Subgroups — C₉×Dic₃×C₄⋊C₄ #13142565

Order 1728.

674 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₉×Dic₃	C₂	1	2	yes	maximal
4	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₉×C₃⋊#95	C₂	1	2	yes	maximal
6	C₃×Dic₃×C₄⋊C₄	C₃	1	1	yes	maximal, characteristic
7	C₄×C₉×C₄⋊C₄	—	3	1	no	maximal
8	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
9	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
11	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
12	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
13	C₃×C₉×C₄⋊C₄	C₄	1	4	yes	complemented
14	C₉×C₄⋊Dic₃	C₄	1	4	yes	complemented
15	C₄×C₉×Dic₃	—	2	4	no	—
16	C₄×C₉×Dic₃	C₄	1	4	yes	complemented
17	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×C₄×Dic₃	C₂×C₃	1	2	yes	—
20	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
21	C₃×C₃⋊#95	C₂×C₃	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	—	2	1	no	—
23	C₂×C₉×C₄⋊C₄	—	3	1	no	—
24	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic
25	C₂×C₄²×C₉	—	3	1	no	—
26	C₂×C₄²×C₉	—	3	2	no	—
27	C₉×#95	—	3	2	no	—
28	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
29	C₂×C₃×C₄×C₉	—	2	2	no	—
30	C₂×C₃×C₄×C₉	—	2	2	no	—
31	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	—
32	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
33	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
35	C₂×C₉×Dic₃	—	2	2	no	—
36	C₂×C₉×Dic₃	—	2	1	no	—
37	C₂×C₉×Dic₃	—	2	1	no	—
38	C₂×C₉×Dic₃	—	2	2	no	—
39	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
40	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	—
41	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
42	C₂×C₉×Dic₃	D₄	1	2	yes	—
43	C₂×C₉×Dic₃	Q₈	1	2	yes	—
44	C₃×C₄×C₄⋊C₄	—	3	1	no	—
45	Dic₃×C₄⋊C₄	C₉	1	1	yes	characteristic, direct product factor
46	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
47	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
49	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
51	C₃²×C₄⋊C₄	C₃×C₄	1	4	yes	—
52	C₃×C₄⋊Dic₃	C₃×C₄	1	4	yes	—
53	C₃×C₄×Dic₃	—	2	4	no	—
54	C₃×C₄×Dic₃	C₃×C₄	1	4	yes	—
55	C₂²×C₄×C₉	—	2	1	no	—
56	C₂²×C₄×C₉	—	2	2	no	—
57	C₂²×C₄×C₉	—	3	1	no	—
58	C₂²×C₄×C₉	—	3	2	no	—
59	C₂²×C₄×C₉	—	3	1	no	—
60	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
61	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
62	C₉×C₄⋊C₄	—	2	4	no	—
63	C₉×C₄⋊C₄	—	3	4	no	—
64	C₉×C₄⋊C₄	Dic₃	1	4	yes	direct product factor
65	C₄²×C₉	—	3	4	no	—
66	C₄²×C₉	—	6	4	no	—
67	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₃×C₉	#41	1	1	yes	characteristic
73	C₂²×C₃×C₉	#41	1	1	yes	characteristic
74	C₃×C₄×C₉	—	2	4	no	—
75	C₃×C₄×C₉	C₄²	1	4	yes	complemented
76	C₉×Dic₃	—	2	2	no	—
77	C₉×Dic₃	—	2	4	no	—
78	C₉×Dic₃	C₄⋊C₄	1	4	yes	direct product factor
79	C₂×C₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₃×C₄⋊C₄	—	3	1	no	—
81	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
82	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
83	C₂×C₃×C₄²	—	3	1	no	—
84	C₂×C₃×C₄²	—	3	2	no	—
85	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic
86	C₂×C₄×Dic₃	C₂×C₉	1	2	yes	—
87	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic
88	C₃×#95	—	3	2	no	—
89	C₃⋊#95	C₂×C₉	1	2	yes	—
90	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
91	C₂×C₃²×C₄	—	2	2	no	—
92	C₂×C₃²×C₄	—	2	2	no	—
93	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
94	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
95	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
