃×C₃⋊C₈	—	3	1	no	—
26	C₃×#830	D₃	1	1	yes	characteristic
27	Dic₃⋊(C₃⋊C₈)	—	3	1	no	—
28	(C₂×D₃)⋊(C₃⋊C₈)	—	3	1	no	—
29	Dic₃×C₃⋊C₈	—	3	1	no	—
30	C₄×#611	D₃	1	1	yes	characteristic
31	C₂²×C₉⋊C₈	—	3	1	no	—
32	C₂²×C₉⋊C₈	—	6	1	no	—
33	C₂×C₈×D₉	—	3	1	no	—
34	C₉×C₂²⋊C₈	—	3	1	no	—
35	(C₂×D₉)⋊C₈	—	3	1	no	—
36	Dic₉⋊C₈	—	3	1	no	—
37	C₈×Dic₉	—	3	1	no	—
38	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×D₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₃×#611	C₈	1	4	yes	complemented
45	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
48	C₃×C₄×D₉	—	2	1	no	—
49	C₃×C₄×D₉	—	2	1	no	—
50	C₃⋊(C₉⋊C₈)	—	2	1	no	—
51	C₃⋊(C₉⋊C₈)	D₄	1	2	yes	complemented
52	C₉×C₃⋊C₈	—	2	1	no	—
53	C₉×C₃⋊C₈	—	2	1	no	—
54	D₄×C₃⋊C₈	—	9	1	no	—
55	#67⋊C₈	—	9	1	no	—
56	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
57	C₂×C₃×#67	—	3	1	no	—
58	C₂×C₃×C₄×D₃	—	3	1	no	—
59	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
60	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
61	C₂×C₃⋊(C₃⋊C₈)	—	6	2	no	—
62	C₃×#217	—	3	1	no	—
63	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
64	C₃×Dic₃⋊C₄	—	3	1	no	—
65	C₃×C₄×Dic₃	—	3	1	no	—
66	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
67	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
68	D₃×C₃⋊C₈	—	6	2	no	—
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
71	C₂×#611	Dic₃	1	1	yes	characteristic
72	C₂×C₄×D₉	C₂×D₃	1	1	yes	characteristic
73	C₂×C₈×C₉	—	3	1	no	—
74	C₂×C₈×C₉	—	3	1	no	—
75	#3676	Dic₃	1	1	yes	characteristic
76	(C₂×D₉)⋊C₄	Dic₃	1	1	yes	characteristic
77	Dic₉⋊C₄	Dic₃	1	1	yes	characteristic
78	C₄×Dic₉	C₂×D₃	1	1	yes	characteristic
79	C₂×C₉⋊C₈	—	3	1	no	—
80	C₂×C₉⋊C₈	—	3	1	no	—
81	C₂×C₉⋊C₈	—	6	2	no	—
82	C₂×C₉⋊C₈	—	6	1	no	—
83	C₂×C₉⋊C₈	—	6	1	no	—
84	C₂×C₉⋊C₈	—	6	4	no	—
85	C₈×D₉	—	6	2	no	—
86	C₂²×C₃×C₉	—	2	1	no	—
87	C₂²×C₃×C₉	—	2	1	no	—
88	C₂²×C₃×C₉	C₂×C₈	1	2	yes	complemented
89	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×D₉	—	2	1	no	—
91	C₂×C₃×D₉	—	2	1	no	—
92	C₂×C₃×D₉	C₂×C₈	1	2	yes	complemented
93	C₃×C₄×C₉	—	2	1	no	—
94	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
95	C₃×C₄×C₉	#41	1	1	yes	characteristic
96	C₃×Dic₉	—	2	1	no	—
97	C₃×Dic₉	—	2	1	no	—
98	C₃×Dic₉	C₂×C₈	1	2	yes	complemented
99	C₃×C₄×D₄	—	9	1	no	—
100	C₄×#67	—	3	1	no	—
101	C₂²×C₃⋊C₈	—	9	1	no	—
102	C₂²×C₃⋊C₈	—	9	1	no	—
103	C₂²×C₃⋊C₈	—	9	1	no	—
104	C₂²×C₃⋊C₈	—	18	1	no	—
105	C₂×D₃×C₈	—	9	1	no	—
106	C₃×C₂²⋊C₈	—	3	1	no	—
107	#830	—	9	1	no	—
108	#830	D₉	1	1	yes	characteristic, complemented
109	(C₂×D₃)⋊C₈	—	9	1	no	—
110	Dic₃⋊C₈	—	9	1	no	—
111	C₈×Dic₃	—	9	1	no	—
112	C₄⋊(C₃⋊C₈)	—	9	1	no	—
113	C₄×C₃⋊C₈	—	9	1	no	—
114	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
115	C₂²×C₃×D₃	—	3	1	no	—
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	—	2	1	no	—
