Subgroups — C₃×#10589932 #13153695

Order 1728.

1166 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63509	C₂	1	2	yes	maximal, complemented
4	C₃×#63502	C₂	1	2	yes	maximal, complemented
5	C₃×#63499	C₂	1	4	yes	maximal, complemented
6	C₃×#63492	C₂	1	4	yes	maximal, complemented
7	C₃×#63488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5830	—	3	1	no	maximal
9	#10589932	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂³×C₃×D₉	C₂²	1	2	yes	—
11	C₃×C₉×#41	—	2	4	no	—
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	complemented
17	C₂×C₃×#611	C₂²	1	8	yes	complemented
18	C₂×C₃×D₃₆	—	2	4	no	—
19	C₂×C₃×D₃₆	C₂²	1	2	yes	—
20	C₂×C₃×D₃₆	C₂²	1	2	yes	—
21	C₃×#3676	C₂²	1	2	yes	—
22	C₃×(C₂×D₉)⋊C₄	C₂²	1	8	yes	complemented
23	C₃×C₄⋊Dic₉	C₂²	1	2	yes	complemented
24	C₃×C₄×Dic₉	C₂²	1	2	yes	complemented
25	C₂×C₃²×#41	D₃	1	1	yes	characteristic
26	C₂²×C₃×D₁₂	—	3	1	no	—
27	C₃×#947	—	3	2	no	—
28	C₃×#940	—	3	2	no	—
29	C₃×#937	—	3	4	no	—
30	C₃×#930	—	3	4	no	—
31	C₃×#926	—	3	1	no	—
32	C₂×C₉×#41	—	2	1	no	—
33	C₂×C₉×#41	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
35	#63509	C₂×C₃	1	2	yes	complemented
36	#63502	C₂×C₃	1	2	yes	complemented
37	#63499	C₂×C₃	1	4	yes	complemented
38	#63492	C₂×C₃	1	4	yes	complemented
39	#63488	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂³×C₃×C₉	C₂³	1	2	yes	—
41	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
42	C₂²×C₃×D₉	—	2	4	no	—
43	C₂²×C₃×D₉	—	4	4	no	—
44	C₂²×C₃×D₉	C₂³	1	4	yes	—
45	C₃×Q₈×C₉	—	2	2	no	—
46	C₃×D₄×C₉	—	2	4	no	—
47	C₃×D₄×C₉	—	2	2	no	—
48	C₂×C₃×C₄×C₉	—	2	4	no	—
49	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
50	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
53	C₃×#611	—	4	8	no	—
54	C₂×C₃×Dic₉	C₂³	1	4	yes	—
55	C₃×D₃₆	—	2	4	no	—
56	C₃×D₃₆	—	2	4	no	—
57	C₃×#535	—	9	1	no	—
58	#5830	—	3	1	no	—
59	C₂³×C₃×D₃	—	3	2	no	—
60	C₃²×#41	—	2	4	no	—
61	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
63	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
65	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
66	C₂×C₃×#67	—	3	8	no	—
67	C₂×C₃×D₁₂	—	3	2	no	—
68	C₂×C₃×D₁₂	—	3	2	no	—
69	C₂×C₃×D₁₂	—	6	4	no	—
70	C₂³×D₉	C₂²×C₃	1	2	yes	—
71	C₃×#217	—	3	2	no	—
72	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
73	C₃×C₄⋊Dic₃	—	3	2	no	—
74	C₃×C₄×Dic₃	—	3	2	no	—
75	C₉×#41	—	2	8	no	—
76	C₉×#41	—	2	4	no	—
77	C₂×Q₈×C₉	—	2	1	no	—
78	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₂×D₄×C₉	—	2	2	no	—
80	C₂×D₄×C₉	—	2	1	no	—
81	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
82	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂²×C₄×C₉	—	2	1	no	—
84	C₂²×C₄×C₉	—	2	2	no	—
85	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₄×C₉	C₂²×C₃	1	2	yes	complemented
87	C₂×#611	C₂²×C₃	1	8	yes	complemented
88	C₂×D₃₆	—	2	4	no	—
89	C₂×D₃₆	C₂²×C₃	1	2	yes	—
90	C₂×D₃₆	C₂²×C₃	1	2	yes	—
91	#3676	C₂²×C₃	1	2	yes	—
92	(C₂×D₉)⋊C₄	C₂²×C₃	1	8	yes	complemented
