Subgroups — C₂×D₃×C₉×C₄⋊C₄ #13152413

Order 1728.

1346 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	C₂²×C₄×D₃×C₉	C₂	1	2	yes	maximal
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
6	D₃×C₉×C₄⋊C₄	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×D₃×C₄⋊C₄	C₃	1	1	yes	maximal, characteristic
8	C₂²×C₉×C₄⋊C₄	—	3	1	no	maximal
9	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
13	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₃×C₉	—	2	8	no	—
15	C₂×C₄×D₃×C₉	C₄	1	8	yes	complemented
16	C₂×C₄×D₃×C₉	C₂²	1	8	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
18	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
19	C₉×C₄⋊Dic₃	C₂²	1	4	yes	complemented
20	C₉×Dic₃⋊C₄	C₂²	1	8	yes	complemented
21	C₂²×C₃×C₄×D₃	C₂×C₃	1	2	yes	—
22	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	2	yes	—
26	C₃×D₃×C₄⋊C₄	C₂×C₃	1	8	yes	—
27	C₂³×C₄×C₉	—	3	1	no	—
28	C₂³×C₄×C₉	—	3	2	no	—
29	C₂×C₉×C₄⋊C₄	—	2	1	no	—
30	C₂×C₉×C₄⋊C₄	—	3	2	no	—
31	C₂×C₉×C₄⋊C₄	—	3	1	no	—
32	C₂×C₉×C₄⋊C₄	—	3	8	no	—
33	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, direct product factor
34	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
35	C₂²×D₃×C₉	C₂×C₄	1	4	yes	—
36	C₂²×D₃×C₉	D₄	1	4	yes	—
37	C₂²×D₃×C₉	Q₈	1	4	yes	—
38	C₂²×D₃×C₉	C₂³	1	2	yes	—
39	C₂×C₃×C₄×C₉	—	2	4	no	—
40	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
41	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
42	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
43	C₂×C₉×Dic₃	—	2	4	no	—
44	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	complemented
45	C₂×C₉×Dic₃	C₂³	1	4	yes	—
46	C₂×C₉×Dic₃	C₂³	1	2	yes	—
47	C₄×D₃×C₉	—	2	16	no	—
48	C₄×D₃×C₉	C₂×C₄	1	16	yes	complemented
49	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
50	C₂×D₃×C₄⋊C₄	C₉	1	1	yes	characteristic, direct product factor
51	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
53	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
55	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₃×C₄×D₃	—	2	8	no	—
57	C₂×C₃×C₄×D₃	C₃×C₄	1	8	yes	—
58	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
59	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
60	C₂⁴×C₉	—	3	1	no	—
61	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
62	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
63	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
64	C₂²×C₄×C₉	—	2	1	no	—
65	C₂²×C₄×C₉	—	2	2	no	—
66	C₂²×C₄×C₉	—	3	1	no	—
67	C₂²×C₄×C₉	—	3	8	no	—
68	C₂²×C₄×C₉	—	3	4	no	—
69	C₂²×C₄×C₉	—	3	2	no	—
70	C₂²×C₄×C₉	—	3	8	no	—
71	C₂²×C₄×C₉	—	6	8	no	—
72	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
73	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
74	C₉×C₄⋊C₄	—	2	4	no	—
75	C₉×C₄⋊C₄	—	3	8	no	—
76	C₉×C₄⋊C₄	—	3	4	no	—
77	C₉×C₄⋊C₄	C₂×D₃	1	4	yes	direct product factor
78	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
79	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
80	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
81	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
82	C₂×D₃×C₉	C₄⋊C₄	1	16	yes	direct product factor
83	C₂×D₃×C₉	C₂²×C₄	1	4	yes	—
84	C₂×D₃×C₉	C₂×D₄	1	4	yes	—
85	C₂×D₃×C₉	C₂×Q₈	1	4	yes	—
86	C₃×C₄×C₉	—	2	4	no	—
87	C₃×C₄×C₉	C₂²×C₄	1	4	yes	complemented
88	C₉×Dic₃	—	2	4	no	—
89	C₉×Dic₃	C₂²×C₄	1	4	yes	complemented
90	C₂³×C₃×C₄	—	3	1	no	—
91	C₂³×C₃×C₄	—	3	2	no	—
92	C₂²×C₄×D₃	C₂×C₉	1	2	yes	—
93	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₃×C₄⋊C₄	—	3	2	no	—
96	C₂×C₃×C₄⋊C₄	—	3	1	no	—
97	C₂×C₃×C₄⋊C₄	—	3	8	no	—
98	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
99	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
100	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
101	C₂×Dic₃⋊C₄	C₂×C₉	1	2	yes	complemented
