Subgroups — #10588688⋊C₃ #13142752

Order 1728.

419 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₂×#3667⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×3₋¹⁺²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#63389⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63389⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊(3₋¹⁺²⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	#63362⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5011	—	3	1	no	maximal
9	#10588688	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄×3₋¹⁺²	C₄	1	1	yes	characteristic
11	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
12	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×3₋¹⁺²	C₄	1	1	yes	characteristic
14	C₂²⋊C₄×3₋¹⁺²	C₄	1	1	yes	characteristic
15	C₂²⋊C₄×3₋¹⁺²	C₄	1	1	yes	characteristic
16	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
17	#3667⋊C₃	—	2	2	no	—
18	C₂×3₋¹⁺²⋊C₈	—	2	2	no	—
19	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
23	C₃²×C₄×D₄	D₃	1	1	yes	characteristic
24	C₂×C₃×#208	—	3	1	no	—
25	C₂²×C₃×C₃⋊C₈	—	3	1	no	—
26	C₃×#830	—	3	1	no	—
27	C₃×#830	—	3	1	no	—
28	C₃×C₄⋊(C₃⋊C₈)	—	3	1	no	—
29	C₃×#803	—	3	1	no	—
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	C₂×C₃	1	1	yes	characteristic
32	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	#63389	C₂×C₃	1	1	yes	characteristic, complemented
35	#63389	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄⋊(C₉⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
37	#63362	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
39	C₂³×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
40	D₄×3₋¹⁺²	—	2	2	no	—
41	C₂×C₄×3₋¹⁺²	—	2	1	no	—
42	C₂×C₄×3₋¹⁺²	—	2	1	no	—
43	C₂×C₄×3₋¹⁺²	—	2	1	no	—
44	C₂×C₄×3₋¹⁺²	—	2	1	no	—
45	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
50	3₋¹⁺²⋊C₈	—	2	1	no	—
51	3₋¹⁺²⋊C₈	—	2	1	no	—
52	3₋¹⁺²⋊C₈	—	2	1	no	—
53	3₋¹⁺²⋊C₈	D₄	1	2	yes	complemented
54	C₃×#435	—	9	1	no	—
55	#5011	—	3	1	no	—
56	C₂×C₃²×D₄	Dic₃	1	1	yes	characteristic
57	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
58	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
59	C₃²×C₄⋊C₄	Dic₃	1	1	yes	characteristic
60	C₃²×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
61	C₃²×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
62	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
63	C₃×#208	—	6	2	no	—
64	C₂×C₃×C₃⋊C₈	—	3	1	no	—
65	C₂×C₃×C₃⋊C₈	—	3	1	no	—
66	C₂×C₃×C₃⋊C₈	—	3	1	no	—
67	C₂×C₃×C₃⋊C₈	—	3	1	no	—
68	C₂×C₃×C₃⋊C₈	—	6	2	no	—
69	C₂×D₄×C₉	—	2	1	no	—
70	C₂×D₄×C₉	C₃×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₉	—	2	1	no	—
72	C₂²×C₄×C₉	—	2	1	no	—
73	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
75	C₉×C₄⋊C₄	—	2	1	no	—
76	C₉×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
77	C₉×C₂²⋊C₄	—	2	1	no	—
78	C₉×C₂²⋊C₄	—	2	1	no	—
