Subgroups — #10589847⋊C₃ #13153395

Order 1728.

808 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3697⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#3667⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63469⋊C₃	C₂	1	4	yes	maximal, complemented
5	M₁₆×AGL(1,ℤ/9)	C₂	1	4	yes	maximal, complemented
6	#63464⋊C₃	C₂	1	4	yes	maximal, complemented
7	C₃×#5745	—	3	1	no	maximal
8	#10589847	C₃	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
10	C₂×#611⋊C₃	C₄	1	2	yes	—
11	#3697⋊C₃	C₄	1	2	yes	—
12	#3697⋊C₃	C₄	1	2	yes	—
13	#3697⋊C₃	C₂²	1	2	yes	—
14	#3697⋊C₃	C₂²	1	2	yes	—
15	C₂×C₄⋊AGL(1,ℤ/9)	C₄	1	1	yes	characteristic
16	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
17	C₂×3₋¹⁺²⋊Q₈	C₄	1	1	yes	characteristic
18	M₁₆×3₋¹⁺²	C₂²	1	2	yes	—
19	M₁₆×3₋¹⁺²	C₂²	1	2	yes	complemented
20	C₂×C₈×3₋¹⁺²	C₂²	1	2	yes	complemented
21	#3667⋊C₃	C₂²	1	2	yes	—
22	#3667⋊C₃	C₂²	1	2	yes	complemented
23	C₂×3₋¹⁺²⋊C₈	C₂²	1	2	yes	complemented
24	#3663⋊C₃	C₂²	1	8	yes	complemented
25	C₈×AGL(1,ℤ/9)	C₂²	1	8	yes	complemented
26	C₂×C₃×#235	—	3	1	no	—
27	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic
28	C₂×C₃×#208	—	3	1	no	—
29	C₃×#907	—	3	4	no	—
30	C₃×D₃×M₁₆	—	3	4	no	—
31	C₃×#901	—	3	4	no	—
32	C₂×#3697	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×M₁₆	—	2	1	no	—
34	C₂×C₉×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
36	#63469	C₂×C₃	1	4	yes	complemented
37	M₁₆×D₉	C₂×C₃	1	4	yes	complemented
38	#63464	C₂×C₃	1	4	yes	complemented
39	C₂³×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
40	C₂²×AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
41	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
45	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
46	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
47	#611⋊C₃	C₂×C₄	1	4	yes	—
48	#611⋊C₃	C₂×C₄	1	4	yes	—
49	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	2	yes	—
50	C₄⋊AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
51	C₄⋊AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
52	C₄×AGL(1,ℤ/9)	C₂×C₄	1	4	yes	—
53	C₄×AGL(1,ℤ/9)	C₂³	1	4	yes	—
54	3₋¹⁺²⋊Q₈	C₂×C₄	1	2	yes	—
55	3₋¹⁺²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₈×3₋¹⁺²	C₂³	1	4	yes	—
57	3₋¹⁺²⋊C₈	C₂³	1	4	yes	—
58	C₃×#568	—	9	1	no	—
59	#5745	—	3	1	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃×#67	—	3	2	no	—
62	C₃×#235	—	3	2	no	—
63	C₃×#235	—	3	2	no	—
64	C₃×#235	—	3	2	no	—
65	C₃×#235	—	3	2	no	—
66	C₂×C₃×D₁₂	—	3	1	no	—
67	C₂×C₃×C₄×D₃	—	3	2	no	—
68	C₂×C₃×Dic₆	—	3	1	no	—
69	C₃²×M₁₆	C₂×D₃	1	2	yes	—
70	C₃²×M₁₆	C₂×D₃	1	2	yes	—
71	C₂×C₃²×C₈	C₂×D₃	1	2	yes	—
72	C₃×#208	—	3	2	no	—