102	D₃×C₄⋊C₄	C₂×C₉	1	8	yes	direct product factor
103	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
104	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
105	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
106	C₂²×C₃×D₃	C₃×Q₈	1	4	yes	—
107	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
108	C₂×C₃²×C₄	—	2	4	no	—
109	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
110	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
111	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
112	C₂×C₃×Dic₃	—	2	4	no	—
113	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
114	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
115	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
116	C₃×C₄×D₃	—	2	16	no	—
117	C₃×C₄×D₃	C₂×C₃×C₄	1	16	yes	—
118	C₂³×C₉	—	2	1	no	—
119	C₂³×C₉	—	3	4	no	—
120	C₂³×C₉	—	3	4	no	—
121	C₂³×C₉	—	3	4	no	—
122	C₂³×C₉	—	3	2	no	—
123	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
124	C₂×C₄×C₉	—	2	4	no	—
125	C₂×C₄×C₉	—	2	4	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	4	no	—
128	C₂×C₄×C₉	—	3	4	no	—
129	C₂×C₄×C₉	—	3	2	no	—
130	C₂×C₄×C₉	—	3	16	no	—
131	C₂×C₄×C₉	—	3	4	no	—
132	C₂×C₄×C₉	—	4	4	no	—
133	C₂×C₄×C₉	—	6	16	no	—
134	C₂×C₄×C₉	—	6	4	no	—
135	C₂×C₄×C₉	C₄×D₃	1	4	yes	complemented
136	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
137	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
138	C₂²×C₄⋊C₄	—	3	1	no	Sylow
139	C₂×C₃×C₉	C₂×C₄⋊C₄	1	4	yes	complemented
140	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
143	D₃×C₉	C₂×C₄⋊C₄	1	8	yes	direct product factor
144	C₂⁴×C₃	—	3	1	no	—
145	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
146	C₂²×C₃×C₄	—	2	1	no	—
147	C₂²×C₃×C₄	—	2	2	no	—
148	C₂²×C₃×C₄	—	3	1	no	—
149	C₂²×C₃×C₄	—	3	8	no	—
150	C₂²×C₃×C₄	—	3	4	no	—
151	C₂²×C₃×C₄	—	3	2	no	—
152	C₂²×C₃×C₄	—	3	8	no	—
153	C₂²×C₃×C₄	—	6	8	no	—
154	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
155	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
157	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
158	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
159	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
160	C₂×C₄×D₃	—	2	8	no	—
161	C₂×C₄×D₃	C₄×C₉	1	8	yes	complemented
162	C₂×C₄×D₃	C₂²×C₉	1	8	yes	—
163	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
164	C₃×C₄⋊C₄	—	2	4	no	—
165	C₃×C₄⋊C₄	—	3	8	no	—
166	C₃×C₄⋊C₄	—	3	4	no	—
167	C₃×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
168	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
169	C₄⋊Dic₃	C₂²×C₉	1	4	yes	complemented
170	Dic₃⋊C₄	C₂²×C₉	1	8	yes	complemented
171	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
172	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
173	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
174	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
175	C₂×C₃×D₃	C₃×C₄⋊C₄	1	16	yes	—
176	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
177	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
178	C₂×C₃×D₃	C₂×C₃×Q₈	1	4	yes	—
179	C₃²×C₄	—	2	4	no	—
180	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
181	C₃×Dic₃	—	2	4	no	—
182	C₃×Dic₃	C₂²×C₃×C₄	1	4	yes	—
183	C₂²×C₉	—	2	1	no	—
184	C₂²×C₉	—	2	2	no	—
185	C₂²×C₉	—	2	2	no	—
186	C₂²×C₉	—	2	2	no	—
187	C₂²×C₉	—	3	16	no	—
188	C₂²×C₉	—	3	4	no	—
189	C₂²×C₉	—	3	4	no	—
190	C₂²×C₉	—	3	4	no	—
191	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
192	C₂²×C₉	D₃×D₄	1	2	yes	—
193	C₂²×C₉	D₃×Q₈	1	2	yes	—
194	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
195	C₄×C₉	—	2	4	no	—
196	C₄×C₉	—	2	4	no	—
197	C₄×C₉	—	3	4	no	—
198	C₄×C₉	—	4	4	no	—
199	C₄×C₉	—	6	4	no	—
200	C₄×C₉	C₂×C₄×D₃	1	4	yes	complemented
201	C₂³×C₄	—	3	1	no	—