79	C₉×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
80	C₉×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
81	C₄²×C₉	—	2	1	no	—
82	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
83	#3667	—	2	2	no	—
84	C₂×C₉⋊C₈	—	2	2	no	—
85	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₂²×3₋¹⁺²	—	2	1	no	—
90	C₂²×3₋¹⁺²	—	2	1	no	—
91	C₂²×3₋¹⁺²	—	2	1	no	—
92	C₂²×3₋¹⁺²	—	2	1	no	—
93	C₂²×3₋¹⁺²	—	2	1	no	—
94	C₂²×3₋¹⁺²	M₁₆	1	2	yes	complemented
95	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
96	C₄×3₋¹⁺²	—	2	1	no	—
97	C₄×3₋¹⁺²	—	2	1	no	—
98	C₄×3₋¹⁺²	—	2	1	no	—
99	C₄×3₋¹⁺²	—	2	1	no	—
100	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
101	C₄×3₋¹⁺²	#41	1	1	yes	characteristic
102	C₂×C₃×M₁₆	—	9	1	no	—
103	C₂²×C₃×C₈	—	9	1	no	—
104	C₃×C₄×D₄	—	3	1	no	—
105	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
106	C₂×#208	—	3	1	no	—
107	C₂²×C₃⋊C₈	—	3	1	no	—
108	C₃×C₄⋊C₈	—	9	1	no	—
109	C₃×C₂²⋊C₈	—	9	1	no	—
110	C₃×C₂²⋊C₈	—	9	1	no	—
111	C₃×#97	—	9	1	no	—
112	#830	—	3	1	no	—
113	#830	—	3	1	no	—
114	C₄⋊(C₃⋊C₈)	—	3	1	no	—
115	#803	—	3	1	no	—
116	C₂³×C₃²	C₂×Dic₃	1	1	yes	characteristic
117	C₂³×C₃²	C₂×Dic₃	1	1	yes	characteristic
118	C₃²×D₄	—	2	2	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	—	2	1	no	—
122	C₂×C₃²×C₄	—	2	1	no	—
123	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂³×C₉	—	2	1	no	—
129	C₂³×C₉	—	2	1	no	—
130	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
132	C₃×C₃⋊C₈	—	3	2	no	—
133	C₃×C₃⋊C₈	—	6	1	no	—
134	C₃×C₃⋊C₈	—	6	1	no	—
135	C₃×C₃⋊C₈	—	6	1	no	—
136	D₄×C₉	—	2	4	no	—
137	D₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	4	1	no	—
148	C₂×C₄×C₉	—	4	1	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	—	4	1	no	—
151	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
156	C₉⋊C₈	—	2	1	no	—
157	C₉⋊C₈	—	2	1	no	—
158	C₉⋊C₈	—	2	1	no	—
159	C₉⋊C₈	C₃×D₄	1	2	yes	complemented
160	#435	—	9	1	no	Sylow
161	C₂×3₋¹⁺²	—	2	2	no	—
162	C₂×3₋¹⁺²	—	4	1	no	—
163	C₂×3₋¹⁺²	C₄×D₄	1	1	yes	characteristic
164	C₂×3₋¹⁺²	C₂×M₁₆	1	1	yes	characteristic
165	C₂×3₋¹⁺²	#131	1	1	yes	characteristic
166	C₂×C₃×D₄	—	3	1	no	—
167	C₂×C₃×D₄	C₃×Dic₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	—	3	1	no	—
169	C₂²×C₃×C₄	—	3	1	no	—
170	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
172	C₃×M₁₆	—	18	2	no	—
173	C₂×C₃×C₈	—	9	1	no	—
174	C₂×C₃×C₈	—	9	1	no	—
175	C₂×C₃×C₈	—	9	1	no	—
176	C₂×C₃×C₈	—	9	1	no	—
177	C₂×C₃×C₈	—	18	2	no	—
178	C₃×C₄⋊C₄	—	3	1	no	—
179	C₃×C₄⋊C₄	C₃×Dic₃	1	1	yes	characteristic
180	C₃×C₂²⋊C₄	—	3	1	no	—
181	C₃×C₂²⋊C₄	—	3	1	no	—
182	C₃×C₂²⋊C₄	C₃×Dic₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	C₃×Dic₃	1	1	yes	characteristic
184	C₃×C₄²	—	3	1	no	—
185	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
186	#208	—	6	2	no	—
187	C₂×C₃⋊C₈	—	3	1	no	—
188	C₂×C₃⋊C₈	—	3	1	no	—
189	C₂×C₃⋊C₈	—	3	1	no	—
190	C₂×C₃⋊C₈	—	3	1	no	—