73	C₃×#208	—	3	2	no	—
74	C₂×C₃×C₃⋊C₈	—	3	2	no	—
75	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
76	C₃×D₃×C₈	—	3	8	no	—
77	C₂²×C₄×C₉	—	2	1	no	—
78	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
79	C₂×#611	C₃×C₄	1	2	yes	—
80	#3697	C₃×C₄	1	2	yes	—
81	#3697	C₃×C₄	1	2	yes	—
82	#3697	C₂²×C₃	1	2	yes	—
83	#3697	C₂²×C₃	1	2	yes	—
84	C₂×D₃₆	C₃×C₄	1	1	yes	characteristic
85	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
86	C₂×Dic₁₈	C₃×C₄	1	1	yes	characteristic
87	C₉×M₁₆	—	2	2	no	—
88	C₉×M₁₆	—	2	2	no	—
89	C₉×M₁₆	C₂²×C₃	1	2	yes	—
90	C₉×M₁₆	C₂²×C₃	1	2	yes	complemented
91	C₂×C₈×C₉	—	2	2	no	—
92	C₂×C₈×C₉	C₂²×C₃	1	2	yes	complemented
93	#3667	C₂²×C₃	1	2	yes	—
94	#3667	C₂²×C₃	1	2	yes	complemented
95	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	complemented
96	#3663	C₂²×C₃	1	8	yes	complemented
97	C₈×D₉	C₂²×C₃	1	8	yes	complemented
98	C₂²×3₋¹⁺²	—	4	1	no	—
99	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
100	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
101	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
102	C₂×AGL(1,ℤ/9)	—	4	2	no	—
103	C₂×AGL(1,ℤ/9)	C₂²×C₄	1	4	yes	—
104	C₄×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
105	C₄×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
106	C₄×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
107	C₄×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
108	3₋¹⁺²⋊C₄	C₂²×C₄	1	4	yes	—
109	C₂×C₃×#41	—	9	1	no	—
110	C₂×#235	—	3	1	no	—
111	C₃×#131	—	9	4	no	—
112	C₃×#131	—	9	4	no	—
113	C₂×C₃×M₁₆	—	3	1	no	—
114	C₂×C₃×M₁₆	—	9	4	no	—
115	C₂×C₃×M₁₆	—	9	1	no	—
116	C₂×C₃×M₁₆	C₃×D₃	1	1	yes	characteristic
117	C₂×#208	—	3	1	no	—
118	#907	—	3	4	no	—
119	D₃×M₁₆	—	3	4	no	—
120	#901	—	3	4	no	—
121	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
122	C₂²×C₃×D₃	—	3	2	no	—
123	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₃×#67	—	3	4	no	—
130	C₃×#67	—	3	4	no	—
131	C₂×C₃×Dic₃	—	3	2	no	—
132	C₃×D₁₂	—	3	2	no	—
133	C₃×D₁₂	—	3	2	no	—
134	C₃×C₄×D₃	—	3	4	no	—
135	C₃×C₄×D₃	—	3	4	no	—
136	C₃×Dic₆	—	3	2	no	—
137	C₃×Dic₆	—	3	2	no	—
138	C₂³×C₉	—	2	1	no	—
139	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂²×D₉	C₂×C₃×C₄	1	2	yes	—
141	C₃²×C₈	C₂²×D₃	1	4	yes	—
142	C₃×C₃⋊C₈	—	3	4	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	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
155	#611	C₂×C₃×C₄	1	4	yes	—
156	#611	C₂×C₃×C₄	1	4	yes	—
157	C₂×Dic₉	C₂×C₃×C₄	1	2	yes	—
158	D₃₆	C₂×C₃×C₄	1	2	yes	—
159	D₃₆	C₂×C₃×C₄	1	2	yes	—
160	C₄×D₉	C₂×C₃×C₄	1	4	yes	—
161	C₄×D₉	C₂³×C₃	1	4	yes	—
162	Dic₁₈	C₂×C₃×C₄	1	2	yes	—
163	Dic₁₈	C₂×C₃×C₄	1	2	yes	—
164	C₈×C₉	—	2	4	no	—
165	C₈×C₉	C₂³×C₃	1	4	yes	—