93	C₄⋊Dic₉	C₂²×C₃	1	2	yes	complemented
94	C₄×Dic₉	C₂²×C₃	1	2	yes	complemented
95	C₂²×C₃×C₉	—	2	2	no	—
96	C₂²×C₃×C₉	—	2	2	no	—
97	C₂²×C₃×C₉	—	2	4	no	—
98	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
99	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×D₉	—	2	4	no	—
101	C₂×C₃×D₉	—	2	8	no	—
102	C₂×C₃×D₉	—	4	8	no	—
103	C₃×C₄×C₉	—	2	2	no	—
104	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
105	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
106	C₃×Dic₉	—	2	4	no	—
107	C₂×C₃×#41	—	2	1	no	—
108	C₂×C₃×#41	D₉	1	1	yes	characteristic, complemented
109	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
110	C₂²×C₃×D₄	—	9	1	no	—
111	C₂²×D₁₂	—	3	1	no	—
112	C₃×#127	—	9	2	no	—
113	C₃×#124	—	9	2	no	—
114	C₃×#121	—	9	4	no	—
115	C₃×#120	—	9	4	no	—
116	C₃×#117	—	9	1	no	—
117	#947	—	3	2	no	—
118	#940	—	3	2	no	—
119	#937	—	3	4	no	—
120	#930	—	3	4	no	—
121	#926	—	3	1	no	—
122	C₂³×C₃²	C₂²×D₃	1	2	yes	—
123	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
124	C₂²×C₃×D₃	—	3	4	no	—
125	C₂²×C₃×D₃	—	6	4	no	—
126	C₂²×C₃×D₃	—	12	4	no	—
127	C₃²×Q₈	—	2	2	no	—
128	C₃²×D₄	—	2	4	no	—
129	C₃²×D₄	—	2	2	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	#67	1	4	yes	—
132	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
133	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
135	C₃×#67	—	12	8	no	—
136	C₂×C₃×Dic₃	—	3	4	no	—
137	C₃×D₁₂	—	6	4	no	—
138	C₃×D₁₂	—	6	4	no	—
139	C₂³×C₉	—	2	2	no	—
140	C₂³×C₉	—	2	1	no	—
141	C₂³×C₉	C₂³×C₃	1	2	yes	—
142	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
143	C₂²×D₉	—	2	4	no	—
144	C₂²×D₉	—	4	4	no	—
145	C₂²×D₉	C₂³×C₃	1	4	yes	—
146	Q₈×C₉	—	2	4	no	—
147	Q₈×C₉	—	2	2	no	—
148	D₄×C₉	—	2	8	no	—
149	D₄×C₉	—	2	4	no	—
150	D₄×C₉	—	2	4	no	—
151	D₄×C₉	—	2	2	no	—
152	C₂×C₄×C₉	—	2	8	no	—
153	C₂×C₄×C₉	—	2	4	no	—
154	C₂×C₄×C₉	—	2	4	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	C₃×D₄	1	4	yes	complemented
159	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
160	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
162	#611	—	4	8	no	—
163	C₂×Dic₉	C₂³×C₃	1	4	yes	—
164	D₃₆	—	2	4	no	—
165	D₃₆	—	2	4	no	—
166	#535	—	9	1	no	Sylow
167	C₂×C₃×C₉	—	2	2	no	—
168	C₂×C₃×C₉	—	4	2	no	—
169	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
171	C₃×D₉	—	4	4	no	—
172	C₂⁴×C₃	—	9	2	no	—
173	C₂³×D₃	—	3	2	no	—
174	C₃×#41	—	2	8	no	—
175	C₃×#41	—	2	4	no	—
176	C₃×#41	—	2	4	no	—
177	C₂×C₃×Q₈	—	2	1	no	—
178	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
179	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	—	2	1	no	—
182	C₂×C₃×D₄	—	9	8	no	—
183	C₂×C₃×D₄	—	9	2	no	—
184	C₂×C₃×D₄	—	9	2	no	—
185	C₂×C₃×D₄	—	18	4	no	—
186	C₂×C₃×D₄	C₂×D₉	1	2	yes	—
187	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic, complemented
188	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
189	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂×D₉	1	2	yes	complemented