191	C₂×C₃⋊C₈	—	6	2	no	—
192	C₂²×C₃²	—	2	1	no	—
193	C₂²×C₃²	—	2	1	no	—
194	C₂²×C₃²	—	2	1	no	—
195	C₂²×C₃²	—	2	1	no	—
196	C₂²×C₃²	—	2	1	no	—
197	C₂²×C₃²	#208	1	2	yes	—
198	C₂²×C₃²	C₂²×Dic₃	1	1	yes	characteristic
199	C₃²×C₄	—	2	1	no	—
200	C₃²×C₄	—	2	1	no	—
201	C₃²×C₄	—	2	1	no	—
202	C₃²×C₄	—	2	1	no	—
203	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
204	C₃²×C₄	#237	1	1	yes	characteristic
205	C₂²×C₉	—	2	1	no	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	2	1	no	—
211	C₂²×C₉	—	2	2	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	4	1	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	—	4	1	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	C₃×M₁₆	1	2	yes	complemented
218	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
219	C₄×C₉	—	2	2	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	2	1	no	—
223	C₄×C₉	—	2	1	no	—
224	C₄×C₉	—	2	1	no	—
225	C₄×C₉	—	2	1	no	—
226	C₄×C₉	—	4	1	no	—
227	C₄×C₉	—	4	1	no	—
228	C₄×C₉	—	4	1	no	—
229	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
230	C₄×C₉	C₃×#41	1	1	yes	characteristic
231	C₂×M₁₆	—	9	1	no	—
232	C₂²×C₈	—	9	1	no	—
233	C₄×D₄	AGL(1,ℤ/9)	1	1	yes	characteristic
234	C₄⋊C₈	—	9	1	no	—
235	C₂²⋊C₈	—	9	1	no	—
236	C₂²⋊C₈	—	9	1	no	—
237	#97	—	9	1	no	—
238	3₋¹⁺²	#435	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₃	—	3	1	no	—
240	C₂³×C₃	—	3	1	no	—
241	C₂³×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
242	C₂³×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
243	C₃×D₄	—	2	2	no	—
244	C₃×D₄	—	6	2	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	3	1	no	—
250	C₂×C₃×C₄	—	3	1	no	—
251	C₂×C₃×C₄	—	3	1	no	—
252	C₂×C₃×C₄	—	3	1	no	—
253	C₂×C₃×C₄	—	3	1	no	—
254	C₂×C₃×C₄	—	6	1	no	—
255	C₂×C₃×C₄	—	6	1	no	—
256	C₂×C₃×C₄	—	6	1	no	—
257	C₂×C₃×C₄	—	6	1	no	—
258	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
263	C₃×C₈	—	9	2	no	—
264	C₃×C₈	—	18	1	no	—
265	C₃×C₈	—	18	1	no	—
266	C₃×C₈	—	18	1	no	—
267	C₃⋊C₈	—	3	2	no	—
268	C₃⋊C₈	—	6	1	no	—
269	C₃⋊C₈	—	6	1	no	—
270	C₃⋊C₈	—	6	1	no	—
271	C₂×C₃²	—	2	2	no	—
272	C₂×C₃²	—	4	1	no	—
273	C₂×C₃²	C₂×#208	1	1	yes	characteristic
274	C₂×C₃²	D₄×Dic₃	1	1	yes	characteristic
275	C₂×C₃²	#948	1	1	yes	characteristic
276	C₂×C₉	—	2	2	no	—
277	C₂×C₉	—	2	1	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	—	2	1	no	—
280	C₂×C₉	—	4	2	no	—
281	C₂×C₉	—	4	2	no	—
282	C₂×C₉	—	4	1	no	—
283	C₂×C₉	C₃×C₄×D₄	1	1	yes	characteristic
284	C₂×C₉	C₂×C₃×M₁₆	1	1	yes	characteristic
285	C₂×C₉	C₃×#131	1	1	yes	characteristic
286	C₂×D₄	3₋¹⁺²⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
288	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
289	M₁₆	—	18	2	no	—
290	C₂×C₈	—	9	1	no	—
291	C₂×C₈	—	9	1	no	—
292	C₂×C₈	—	9	1	no	—
293	C₂×C₈	—	9	1	no	—
294	C₂×C₈	—	18	2	no	—
295	C₄⋊C₄	3₋¹⁺²⋊C₄	1	1	yes	characteristic
296	C₂²⋊C₄	3₋¹⁺²⋊C₄	1	1	yes	characteristic
297	C₂²⋊C₄	3₋¹⁺²⋊C₄	1	1	yes	characteristic