202	C₂³×C₄	—	3	2	no	—
203	C₂×C₄⋊C₄	—	3	2	no	—
204	C₂×C₄⋊C₄	—	3	1	no	—
205	C₂×C₄⋊C₄	—	3	8	no	—
206	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, direct product factor
207	C₃×C₉	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
208	C₂³×C₃	—	2	1	no	—
209	C₂³×C₃	—	3	2	no	—
210	C₂³×C₃	—	3	4	no	—
211	C₂³×C₃	—	3	4	no	—
212	C₂³×C₃	—	3	4	no	—
213	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
214	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
215	C₂²×D₃	C₂×C₄×C₉	1	4	yes	—
216	C₂²×D₃	D₄×C₉	1	4	yes	—
217	C₂²×D₃	Q₈×C₉	1	4	yes	—
218	C₂²×D₃	C₂³×C₉	1	2	yes	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	4	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	3	2	no	—
225	C₂×C₃×C₄	—	3	4	no	—
226	C₂×C₃×C₄	—	3	16	no	—
227	C₂×C₃×C₄	—	3	4	no	—
228	C₂×C₃×C₄	—	4	4	no	—
229	C₂×C₃×C₄	—	6	16	no	—
230	C₂×C₃×C₄	—	6	4	no	—
231	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
232	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
233	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
234	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
235	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
236	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
237	C₂×Dic₃	—	2	4	no	—
238	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	complemented
239	C₂×Dic₃	C₂³×C₉	1	4	yes	—
240	C₂×Dic₃	C₂³×C₉	1	2	yes	—
241	C₄×D₃	—	2	16	no	—
242	C₄×D₃	C₂×C₄×C₉	1	16	yes	complemented
243	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	4	yes	—
244	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
245	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
246	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
247	C₃×D₃	C₂×C₃×C₄⋊C₄	1	8	yes	—
248	C₂×C₉	—	2	4	no	—
249	C₂×C₉	—	2	1	no	—
250	C₂×C₉	—	2	1	no	—
251	C₂×C₉	—	2	1	no	—
252	C₂×C₉	—	3	8	no	—
253	C₂×C₉	D₃×C₄⋊C₄	1	4	yes	direct product factor
254	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
255	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
256	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
257	C₂⁴	—	3	1	no	—
258	C₂²×C₄	—	3	1	no	—
259	C₂²×C₄	—	3	8	no	—
260	C₂²×C₄	—	3	4	no	—
261	C₂²×C₄	—	3	2	no	—
262	C₂²×C₄	—	3	8	no	—
263	C₂²×C₄	—	6	8	no	—
264	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
265	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
266	C₄⋊C₄	—	3	8	no	—
267	C₄⋊C₄	—	3	4	no	—
268	C₄⋊C₄	C₂×D₃×C₉	1	4	yes	direct product factor
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	2	2	no	—
272	C₂²×C₃	—	2	2	no	—
273	C₂²×C₃	—	3	16	no	—
274	C₂²×C₃	—	3	4	no	—
275	C₂²×C₃	—	3	4	no	—
276	C₂²×C₃	—	3	4	no	—
277	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
278	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
279	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	—
280	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
282	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
283	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
284	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
285	C₂×D₃	C₉×C₄⋊C₄	1	16	yes	direct product factor
286	C₂×D₃	C₂²×C₄×C₉	1	4	yes	—
287	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
288	C₂×D₃	C₂×Q₈×C₉	1	4	yes	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	2	4	no	—
292	C₃×C₄	—	3	4	no	—
293	C₃×C₄	—	4	4	no	—
294	C₃×C₄	—	6	4	no	—
295	C₃×C₄	C₂²×C₄×C₉	1	4	yes	complemented
296	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
297	Dic₃	—	2	4	no	—
298	Dic₃	C₂²×C₄×C₉	1	4	yes	complemented
299	C₃²	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
300	C₉	—	2	1	no	—
301	C₉	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic, direct product factor
302	C₂³	—	3	2	no	—
303	C₂³	—	3	4	no	—
304	C₂³	—	3	4	no	—