166	C₉⋊C₈	C₂³×C₃	1	4	yes	—
167	#568	—	9	1	no	Sylow
168	C₂×3₋¹⁺²	—	2	1	no	—
169	C₂×3₋¹⁺²	—	2	1	no	—
170	C₂×3₋¹⁺²	—	2	1	no	—
171	C₂×3₋¹⁺²	C₂³×C₄	1	1	yes	characteristic
172	AGL(1,ℤ/9)	—	2	4	no	—
173	C₃×#41	—	9	2	no	—
174	C₃×#41	—	9	2	no	—
175	C₃×#41	—	9	2	no	—
176	C₃×#41	—	9	2	no	—
177	C₂×C₃×Q₈	—	9	1	no	—
178	C₂×C₃×D₄	—	9	1	no	—
179	C₂×C₃×D₄	—	9	2	no	—
180	C₂²×C₃×C₄	—	3	1	no	—
181	C₂²×C₃×C₄	—	9	2	no	—
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂×#67	—	3	2	no	—
184	#235	—	3	2	no	—
185	#235	—	3	2	no	—
186	#235	—	3	2	no	—
187	#235	—	3	2	no	—
188	C₂×D₁₂	—	3	1	no	—
189	C₂×C₄×D₃	—	3	2	no	—
190	C₂×Dic₆	—	3	1	no	—
191	C₃×M₁₆	—	3	2	no	—
192	C₃×M₁₆	—	3	2	no	—
193	C₃×M₁₆	—	9	8	no	—
194	C₃×M₁₆	—	9	2	no	—
195	C₃×M₁₆	—	9	2	no	—
196	C₃×M₁₆	C₂×C₃×D₃	1	2	yes	—
197	C₃×M₁₆	C₂×C₃×D₃	1	2	yes	—
198	C₂×C₃×C₈	—	3	2	no	—
199	C₂×C₃×C₈	—	9	8	no	—
200	C₂×C₃×C₈	—	9	2	no	—
201	C₂×C₃×C₈	C₂×C₃×D₃	1	2	yes	—
202	#208	—	3	2	no	—
203	#208	—	3	2	no	—
204	C₂×C₃⋊C₈	—	3	2	no	—
205	ΓL(1,𝔽₂₅)	—	3	8	no	—
206	D₃×C₈	—	3	8	no	—
207	C₂²×C₃²	—	4	1	no	—
208	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
209	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
210	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
211	C₂×C₃×D₃	—	3	4	no	—
212	C₂×C₃×D₃	—	12	2	no	—
213	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
214	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
215	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
216	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
217	C₃×Dic₃	—	3	4	no	—
218	C₂²×C₉	—	2	1	no	—
219	C₂²×C₉	—	2	1	no	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	4	1	no	—
222	C₂²×C₉	—	4	2	no	—
223	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
226	C₂×D₉	—	4	2	no	—
227	C₂×D₉	C₂²×C₃×C₄	1	4	yes	—
228	C₄×C₉	—	2	1	no	—
229	C₄×C₉	—	2	1	no	—
230	C₄×C₉	—	2	1	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
233	C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
235	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
236	Dic₉	C₂²×C₃×C₄	1	4	yes	—
237	C₂×#41	—	9	1	no	—
238	#131	—	9	4	no	—
239	#131	—	9	4	no	—
240	C₂×M₁₆	—	9	1	no	—
241	C₂×M₁₆	—	9	4	no	—
242	C₂×M₁₆	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
243	3₋¹⁺²	#568	1	1	yes	characteristic, complemented, Sylow
244	C₂³×C₃	—	3	1	no	—
245	C₂³×C₃	—	9	2	no	—
246	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
247	C₂²×D₃	—	3	2	no	—
248	C₃×Q₈	—	9	2	no	—
249	C₃×Q₈	—	9	2	no	—
250	C₃×D₄	—	9	2	no	—
251	C₃×D₄	—	9	2	no	—
252	C₃×D₄	—	9	4	no	—
253	C₃×D₄	—	9	4	no	—
254	C₂×C₃×C₄	—	3	1	no	—
255	C₂×C₃×C₄	—	3	1	no	—
256	C₂×C₃×C₄	—	3	1	no	—