96	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
97	C₂×C₃×Dic₃	—	2	2	no	—
98	C₂×C₃×Dic₃	—	2	1	no	—
99	C₂×C₃×Dic₃	—	2	1	no	—
100	C₂×C₃×Dic₃	—	2	2	no	—
101	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
102	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
103	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
104	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
105	C₂×C₃×Dic₃	C₃×Q₈	1	2	yes	—
106	C₂³×C₉	—	2	1	no	—
107	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
108	C₂×C₄×C₉	—	2	2	no	—
109	C₂×C₄×C₉	—	2	2	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	2	no	—
113	C₂×C₄×C₉	—	2	4	no	—
114	C₂×C₄×C₉	—	3	2	no	—
115	C₂×C₄×C₉	—	3	2	no	—
116	C₂×C₄×C₉	—	3	2	no	—
117	C₂×C₄×C₉	—	3	2	no	—
118	C₂×C₄×C₉	—	3	4	no	—
119	C₂×C₄×C₉	—	4	2	no	—
120	C₂×C₄×C₉	—	4	2	no	—
121	C₂×C₄×C₉	—	6	2	no	—
122	C₂×C₄×C₉	—	6	1	no	—
123	C₂×C₄×C₉	—	6	1	no	—
124	C₂×C₄×C₉	—	6	2	no	—
125	C₂×C₄×C₉	C₄×D₃	1	2	yes	—
126	C₂×C₄×C₉	C₄×D₃	1	2	yes	—
127	C₂×C₄×C₉	C₂×Dic₃	1	4	yes	—
128	C₂×C₄×C₉	C₂×Dic₃	1	2	yes	—
129	C₄×C₄⋊C₄	—	3	1	no	Sylow
130	C₂×C₃×C₉	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₃×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₃×C₉	#117	1	1	yes	characteristic
133	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
134	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₃×C₉	C₄×Q₈	1	1	yes	characteristic
136	C₂×C₃×C₉	C₄×Q₈	1	1	yes	characteristic
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	—	3	1	no	—
140	C₂²×C₃×C₄	—	3	1	no	—
141	C₂²×C₃×C₄	—	3	2	no	—
142	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
143	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
145	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
146	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
147	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
148	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
149	C₃×C₄⋊C₄	—	2	4	no	—
150	C₃×C₄⋊C₄	—	3	4	no	—
151	C₃×C₄⋊C₄	C₄×C₉	1	4	yes	complemented
152	C₃×C₄⋊C₄	C₃×Dic₃	1	4	yes	—
153	C₃×C₄²	—	3	4	no	—
154	C₃×C₄²	—	6	4	no	—
155	C₄⋊Dic₃	C₄×C₉	1	4	yes	complemented
156	C₄×Dic₃	—	2	4	no	—
157	C₄×Dic₃	C₄×C₉	1	4	yes	complemented
158	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
159	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
160	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
161	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
162	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
163	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
164	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
165	C₃²×C₄	—	2	4	no	—
166	C₃²×C₄	C₃×C₄²	1	4	yes	—
167	C₃×Dic₃	—	2	2	no	—
168	C₃×Dic₃	—	2	4	no	—
169	C₃×Dic₃	C₃×C₄⋊C₄	1	4	yes	—
170	C₂²×C₉	—	2	1	no	—
171	C₂²×C₉	—	2	1	no	—
172	C₂²×C₉	—	2	1	no	—
173	C₂²×C₉	—	2	1	no	—
174	C₂²×C₉	—	2	1	no	—
175	C₂²×C₉	—	2	1	no	—
176	C₂²×C₉	—	2	1	no	—
177	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
178	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
179	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
180	C₂²×C₉	#237	1	1	yes	characteristic
181	C₂²×C₉	D₃×Q₈	1	1	yes	characteristic
182	C₂²×C₉	#239	1	1	yes	characteristic
183	C₂²×C₉	C₂²×Dic₃	1	1	yes	characteristic
184	C₄×C₉	—	2	4	no	—
185	C₄×C₉	—	2	4	no	—
186	C₄×C₉	—	3	4	no	—
187	C₄×C₉	—	4	4	no	—
188	C₄×C₉	—	6	2	no	—
189	C₄×C₉	—	6	4	no	—
190	C₄×C₉	C₄×Dic₃	1	4	yes	complemented
191	C₂×C₄⋊C₄	—	3	1	no	—
