Subgroups — C₃×#10589828 #13153296

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3701	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63508	C₂	1	2	yes	maximal, complemented
4	C₃×#63457	C₂	1	2	yes	maximal, complemented
5	C₃×#63456	C₂	1	4	yes	maximal, complemented
6	C₃×C₄⋊C₄×D₉	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5726	—	3	1	no	maximal
10	#10589828	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₃×#3701	—	2	8	no	—
13	C₂×C₃×D₃₆	C₂²	1	4	yes	—
14	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
17	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
18	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
24	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
25	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
27	C₃×Dic₉⋊C₄	C₂²	1	4	yes	—
28	C₂×C₃×#239	—	3	2	no	—
29	C₃²×C₄⋊Q₈	D₃	1	1	yes	characteristic
30	C₃×#946	—	3	2	no	—
31	C₃×#895	—	3	2	no	—
32	C₃×#894	—	3	4	no	—
33	C₃×D₃×C₄⋊C₄	—	3	2	no	—
34	C₃×C₄×D₁₂	—	3	1	no	—
35	C₃×C₄×D₁₂	—	3	1	no	—
36	C₂×#3701	C₂×C₃	1	2	yes	complemented
37	C₉×C₄⋊Q₈	—	2	1	no	—
38	C₉×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
39	#63508	C₂×C₃	1	2	yes	complemented
40	#63457	C₂×C₃	1	2	yes	complemented
41	#63456	C₂×C₃	1	4	yes	complemented
42	C₄⋊C₄×D₉	C₂×C₃	1	2	yes	complemented
43	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
44	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×C₃×D₉	C₂³	1	2	yes	—
46	C₂²×C₃×D₉	C₂³	1	2	yes	—
47	C₃×Q₈×C₉	—	2	4	no	—
48	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂×C₃×Dic₉	C₂³	1	2	yes	—
53	C₂×C₃×Dic₉	C₂³	1	2	yes	—
54	C₃×D₃₆	—	2	8	no	—
55	C₃×D₃₆	—	2	2	no	—
56	C₃×D₃₆	D₄	1	4	yes	complemented
57	C₃×C₄×D₉	—	2	8	no	—
58	C₃×C₄×D₉	—	2	4	no	—
59	C₃×C₄×D₉	—	2	4	no	—
60	C₃×#547	—	9	1	no	—
61	#5726	—	3	1	no	—
62	C₂×C₃²×Q₈	C₂×D₃	1	2	yes	—
63	C₃×#239	—	6	8	no	—
64	C₂×C₃×D₁₂	—	3	1	no	—
65	C₂×C₃×D₁₂	—	3	4	no	—
66	C₂×C₃×D₁₂	—	3	1	no	—
67	C₂×C₃×C₄×D₃	—	3	4	no	—
68	C₂×C₃×C₄×D₃	—	3	2	no	—
69	C₂×C₃×C₄×D₃	—	3	2	no	—
70	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
71	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
72	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
73	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
75	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
76	C₃×C₄⋊Dic₃	—	3	1	no	—
77	C₃×C₄⋊Dic₃	—	3	1	no	—
78	C₃×Dic₃⋊C₄	—	3	4	no	—
79	C₂×Q₈×C₉	—	2	2	no	—
80	C₂×Q₈×C₉	C₂²×C₃	1	2	yes	—
81	#3701	—	2	8	no	—
82	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
83	C₂×D₃₆	C₂²×C₃	1	4	yes	—
84	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
86	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
87	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	2	2	no	—
90	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₄²×C₉	—	2	1	no	—
93	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
94	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
95	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
96	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
97	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