118	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
120	C₃×#67	—	3	4	no	—
121	C₂×C₃×Dic₃	—	3	1	no	—
122	C₂×C₃×Dic₃	—	3	1	no	—
123	C₂×C₃×Dic₃	—	3	1	no	—
124	C₃×C₄×D₃	—	6	1	no	—
125	C₃×C₄×D₃	—	6	1	no	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	C₂×Dic₃	1	1	yes	characteristic
128	C₂²×D₉	C₂×Dic₃	1	1	yes	characteristic
129	C₃⋊(C₃⋊C₈)	—	3	2	no	—
130	C₃⋊(C₃⋊C₈)	—	6	1	no	—
131	C₃×C₃⋊C₈	—	2	1	no	—
132	C₃×C₃⋊C₈	—	2	1	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	C₂×Dic₃	1	1	yes	characteristic
140	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
141	#611	C₃⋊C₈	1	4	yes	complemented
142	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
143	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
144	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
145	C₄×D₉	—	2	1	no	—
146	C₄×D₉	—	2	1	no	—
147	C₈×C₉	—	6	1	no	—
148	C₈×C₉	—	6	1	no	—
149	C₉⋊C₈	—	3	2	no	—
150	C₉⋊C₈	—	6	2	no	—
151	C₉⋊C₈	—	6	2	no	—
152	C₉⋊C₈	—	6	1	no	—
153	C₈×D₄	—	27	1	no	Sylow
154	C₂×C₃×C₉	—	2	2	no	—
155	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₃×C₉	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₃×C₉	#131	1	1	yes	characteristic
158	C₃×D₉	—	2	2	no	—
159	C₂×C₃×D₄	—	9	1	no	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	9	1	no	—
162	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
163	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
164	C₂×#67	—	3	1	no	—
165	C₂×C₄×D₃	—	3	1	no	—
166	C₂×C₃×C₈	—	3	1	no	—
167	C₂×C₃×C₈	—	3	1	no	—
168	C₃×C₄⋊C₄	—	9	1	no	—
169	C₃×C₂²⋊C₄	—	9	1	no	—
170	C₃×C₂²⋊C₄	—	9	1	no	—
171	C₃×C₄²	—	9	1	no	—
172	#217	—	3	1	no	—
173	(C₂×D₃)⋊C₄	—	3	1	no	—
174	Dic₃⋊C₄	—	3	1	no	—
175	C₄×Dic₃	—	3	1	no	—
176	C₂×C₃⋊C₈	—	9	1	no	—
177	C₂×C₃⋊C₈	—	9	1	no	—
178	C₂×C₃⋊C₈	—	9	1	no	—
179	C₂×C₃⋊C₈	—	9	1	no	—
180	C₂×C₃⋊C₈	—	18	1	no	—
181	C₂×C₃⋊C₈	—	18	1	no	—
182	C₂×C₃⋊C₈	—	18	2	no	—
183	C₂×C₃⋊C₈	—	18	2	no	—
184	C₂×C₃⋊C₈	—	18	2	no	—
185	C₂×C₃⋊C₈	—	18	4	no	—
186	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
187	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
188	D₃×C₈	—	18	2	no	—
189	C₂²×C₃²	—	2	1	no	—
190	C₂²×C₃²	—	2	1	no	—
191	C₂²×C₃²	D₃×C₈	1	2	yes	—
192	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
193	C₂×C₃×D₃	—	3	2	no	—
194	C₂×C₃×D₃	—	6	1	no	—
195	C₂×C₃×D₃	—	6	1	no	—
196	C₃²×C₄	—	2	1	no	—
197	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
198	C₃²×C₄	#237	1	1	yes	characteristic
199	C₃×Dic₃	—	3	2	no	—
200	C₃×Dic₃	—	6	1	no	—
201	C₃×Dic₃	—	6	1	no	—
202	C₂²×C₉	—	2	2	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	2	1	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	C₂×C₃⋊C₈	1	2	yes	complemented
209	C₂²×C₉	C₂²×Dic₃	1	1	yes	characteristic
210	C₂×D₉	—	2	1	no	—