192	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic
193	C₂×C₄²	—	3	1	no	—
194	C₂×C₄²	—	3	2	no	—
195	#95	—	3	2	no	—
196	C₃×C₉	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
197	C₂³×C₃	—	2	1	no	—
198	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
199	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
200	C₂×C₃×C₄	—	2	2	no	—
201	C₂×C₃×C₄	—	2	2	no	—
202	C₂×C₃×C₄	—	2	2	no	—
203	C₂×C₃×C₄	—	2	2	no	—
204	C₂×C₃×C₄	—	2	2	no	—
205	C₂×C₃×C₄	—	2	2	no	—
206	C₂×C₃×C₄	—	2	2	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	3	2	no	—
209	C₂×C₃×C₄	—	3	2	no	—
210	C₂×C₃×C₄	—	3	2	no	—
211	C₂×C₃×C₄	—	3	2	no	—
212	C₂×C₃×C₄	—	3	4	no	—
213	C₂×C₃×C₄	—	4	2	no	—
214	C₂×C₃×C₄	—	4	2	no	—
215	C₂×C₃×C₄	—	6	2	no	—
216	C₂×C₃×C₄	—	6	1	no	—
217	C₂×C₃×C₄	—	6	1	no	—
218	C₂×C₃×C₄	—	6	2	no	—
219	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
220	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
221	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	—
222	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
223	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
224	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
225	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
226	C₂×C₃×C₄	C₂×C₃×Dic₃	1	2	yes	—
227	C₂×Dic₃	—	2	2	no	—
228	C₂×Dic₃	—	2	1	no	—
229	C₂×Dic₃	—	2	1	no	—
230	C₂×Dic₃	—	2	2	no	—
231	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
232	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	—
233	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
234	C₂×Dic₃	D₄×C₉	1	2	yes	—
235	C₂×Dic₃	Q₈×C₉	1	2	yes	—
236	C₂×C₃²	C₂×C₃×C₄²	1	1	yes	characteristic
237	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₃²	C₃×#117	1	1	yes	characteristic
239	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
240	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
241	C₂×C₃²	C₃×C₄×Q₈	1	1	yes	characteristic
242	C₂×C₃²	C₃×C₄×Q₈	1	1	yes	characteristic
243	C₂×C₉	—	2	1	no	—
244	C₂×C₉	—	2	1	no	—
245	C₂×C₉	—	2	1	no	—
246	C₂×C₉	—	2	1	no	—
247	C₂×C₉	—	2	1	no	—
248	C₂×C₉	—	2	1	no	—
249	C₂×C₉	—	2	1	no	—
250	C₂×C₉	#887	1	1	yes	characteristic
251	C₂×C₉	D₃×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₉	#892	1	1	yes	characteristic
253	C₂×C₉	#893	1	1	yes	characteristic
254	C₂×C₉	C₂×C₄×Dic₃	1	1	yes	characteristic
255	C₂×C₉	D₄×Dic₃	1	1	yes	characteristic
256	C₂×C₉	Q₈×Dic₃	1	1	yes	characteristic
257	C₂²×C₄	—	3	1	no	—
258	C₂²×C₄	—	3	1	no	—
259	C₂²×C₄	—	3	2	no	—
260	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
261	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
262	C₄⋊C₄	—	3	4	no	—
263	C₄⋊C₄	C₉×Dic₃	1	4	yes	direct product factor
264	C₄²	—	3	4	no	—
265	C₄²	—	6	4	no	—
266	C₂²×C₃	—	2	1	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
274	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
275	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
276	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
277	C₂²×C₃	C₂×Q₈×C₉	1	1	yes	characteristic
278	C₂²×C₃	C₉×#41	1	1	yes	characteristic
279	C₂²×C₃	C₉×#41	1	1	yes	characteristic
280	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
282	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
283	C₂²×C₃	C₃×#237	1	1	yes	characteristic
284	C₂²×C₃	C₃×D₃×Q₈	1	1	yes	characteristic
285	C₂²×C₃	C₃×#239	1	1	yes	characteristic
286	C₂²×C₃	C₂²×C₃×Dic₃	1	1	yes	characteristic
287	C₃×C₄	—	2	4	no	—
288	C₃×C₄	—	2	4	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	3	4	no	—