298	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
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	1	no	—
304	C₂²×C₃	—	3	1	no	—
305	C₂²×C₃	—	3	2	no	—
306	C₂²×C₃	—	6	1	no	—
307	C₂²×C₃	—	6	1	no	—
308	C₂²×C₃	—	6	1	no	—
309	C₂²×C₃	—	6	1	no	—
310	C₂²×C₃	—	6	1	no	—
311	C₂²×C₃	C₃×#208	1	2	yes	—
312	C₂²×C₃	C₂²×C₃×Dic₃	1	1	yes	characteristic
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	3	1	no	—
318	C₃×C₄	—	3	1	no	—
319	C₃×C₄	—	6	1	no	—
320	C₃×C₄	—	6	1	no	—
321	C₃×C₄	—	6	1	no	—
322	C₃×C₄	—	6	1	no	—
323	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
324	C₃×C₄	C₃×#237	1	1	yes	characteristic
325	C₃²	#5011	1	1	yes	characteristic
326	C₉	—	2	1	no	—
327	C₉	C₃×#435	1	1	yes	characteristic, complemented
328	C₂³	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
329	C₂³	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
340	C₈	—	9	2	no	—
341	C₈	—	18	1	no	—
342	C₈	—	18	1	no	—
343	C₈	—	18	1	no	—
344	C₂×C₃	—	2	2	no	—
345	C₂×C₃	—	3	1	no	—
346	C₂×C₃	—	3	1	no	—
347	C₂×C₃	—	3	1	no	—
348	C₂×C₃	—	4	1	no	—
349	C₂×C₃	—	6	2	no	—
350	C₂×C₃	—	12	1	no	—
351	C₂×C₃	C₂×C₃×#208	1	1	yes	characteristic
352	C₂×C₃	C₃×D₄×Dic₃	1	1	yes	characteristic
353	C₂×C₃	C₃×#948	1	1	yes	characteristic
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	#3667⋊C₃	1	2	yes	complemented
360	C₂²	C₂²×3₋¹⁺²⋊C₄	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
366	C₄	#3699⋊C₃	1	1	yes	characteristic
367	C₃	—	3	1	no	—
368	C₃	C₃×#5011	1	1	yes	characteristic
369	C₂	—	2	2	no	—
370	C₂	—	4	1	no	—
371	C₂	C₂×#3667⋊C₃	1	1	yes	characteristic
372	C₂	D₄×3₋¹⁺²⋊C₄	1	1	yes	characteristic
373	C₂	#11721693	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×AGL(1,ℤ/9)
commutator	C₂²×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₄×D₄×3₋¹⁺²	C₂
socle	C₂²×C₃	C₂²×C₃×Dic₃
prime radical	C₂×C₃²×D₄	Dic₃
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	C₄×D₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#435
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#3667⋊C₃	C₂	semidirect
3. C₂²×3₋¹⁺²⋊C₈	C₂	semidirect
4. #63389⋊C₃	C₂	semidirect
5. #63389⋊C₃	C₂	semidirect
6. C₄⋊(3₋¹⁺²⋊C₈)	C₂	semidirect
7. #63362⋊C₃	C₂	semidirect
9. #10588688	C₃	semidirect
32. C₂×#3667	C₂×C₃	semidirect
33. C₂²×C₉⋊C₈	C₂×C₃	semidirect
34. #63389	C₂×C₃	semidirect
35. #63389	C₂×C₃	semidirect
36. C₄⋊(C₉⋊C₈)	C₂×C₃	semidirect
37. #63362	C₂×C₃	semidirect
53. 3₋¹⁺²⋊C₈	D₄	semidirect
94. C₂²×3₋¹⁺²	M₁₆	semidirect
159. C₉⋊C₈	C₃×D₄	semidirect
217. C₂²×C₉	C₃×M₁₆	semidirect
238. 3₋¹⁺²	#435	semidirect
327. C₉	C₃×#435	semidirect
359. C₂²	#3667⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×3₋¹⁺²	2
C₂×#3667⋊C₃	2
C₂²×3₋¹⁺²⋊C₈	2
#63389⋊C₃	2
C₄⋊(3₋¹⁺²⋊C₈)	2
#63362⋊C₃	2
C₃×#5011	3
#10588688	3

Subgroups — #10588688⋊C3 #13142752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588688⋊C₃ #13142752