257	C₂×C₃×C₄	—	3	1	no	—
258	C₂×C₃×C₄	—	3	1	no	—
259	C₂×C₃×C₄	—	3	1	no	—
260	C₂×C₃×C₄	—	9	4	no	—
261	C₂×C₃×C₄	—	9	4	no	—
262	C₂×C₃×C₄	—	9	2	no	—
263	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
264	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
265	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
269	#67	—	3	4	no	—
270	#67	—	3	4	no	—
271	C₂×Dic₃	—	3	2	no	—
272	D₁₂	—	3	2	no	—
273	D₁₂	—	3	2	no	—
274	C₄×D₃	—	3	4	no	—
275	C₄×D₃	—	3	4	no	—
276	Dic₆	—	3	2	no	—
277	Dic₆	—	3	2	no	—
278	C₃×C₈	—	3	4	no	—
279	C₃×C₈	—	9	4	no	—
280	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
281	C₃⋊C₈	—	3	4	no	—
282	C₂×C₃²	—	2	1	no	—
283	C₂×C₃²	—	2	1	no	—
284	C₂×C₃²	—	2	1	no	—
285	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
286	C₃×D₃	—	6	4	no	—
287	C₂×C₉	—	2	2	no	—
288	C₂×C₉	—	2	1	no	—
289	C₂×C₉	—	2	1	no	—
290	C₂×C₉	—	2	1	no	—
291	C₂×C₉	—	2	1	no	—
292	C₂×C₉	—	4	1	no	—
293	C₂×C₉	—	4	1	no	—
294	C₂×C₉	C₂³×C₃×C₄	1	1	yes	characteristic
295	D₉	—	2	4	no	—
296	#41	—	9	2	no	—
297	#41	—	9	2	no	—
298	#41	—	9	2	no	—
299	#41	—	9	2	no	—
300	C₂×Q₈	—	9	1	no	—
301	C₂×D₄	—	9	2	no	—
302	C₂×D₄	—	9	1	no	—
303	C₂²×C₄	—	9	2	no	—
304	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
305	M₁₆	—	9	2	no	—
306	M₁₆	—	9	2	no	—
307	M₁₆	—	9	8	no	—
308	M₁₆	C₂×AGL(1,ℤ/9)	1	2	yes	—
309	M₁₆	C₂×AGL(1,ℤ/9)	1	2	yes	complemented
310	C₂×C₈	—	9	2	no	—
311	C₂×C₈	—	9	8	no	—
312	C₂×C₈	C₂×AGL(1,ℤ/9)	1	2	yes	complemented
313	C₂²×C₃	—	3	1	no	—
314	C₂²×C₃	—	3	1	no	—
315	C₂²×C₃	—	3	1	no	—
316	C₂²×C₃	—	4	1	no	—
317	C₂²×C₃	—	9	4	no	—
318	C₂²×C₃	—	12	1	no	—
319	C₂²×C₃	—	36	2	no	—
320	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
321	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
323	C₂×D₃	—	3	4	no	—
324	C₂×D₃	—	12	2	no	—
325	C₃×C₄	—	3	1	no	—
326	C₃×C₄	—	3	1	no	—
327	C₃×C₄	—	3	1	no	—
328	C₃×C₄	—	3	1	no	—
329	C₃×C₄	—	9	4	no	—
330	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
331	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
332	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
333	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
334	Dic₃	—	3	4	no	—
335	C₃²	#5745	1	1	yes	characteristic
336	C₉	—	2	1	no	—
337	C₉	C₃×#568	1	1	yes	characteristic, complemented
338	C₂³	—	9	2	no	—
339	C₂³	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
340	Q₈	—	9	2	no	—
341	Q₈	—	9	2	no	—
342	D₄	—	9	4	no	—
343	D₄	—	9	4	no	—
344	D₄	—	9	2	no	—
345	D₄	—	9	2	no	—
346	C₂×C₄	—	9	2	no	—
347	C₂×C₄	—	9	4	no	—
348	C₂×C₄	—	9	4	no	—
349	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
350	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