211	C₂×D₉	—	2	1	no	—
212	C₂×D₉	C₂×C₃⋊C₈	1	2	yes	complemented
213	C₄×C₉	—	2	2	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	1	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	D₃×D₄	1	1	yes	characteristic
218	C₄×C₉	#237	1	1	yes	characteristic
219	Dic₉	—	2	1	no	—
220	Dic₉	—	2	1	no	—
221	Dic₉	C₂×C₃⋊C₈	1	2	yes	complemented
222	C₂²×C₈	—	27	1	no	—
223	C₂²×C₈	—	27	1	no	—
224	C₄×D₄	—	9	1	no	—
225	C₄⋊C₈	—	27	1	no	—
226	C₂²⋊C₈	—	3	1	no	—
227	C₂²⋊C₈	—	27	1	no	—
228	C₄×C₈	—	27	1	no	—
229	C₃×C₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₃	—	2	1	no	—
231	C₂³×C₃	—	9	1	no	—
232	C₂³×C₃	C₄×D₉	1	1	yes	characteristic
233	C₂³×C₃	D₃×Dic₃	1	1	yes	characteristic
234	C₂²×D₃	—	3	1	no	—
235	C₃×D₄	—	9	4	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	9	1	no	—
245	C₂×C₃×C₄	—	9	1	no	—
246	C₂×C₃×C₄	—	9	1	no	—
247	C₂×C₃×C₄	—	18	1	no	—
248	C₂×C₃×C₄	—	18	1	no	—
249	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
251	C₂×C₃×C₄	D₃×Dic₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
253	#67	—	3	4	no	—
254	C₂×Dic₃	—	3	1	no	—
255	C₂×Dic₃	—	3	1	no	—
256	C₂×Dic₃	—	3	1	no	—
257	C₄×D₃	—	6	1	no	—
258	C₄×D₃	—	6	1	no	—
259	C₃×C₈	—	6	1	no	—
260	C₃×C₈	—	6	1	no	—
261	C₃⋊C₈	—	2	1	no	—
262	C₃⋊C₈	—	2	1	no	—
263	C₃⋊C₈	—	9	2	no	—
264	C₃⋊C₈	—	9	2	no	—
265	C₃⋊C₈	—	18	2	no	—
266	C₃⋊C₈	—	18	2	no	—
267	C₃⋊C₈	—	18	1	no	—
268	C₃⋊C₈	—	18	1	no	—
269	C₂×C₃²	—	2	2	no	—
270	C₂×C₃²	#67⋊C₄	1	1	yes	characteristic
271	C₂×C₃²	C₂×D₃×C₈	1	1	yes	characteristic
272	C₂×C₃²	#907	1	1	yes	characteristic
273	C₃×D₃	—	6	2	no	—
274	C₂×C₉	—	2	4	no	—
275	C₂×C₉	—	2	2	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	—	2	1	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	C₂²×C₃⋊C₈	1	1	yes	characteristic
280	C₂×C₉	D₄×Dic₃	1	1	yes	characteristic
281	C₂×C₉	#948	1	1	yes	characteristic
282	D₉	—	2	2	no	—
283	C₂×D₄	—	9	1	no	—
284	C₂²×C₄	—	9	1	no	—
285	C₂²×C₄	D₃×D₉	1	1	yes	characteristic
286	C₂×C₈	—	3	1	no	—
287	C₂×C₈	—	3	1	no	—
288	C₂×C₈	—	27	1	no	—
289	C₂×C₈	—	27	1	no	—
290	C₂×C₈	—	54	2	no	—
291	C₂×C₈	—	54	2	no	—
292	C₄⋊C₄	—	9	1	no	—
293	C₂²⋊C₄	—	9	1	no	—
294	C₂²⋊C₄	—	9	1	no	—
295	C₄²	—	9	1	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	9	2	no	—
305	C₂²×C₃	—	18	1	no	—
306	C₂²×C₃	—	18	1	no	—
307	C₂²×C₃	C₈×D₉	1	2	yes	complemented
308	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
309	C₂²×C₃	D₃×C₃⋊C₈	1	2	yes	—
310	C₂²×C₃	C₂×D₃×Dic₃	1	1	yes	characteristic
311	C₂×D₃	—	3	2	no	—
312	C₂×D₃	—	6	1	no	—
313	C₂×D₃	—	6	1	no	—
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	9	2	no	—
320	C₃×C₄	—	18	1	no	—
321	C₃×C₄	—	18	1	no	—
322	C₃×C₄	D₄×D₉	1	1	yes	characteristic
323	C₃×C₄	#3699	1	1	yes	characteristic
324	C₃×C₄	#3805	1	1	yes	characteristic
325	C₃×C₄	#3811	1	1	yes	characteristic