98	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
99	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
100	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
101	C₂×C₃×D₉	—	2	2	no	—
102	C₂×C₃×D₉	—	2	2	no	—
103	C₂×C₃×D₉	—	2	2	no	—
104	C₂×C₃×D₉	—	2	2	no	—
105	C₂×C₃×D₉	—	2	2	no	—
106	C₂×C₃×D₉	C₂×D₄	1	4	yes	—
107	C₃×C₄×C₉	—	2	4	no	—
108	C₃×C₄×C₉	—	2	1	no	—
109	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
110	C₃×C₄×C₉	#41	1	2	yes	complemented
111	C₃×Dic₉	—	2	2	no	—
112	C₃×Dic₉	—	2	2	no	—
113	C₂×C₃×#41	—	9	2	no	—
114	C₂×#239	—	3	2	no	—
115	C₃×C₄⋊Q₈	—	2	1	no	—
116	C₃×C₄⋊Q₈	D₉	1	1	yes	characteristic, complemented
117	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
118	C₃×#123	—	9	4	no	—
119	C₃×C₂²⋊Q₈	—	9	2	no	—
120	C₃×#121	—	9	2	no	—
121	C₃×C₄×D₄	—	9	1	no	—
122	C₃×C₄×D₄	—	9	1	no	—
123	C₂×C₃×C₄⋊C₄	—	9	2	no	—
124	#946	—	3	2	no	—
125	#895	—	3	2	no	—
126	#894	—	3	4	no	—
127	D₃×C₄⋊C₄	—	3	2	no	—
128	C₄×D₁₂	—	3	1	no	—
129	C₄×D₁₂	—	3	1	no	—
130	C₂²×C₃×D₃	—	3	2	no	—
131	C₂²×C₃×D₃	—	3	2	no	—
132	C₃²×Q₈	—	2	4	no	—
133	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
134	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
137	C₂×C₃×Dic₃	—	3	2	no	—
138	C₂×C₃×Dic₃	—	3	2	no	—
139	C₃×D₁₂	—	3	4	no	—
140	C₃×D₁₂	—	6	8	no	—
141	C₃×D₁₂	—	6	2	no	—
142	C₃×C₄×D₃	—	6	8	no	—
143	C₃×C₄×D₃	—	6	4	no	—
144	C₃×C₄×D₃	—	6	4	no	—
145	C₂²×D₉	C₂³×C₃	1	2	yes	—
146	C₂²×D₉	C₂³×C₃	1	2	yes	—
147	Q₈×C₉	—	2	4	no	—
148	Q₈×C₉	—	4	4	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	4	no	—
153	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
154	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
157	C₂×Dic₉	C₂³×C₃	1	2	yes	—
158	C₂×Dic₉	C₂³×C₃	1	2	yes	—
159	D₃₆	—	2	8	no	—
160	D₃₆	—	2	2	no	—
161	D₃₆	C₃×D₄	1	4	yes	complemented
162	C₄×D₉	—	2	8	no	—
163	C₄×D₉	—	2	4	no	—
164	C₄×D₉	—	2	4	no	—
165	#547	—	9	1	no	Sylow
166	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
169	C₃×D₉	—	2	4	no	—
170	C₃×D₉	—	4	2	no	—
171	C₃×#41	—	18	8	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	C₂×D₉	1	2	yes	—
174	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
175	C₂×C₃×D₄	—	9	1	no	—
176	C₂×C₃×D₄	—	9	1	no	—
177	C₂×C₃×D₄	—	9	4	no	—
178	C₂²×C₃×C₄	—	9	2	no	—
179	C₂²×C₃×C₄	—	9	4	no	—
180	C₂²×C₃×C₄	—	9	2	no	—
181	#239	—	6	8	no	—
182	C₂×D₁₂	—	3	1	no	—
183	C₂×D₁₂	—	3	1	no	—
184	C₂×D₁₂	—	3	4	no	—
185	C₂×C₄×D₃	—	3	2	no	—
186	C₂×C₄×D₃	—	3	2	no	—
187	C₂×C₄×D₃	—	3	4	no	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	9	4	no	—
191	C₃×C₄⋊C₄	—	9	1	no	—
192	C₃×C₄⋊C₄	—	9	1	no	—
193	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
194	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
195	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
196	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
197	C₃×C₂²⋊C₄	—	9	2	no	—
198	C₃×C₂²⋊C₄	—	9	2	no	—
199	C₃×C₂²⋊C₄	—	9	4	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
202	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
203	(C₂×D₃)⋊C₄	—	3	2	no	—
204	(C₂×D₃)⋊C₄	—	3	2	no	—
205	(C₂×D₃)⋊C₄	—	3	4	no	—
206	C₄⋊Dic₃	—	3	1	no	—
207	C₄⋊Dic₃	—	3	1	no	—