305	C₂³	—	3	4	no	—
306	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	3	2	no	—
309	C₂×C₄	—	3	4	no	—
310	C₂×C₄	—	3	16	no	—
311	C₂×C₄	—	3	4	no	—
312	C₂×C₄	—	6	16	no	—
313	C₂×C₄	—	6	4	no	—
314	C₂×C₄	C₄×D₃×C₉	1	4	yes	complemented
315	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
316	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
317	C₂×C₃	—	2	1	no	—
318	C₂×C₃	—	2	1	no	—
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	—	2	4	no	—
321	C₂×C₃	—	3	8	no	—
322	C₂×C₃	C₂×C₉×C₄⋊C₄	1	4	yes	complemented
323	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
324	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
325	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
326	C₂×C₃	C₃×D₃×C₄⋊C₄	1	4	yes	—
327	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
328	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
329	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
330	D₃	C₂×C₉×C₄⋊C₄	1	8	yes	direct product factor
331	C₂²	—	3	4	no	—
332	C₂²	—	3	4	no	—
333	C₂²	—	3	4	no	—
334	C₂²	—	3	16	no	—
335	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
336	C₂²	D₃×D₄×C₉	1	2	yes	—
337	C₂²	D₃×Q₈×C₉	1	2	yes	—
338	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
339	C₄	—	2	4	no	—
340	C₄	—	3	4	no	—
341	C₄	—	6	4	no	—
342	C₄	C₂×C₄×D₃×C₉	1	4	yes	complemented
343	C₃	—	2	1	no	—
344	C₃	C₂²×C₉×C₄⋊C₄	1	1	yes	characteristic, complemented
345	C₃	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
346	C₂	—	3	8	no	—
347	C₂	D₃×C₉×C₄⋊C₄	1	4	yes	direct product factor
348	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
349	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
350	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₂²×C₉×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
4. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
5. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
6. D₃×C₉×C₄⋊C₄	C₂	direct (N × H)
15. C₂×C₄×D₃×C₉	C₄	semidirect
18. C₃×C₉×C₄⋊C₄	C₂²	semidirect
19. C₉×C₄⋊Dic₃	C₂²	semidirect
20. C₉×Dic₃⋊C₄	C₂²	semidirect
33. C₂×C₉×C₄⋊C₄	D₃	direct (N × H)
40. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
44. C₂×C₉×Dic₃	C₂×C₄	semidirect
48. C₄×D₃×C₉	C₂×C₄	semidirect
50. C₂×D₃×C₄⋊C₄	C₉	direct (N × H)
77. C₉×C₄⋊C₄	C₂×D₃	direct (N × H)
82. C₂×D₃×C₉	C₄⋊C₄	direct (N × H)
87. C₃×C₄×C₉	C₂²×C₄	semidirect
89. C₉×Dic₃	C₂²×C₄	semidirect
98. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
100. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
101. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
102. D₃×C₄⋊C₄	C₂×C₉	direct (N × H)
135. C₂×C₄×C₉	C₄×D₃	semidirect
139. C₂×C₃×C₉	C₂×C₄⋊C₄	semidirect
143. D₃×C₉	C₂×C₄⋊C₄	direct (N × H)
161. C₂×C₄×D₃	C₄×C₉	semidirect
167. C₃×C₄⋊C₄	C₂²×C₉	semidirect
169. C₄⋊Dic₃	C₂²×C₉	semidirect
170. Dic₃⋊C₄	C₂²×C₉	semidirect
200. C₄×C₉	C₂×C₄×D₃	semidirect
206. C₂×C₄⋊C₄	D₃×C₉	direct (N × H)
207. C₃×C₉	C₂²×C₄⋊C₄	semidirect
231. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
238. C₂×Dic₃	C₂×C₄×C₉	semidirect
242. C₄×D₃	C₂×C₄×C₉	semidirect
253. C₂×C₉	D₃×C₄⋊C₄	direct (N × H)
268. C₄⋊C₄	C₂×D₃×C₉	direct (N × H)
285. C₂×D₃	C₉×C₄⋊C₄	direct (N × H)
295. C₃×C₄	C₂²×C₄×C₉	semidirect
298. Dic₃	C₂²×C₄×C₉	semidirect
301. C₉	C₂×D₃×C₄⋊C₄	direct (N × H)
314. C₂×C₄	C₄×D₃×C₉	semidirect
322. C₂×C₃	C₂×C₉×C₄⋊C₄	semidirect
330. D₃	C₂×C₉×C₄⋊C₄	direct (N × H)
342. C₄	C₂×C₄×D₃×C₉	semidirect
344. C₃	C₂²×C₉×C₄⋊C₄	semidirect
347. C₂	D₃×C₉×C₄⋊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
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₉×Dic₃⋊C₄	2
D₃×C₉×C₄⋊C₄	2
C₂×C₃×D₃×C₄⋊C₄	3
C₂²×C₉×C₄⋊C₄	3

Subgroups — C2×D3×C9×C4⋊C4 #13152413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₉×C₄⋊C₄ #13152413