291	C₃×C₄	—	4	4	no	—
292	C₃×C₄	—	6	2	no	—
293	C₃×C₄	—	6	4	no	—
294	C₃×C₄	C₄²×C₉	1	4	yes	complemented
295	C₃×C₄	C₃×C₄×Dic₃	1	4	yes	—
296	Dic₃	—	2	2	no	—
297	Dic₃	—	2	4	no	—
298	Dic₃	C₉×C₄⋊C₄	1	4	yes	direct product factor
299	C₃²	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
300	C₉	—	2	1	no	—
301	C₉	Dic₃×C₄⋊C₄	1	1	yes	characteristic, direct product factor
302	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	3	2	no	—
306	C₂×C₄	—	3	2	no	—
307	C₂×C₄	—	3	2	no	—
308	C₂×C₄	—	3	2	no	—
309	C₂×C₄	—	3	4	no	—
310	C₂×C₄	—	6	2	no	—
311	C₂×C₄	—	6	1	no	—
312	C₂×C₄	—	6	1	no	—
313	C₂×C₄	—	6	2	no	—
314	C₂×C₄	C₄×D₃×C₉	1	2	yes	—
315	C₂×C₄	C₄×D₃×C₉	1	2	yes	—
316	C₂×C₄	C₂×C₉×Dic₃	1	4	yes	—
317	C₂×C₄	C₂×C₉×Dic₃	1	2	yes	—
318	C₂×C₃	—	2	1	no	—
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	—	2	1	no	—
322	C₂×C₃	—	2	1	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	C₂×C₄²×C₉	1	1	yes	characteristic
326	C₂×C₃	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₃	C₉×#117	1	1	yes	characteristic
328	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
329	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
330	C₂×C₃	C₄×Q₈×C₉	1	1	yes	characteristic
331	C₂×C₃	C₄×Q₈×C₉	1	1	yes	characteristic
332	C₂×C₃	C₃×#887	1	1	yes	characteristic
333	C₂×C₃	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
334	C₂×C₃	C₃×#892	1	1	yes	characteristic
335	C₂×C₃	C₃×#893	1	1	yes	characteristic
336	C₂×C₃	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
337	C₂×C₃	C₃×D₄×Dic₃	1	1	yes	characteristic
338	C₂×C₃	C₃×Q₈×Dic₃	1	1	yes	characteristic
339	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
340	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
341	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
342	C₂²	C₉×#237	1	1	yes	characteristic
343	C₂²	D₃×Q₈×C₉	1	1	yes	characteristic
344	C₂²	C₉×#239	1	1	yes	characteristic
345	C₂²	C₂²×C₉×Dic₃	1	1	yes	characteristic
346	C₄	—	2	4	no	—
347	C₄	—	3	4	no	—
348	C₄	—	6	2	no	—
349	C₄	—	6	4	no	—
350	C₄	C₄×C₉×Dic₃	1	4	yes	complemented
351	C₃	—	2	1	no	—
352	C₃	C₄×C₉×C₄⋊C₄	1	1	yes	characteristic, complemented
353	C₃	C₃×Dic₃×C₄⋊C₄	1	1	yes	characteristic
354	C₂	C₉×#887	1	1	yes	characteristic
355	C₂	D₃×C₉×C₄⋊C₄	1	1	yes	characteristic
356	C₂	C₉×#892	1	1	yes	characteristic
357	C₂	C₉×#893	1	1	yes	characteristic
358	C₂	C₂×C₄×C₉×Dic₃	1	1	yes	characteristic
359	C₂	D₄×C₉×Dic₃	1	1	yes	characteristic
360	C₂	Q₈×C₉×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂×C₃	C₂×C₄²×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle, prime radical, cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₄×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
13. C₃×C₉×C₄⋊C₄	C₄	semidirect
14. C₉×C₄⋊Dic₃	C₄	semidirect
16. C₄×C₉×Dic₃	C₄	semidirect
45. Dic₃×C₄⋊C₄	C₉	direct (N × H)
64. C₉×C₄⋊C₄	Dic₃	direct (N × H)
75. C₃×C₄×C₉	C₄²	semidirect
78. C₉×Dic₃	C₄⋊C₄	direct (N × H)
151. C₃×C₄⋊C₄	C₄×C₉	semidirect
155. C₄⋊Dic₃	C₄×C₉	semidirect
157. C₄×Dic₃	C₄×C₉	semidirect
190. C₄×C₉	C₄×Dic₃	semidirect
196. C₃×C₉	C₄×C₄⋊C₄	semidirect
263. C₄⋊C₄	C₉×Dic₃	direct (N × H)
294. C₃×C₄	C₄²×C₉	semidirect
298. Dic₃	C₉×C₄⋊C₄	direct (N × H)
301. C₉	Dic₃×C₄⋊C₄	direct (N × H)
350. C₄	C₄×C₉×Dic₃	semidirect
352. C₃	C₄×C₉×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₄×C₉×Dic₃	2
C₉×C₃⋊#95	2
C₃×Dic₃×C₄⋊C₄	3
C₄×C₉×C₄⋊C₄	3

Subgroups — C9×Dic3×C4⋊C4 #13142565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₃×C₄⋊C₄ #13142565