208	Dic₃⋊C₄	—	3	4	no	—
209	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
210	C₂×C₃×D₃	—	3	4	no	—
211	C₂×C₃×D₃	—	6	2	no	—
212	C₂×C₃×D₃	—	6	2	no	—
213	C₂×C₃×D₃	—	6	2	no	—
214	C₂×C₃×D₃	—	6	2	no	—
215	C₂×C₃×D₃	—	6	2	no	—
216	C₃²×C₄	—	2	1	no	—
217	C₃²×C₄	—	2	4	no	—
218	C₃²×C₄	D₃×D₄	1	2	yes	—
219	C₃²×C₄	#239	1	2	yes	—
220	C₃×Dic₃	—	6	2	no	—
221	C₃×Dic₃	—	6	2	no	—
222	C₂²×C₉	—	2	1	no	—
223	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
224	C₂×D₉	—	2	2	no	—
225	C₂×D₉	—	2	2	no	—
226	C₂×D₉	—	2	2	no	—
227	C₂×D₉	—	2	2	no	—
228	C₂×D₉	—	2	2	no	—
229	C₂×D₉	C₂×C₃×D₄	1	4	yes	—
230	C₄×C₉	—	2	2	no	—
231	C₄×C₉	—	2	4	no	—
232	C₄×C₉	—	2	1	no	—
233	C₄×C₉	—	2	2	no	—
234	C₄×C₉	—	2	2	no	—
235	C₄×C₉	—	4	4	no	—
236	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
237	C₄×C₉	C₃×#41	1	2	yes	complemented
238	Dic₉	—	2	2	no	—
239	Dic₉	—	2	2	no	—
240	C₂×#41	—	9	2	no	—
241	C₄⋊Q₈	C₃×D₉	1	1	yes	characteristic, complemented
242	#123	—	9	4	no	—
243	C₂²⋊Q₈	—	9	2	no	—
244	#121	—	9	2	no	—
245	C₄×D₄	—	9	1	no	—
246	C₄×D₄	—	9	1	no	—
247	C₂×C₄⋊C₄	—	9	2	no	—
248	C₃×C₉	#547	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₃	—	9	2	no	—
250	C₂³×C₃	—	9	2	no	—
251	C₂²×D₃	—	3	2	no	—
252	C₂²×D₃	—	3	2	no	—
253	C₃×Q₈	—	2	4	no	—
254	C₃×Q₈	—	2	4	no	—
255	C₃×Q₈	—	4	4	no	—
256	C₃×D₄	—	9	4	no	—
257	C₃×D₄	—	18	8	no	—
258	C₃×D₄	—	18	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	9	2	no	—
264	C₂×C₃×C₄	—	9	2	no	—
265	C₂×C₃×C₄	—	18	8	no	—
266	C₂×C₃×C₄	—	18	4	no	—
267	C₂×C₃×C₄	—	18	4	no	—
268	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂²×D₉	1	4	yes	—
270	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
273	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
276	C₂×Dic₃	—	3	2	no	—
277	C₂×Dic₃	—	3	2	no	—
278	D₁₂	—	3	4	no	—
279	D₁₂	—	6	8	no	—
280	D₁₂	—	6	2	no	—
281	C₄×D₃	—	6	8	no	—
282	C₄×D₃	—	6	4	no	—
283	C₄×D₃	—	6	4	no	—
284	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
285	C₂×C₃²	C₂×#239	1	1	yes	characteristic
286	C₂×C₃²	#1007	1	1	yes	characteristic
287	C₃×D₃	—	6	4	no	—
288	C₃×D₃	—	12	2	no	—
289	C₂×C₉	—	2	1	no	—
290	C₂×C₉	—	2	1	no	—
291	C₂×C₉	—	2	1	no	—
292	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
293	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
294	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
295	D₉	—	2	4	no	—
296	D₉	—	4	2	no	—
297	#41	—	18	8	no	—
298	C₂×Q₈	C₂×C₃×D₉	1	2	yes	—
299	C₂×D₄	—	9	1	no	—
300	C₂×D₄	—	9	1	no	—
301	C₂×D₄	—	9	4	no	—
302	C₂²×C₄	—	9	2	no	—
303	C₂²×C₄	—	9	4	no	—
304	C₂²×C₄	—	9	2	no	—
305	C₄⋊C₄	—	9	1	no	—
306	C₄⋊C₄	—	9	4	no	—
307	C₄⋊C₄	—	9	1	no	—
308	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
309	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
310	C₂²⋊C₄	—	9	2	no	—
311	C₂²⋊C₄	—	9	2	no	—
312	C₂²⋊C₄	—	9	4	no	—
313	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	9	4	no	—
316	C₂²×C₃	—	18	2	no	—
317	C₂²×C₃	—	18	2	no	—
318	C₂²×C₃	—	18	2	no	—
319	C₂²×C₃	—	18	2	no	—
320	C₂²×C₃	—	18	2	no	—
321	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
322	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