351	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
352	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
353	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
354	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
355	C₈	—	9	4	no	—
356	C₈	C₂²×AGL(1,ℤ/9)	1	4	yes	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	3	1	no	—
361	C₂×C₃	—	6	1	no	—
362	C₂×C₃	—	6	1	no	—
363	C₂×C₃	—	6	1	no	—
364	C₂×C₃	—	18	4	no	—
365	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
366	D₃	—	6	4	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	9	4	no	—
369	C₂²	—	36	2	no	—
370	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
371	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
372	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
373	C₄	—	9	4	no	—
374	C₄	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
375	C₄	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
376	C₄	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
377	C₄	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
378	C₃	—	3	1	no	—
379	C₃	C₃×#5745	1	1	yes	characteristic
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	18	4	no	—
384	C₂	C₂²×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂³×AGL(1,ℤ/9)
commutator	C₂×C₉	C₂³×C₃×C₄
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×M₁₆×3₋¹⁺²	C₂
socle	C₂×C₃	C₂²×C₃×C₄×D₃
prime radical	C₂×#3697⋊C₃	C₂
cosocle	C₄×C₉	C₂⁴×C₃
hypercenter	C₂×M₁₆	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#568
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×3₋¹⁺²	C₂	semidirect
3. C₂×#3667⋊C₃	C₂	semidirect
4. #63469⋊C₃	C₂	semidirect
5. M₁₆×AGL(1,ℤ/9)	C₂	semidirect
6. #63464⋊C₃	C₂	semidirect
8. #10589847	C₃	semidirect
19. M₁₆×3₋¹⁺²	C₂²	semidirect
20. C₂×C₈×3₋¹⁺²	C₂²	semidirect
22. #3667⋊C₃	C₂²	semidirect
23. C₂×3₋¹⁺²⋊C₈	C₂²	semidirect
24. #3663⋊C₃	C₂²	semidirect
25. C₈×AGL(1,ℤ/9)	C₂²	semidirect
34. C₂×C₉×M₁₆	C₂×C₃	semidirect
35. C₂×#3667	C₂×C₃	semidirect
36. #63469	C₂×C₃	semidirect
37. M₁₆×D₉	C₂×C₃	semidirect
38. #63464	C₂×C₃	semidirect
90. C₉×M₁₆	C₂²×C₃	semidirect
92. C₂×C₈×C₉	C₂²×C₃	semidirect
94. #3667	C₂²×C₃	semidirect
95. C₂×C₉⋊C₈	C₂²×C₃	semidirect
96. #3663	C₂²×C₃	semidirect
97. C₈×D₉	C₂²×C₃	semidirect
242. C₂×M₁₆	AGL(1,ℤ/9)	semidirect
243. 3₋¹⁺²	#568	semidirect
309. M₁₆	C₂×AGL(1,ℤ/9)	semidirect
312. C₂×C₈	C₂×AGL(1,ℤ/9)	semidirect
337. C₉	C₃×#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3697⋊C₃	2
C₂×M₁₆×3₋¹⁺²	2
C₂×#3667⋊C₃	2
#63469⋊C₃	2
M₁₆×AGL(1,ℤ/9)	2
#63464⋊C₃	2
C₃×#5745	3
#10589847	3

Subgroups — #10589847⋊C3 #13153395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589847⋊C₃ #13153395