326	Dic₃	—	3	2	no	—
327	Dic₃	—	6	1	no	—
328	Dic₃	—	6	1	no	—
329	C₃²	#67⋊C₈	1	1	yes	characteristic
330	C₉	—	2	1	no	—
331	C₉	D₄×C₃⋊C₈	1	1	yes	characteristic, complemented
332	C₂³	—	9	1	no	—
333	C₂³	Dic₃×D₉	1	1	yes	characteristic
334	D₄	—	9	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	9	1	no	—
338	C₂×C₄	—	9	1	no	—
339	C₂×C₄	—	9	1	no	—
340	C₂×C₄	—	18	1	no	—
341	C₂×C₄	—	18	1	no	—
342	C₂×C₄	Dic₃×D₉	1	1	yes	characteristic
343	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
344	C₈	—	6	1	no	—
345	C₈	—	6	1	no	—
346	C₈	—	27	2	no	—
347	C₈	—	54	1	no	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	18	2	no	—
355	C₂×C₃	#611⋊C₄	1	1	yes	characteristic
356	C₂×C₃	C₂×C₈×D₉	1	1	yes	characteristic
357	C₂×C₃	#63469	1	1	yes	characteristic
358	C₂×C₃	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
359	C₂×C₃	#63815	1	1	yes	characteristic
360	C₂×C₃	#67⋊Dic₃	1	1	yes	characteristic
361	D₃	—	6	2	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	9	2	no	—
365	C₂²	—	18	1	no	—
366	C₂²	—	18	1	no	—
367	C₂²	D₉×C₃⋊C₈	1	2	yes	complemented
368	C₂²	C₂×Dic₃×D₉	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	9	2	no	—
371	C₄	—	18	1	no	—
372	C₄	—	18	1	no	—
373	C₄	#88663	1	1	yes	characteristic
374	C₄	#88668	1	1	yes	characteristic
375	C₃	—	2	1	no	—
376	C₃	#611⋊C₈	1	1	yes	characteristic, complemented
377	C₃	#67⋊(C₃⋊C₈)	1	1	yes	characteristic
378	C₂	—	2	2	no	—
379	C₂	—	18	2	no	—
380	C₂	C₂×D₉×C₃⋊C₈	1	1	yes	characteristic
381	C₂	#11720859	1	1	yes	characteristic
382	C₂	#611⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₉
commutator	C₂×C₃×C₉	C₂²×C₈
Frattini	C₂×C₃×C₄	C₂×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂²×C₃²	C₂×C₄×D₃
prime radical	C₂×C₃×#611	C₄
cosocle	C₂×C₃×C₄×C₉	C₂³
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	C₈×D₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃⋊(C₉⋊C₈)	C₂	semidirect
3. C₂×D₉×C₃⋊C₈	C₂	semidirect
4. C₉×#830	C₂	semidirect
5. (C₂×D₉)⋊(C₃⋊C₈)	C₂	semidirect
6. Dic₉⋊(C₃⋊C₈)	C₂	semidirect
7. C₃⋊C₈×Dic₉	C₂	semidirect
44. C₃×#611	C₈	semidirect
51. C₃⋊(C₉⋊C₈)	D₄	semidirect
88. C₂²×C₃×C₉	C₂×C₈	semidirect
92. C₂×C₃×D₉	C₂×C₈	semidirect
98. C₃×Dic₉	C₂×C₈	semidirect
108. #830	D₉	semidirect
141. #611	C₃⋊C₈	semidirect
208. C₂²×C₉	C₂×C₃⋊C₈	semidirect
212. C₂×D₉	C₂×C₃⋊C₈	semidirect
221. Dic₉	C₂×C₃⋊C₈	semidirect
229. C₃×C₉	C₈×D₄	semidirect
307. C₂²×C₃	C₈×D₉	semidirect
331. C₉	D₄×C₃⋊C₈	semidirect
367. C₂²	D₉×C₃⋊C₈	semidirect
376. C₃	#611⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃⋊(C₉⋊C₈)	2
C₃×C₄×#611	2
C₂×D₉×C₃⋊C₈	2
C₉×#830	2
(C₂×D₉)⋊(C₃⋊C₈)	2
Dic₉⋊(C₃⋊C₈)	2
C₃⋊C₈×Dic₉	2
#67⋊(C₃⋊C₈)	3
#611⋊C₈	3

Subgroups — #611⋊(C3⋊C8) #13139485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #611⋊(C₃⋊C₈) #13139485