323	C₂×D₃	—	3	4	no	—
324	C₂×D₃	—	6	2	no	—
325	C₂×D₃	—	6	2	no	—
326	C₂×D₃	—	6	2	no	—
327	C₂×D₃	—	6	2	no	—
328	C₂×D₃	—	6	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	18	2	no	—
338	C₃×C₄	—	18	2	no	—
339	C₃×C₄	D₄×D₉	1	2	yes	—
340	C₃×C₄	#3701	1	2	yes	complemented
341	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
342	C₃×C₄	C₃×#239	1	2	yes	—
343	Dic₃	—	6	2	no	—
344	Dic₃	—	6	2	no	—
345	C₃²	#5726	1	1	yes	characteristic
346	C₉	—	2	1	no	—
347	C₉	C₃×#547	1	1	yes	characteristic, complemented
348	C₂³	—	9	2	no	—
349	C₂³	—	9	2	no	—
350	Q₈	—	2	4	no	—
351	D₄	—	9	4	no	—
352	D₄	—	18	8	no	—
353	D₄	—	18	2	no	—
354	C₂×C₄	—	9	2	no	—
355	C₂×C₄	—	9	2	no	—
356	C₂×C₄	—	18	8	no	—
357	C₂×C₄	—	18	4	no	—
358	C₂×C₄	—	18	4	no	—
359	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₃×D₉	1	4	yes	—
361	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
362	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	18	4	no	—
367	C₂×C₃	—	36	2	no	—
368	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
369	C₂×C₃	C₂×#3701	1	1	yes	characteristic
370	C₂×C₃	#63713	1	1	yes	characteristic
371	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
372	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
373	C₂×C₃	C₃×#1007	1	1	yes	characteristic
374	D₃	—	6	4	no	—
375	D₃	—	12	2	no	—
376	C₂²	—	9	4	no	—
377	C₂²	—	18	2	no	—
378	C₂²	—	18	2	no	—
379	C₂²	—	18	2	no	—
380	C₂²	—	18	2	no	—
381	C₂²	—	18	2	no	—
382	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	2	1	no	—
385	C₄	—	18	2	no	—
386	C₄	—	18	2	no	—
387	C₄	C₃×D₄×D₉	1	2	yes	—
388	C₄	C₃×#3701	1	2	yes	complemented
389	C₃	—	2	1	no	—
390	C₃	#10589828	1	1	yes	characteristic, direct product factor
391	C₃	C₃×#5726	1	1	yes	characteristic
392	C₂	—	18	4	no	—
393	C₂	—	36	2	no	—
394	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
395	C₂	C₂×C₃×#3701	1	1	yes	characteristic
396	C₂	C₃×#63713	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₃×C₄⋊Q₈	D₉
hypocenter	C₉	C₃×#547
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3701	C₂	semidirect
2. C₃×C₉×C₄⋊Q₈	C₂	semidirect
3. C₃×#63508	C₂	semidirect
4. C₃×#63457	C₂	semidirect
5. C₃×#63456	C₂	semidirect
6. C₃×C₄⋊C₄×D₉	C₂	semidirect
7. C₃×C₄×D₃₆	C₂	semidirect
8. C₃×C₄×D₃₆	C₂	semidirect
10. #10589828	C₃	direct (N × H)
36. C₂×#3701	C₂×C₃	semidirect
38. C₉×C₄⋊Q₈	C₂×C₃	semidirect
39. #63508	C₂×C₃	semidirect
40. #63457	C₂×C₃	semidirect
41. #63456	C₂×C₃	semidirect
42. C₄⋊C₄×D₉	C₂×C₃	semidirect
43. C₄×D₃₆	C₂×C₃	semidirect
44. C₄×D₃₆	C₂×C₃	semidirect
56. C₃×D₃₆	D₄	semidirect
110. C₃×C₄×C₉	#41	semidirect
116. C₃×C₄⋊Q₈	D₉	semidirect
161. D₃₆	C₃×D₄	semidirect
237. C₄×C₉	C₃×#41	semidirect
241. C₄⋊Q₈	C₃×D₉	semidirect
248. C₃×C₉	#547	semidirect
340. C₃×C₄	#3701	semidirect
347. C₉	C₃×#547	semidirect
388. C₄	C₃×#3701	semidirect
390. C₃	#10589828	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3701	2
C₃×C₉×C₄⋊Q₈	2
C₃×#63508	2
C₃×#63457	2
C₃×#63456	2
C₃×C₄⋊C₄×D₉	2
C₃×C₄×D₃₆	2
C₃×#5726	3
#10589828	3

Subgroups — C3×#10589828 #13153296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589828 #13153296