194	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
196	C₂×#67	—	3	8	no	—
197	C₂×D₁₂	—	3	2	no	—
198	C₂×D₁₂	—	3	2	no	—
199	C₂×D₁₂	—	6	4	no	—
200	C₃×C₄⋊C₄	—	9	2	no	—
201	C₃×C₂²⋊C₄	—	9	2	no	—
202	C₃×C₂²⋊C₄	—	9	8	no	—
203	C₃×C₄²	—	9	2	no	—
204	#217	—	3	2	no	—
205	(C₂×D₃)⋊C₄	—	3	8	no	—
206	C₄⋊Dic₃	—	3	2	no	—
207	C₄×Dic₃	—	3	2	no	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	2	no	—
210	C₂²×C₃²	—	2	4	no	—
211	C₂²×C₃²	C₂×#67	1	2	yes	—
212	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
213	C₂×C₃×D₃	—	6	8	no	—
214	C₂×C₃×D₃	—	6	4	no	—
215	C₂×C₃×D₃	—	12	8	no	—
216	C₃²×C₄	—	2	2	no	—
217	C₃²×C₄	C₂×#67	1	2	yes	—
218	C₃²×C₄	C₂×#67	1	2	yes	—
219	C₃×Dic₃	—	6	4	no	—
220	C₂²×C₉	—	2	2	no	—
221	C₂²×C₉	—	2	4	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	4	no	—
224	C₂²×C₉	—	2	1	no	—
225	C₂²×C₉	—	2	2	no	—
226	C₂²×C₉	—	4	2	no	—
227	C₂²×C₉	—	4	4	no	—
228	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
229	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
230	C₂×D₉	—	2	4	no	—
231	C₂×D₉	—	2	8	no	—
232	C₂×D₉	—	4	8	no	—
233	C₄×C₉	—	2	4	no	—
234	C₄×C₉	—	2	2	no	—
235	C₄×C₉	—	2	2	no	—
236	C₄×C₉	—	2	2	no	—
237	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
238	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
239	Dic₉	—	2	4	no	—
240	C₂×#41	C₃×D₉	1	1	yes	characteristic, complemented
241	C₂²×D₄	—	9	1	no	—
242	#127	—	9	2	no	—
243	#124	—	9	2	no	—
244	#121	—	9	4	no	—
245	#120	—	9	4	no	—
246	#117	—	9	1	no	—
247	C₃×C₉	#535	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	2	no	—
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	—	9	4	no	—
251	C₂³×C₃	—	18	4	no	—
252	C₂³×C₃	—	36	4	no	—
253	C₂³×C₃	C₂²×D₉	1	2	yes	—
254	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
255	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
256	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
257	C₂²×D₃	—	3	4	no	—
258	C₂²×D₃	—	6	4	no	—
259	C₂²×D₃	—	12	4	no	—
260	C₃×Q₈	—	2	4	no	—
261	C₃×Q₈	—	2	2	no	—
262	C₃×Q₈	—	2	2	no	—
263	C₃×D₄	—	2	8	no	—
264	C₃×D₄	—	2	4	no	—
265	C₃×D₄	—	2	4	no	—
266	C₃×D₄	—	2	4	no	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	18	4	no	—
270	C₃×D₄	—	18	4	no	—
271	C₃×D₄	—	36	8	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	9	4	no	—
280	C₂×C₃×C₄	#611	1	4	yes	complemented
281	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
282	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
284	C₂×C₃×C₄	C₃×#67	1	4	yes	—
285	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
286	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
288	#67	—	12	8	no	—
289	C₂×Dic₃	—	3	4	no	—
290	D₁₂	—	6	4	no	—
291	D₁₂	—	6	4	no	—
292	C₂×C₃²	—	2	2	no	—
293	C₂×C₃²	—	4	2	no	—
294	C₂×C₃²	#1009	1	2	yes	—
295	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
296	C₃×D₃	—	12	4	no	—
297	C₂×C₉	—	2	2	no	—
298	C₂×C₉	—	2	2	no	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	4	2	no	—
301	C₂×C₉	—	4	4	no	—
302	C₂×C₉	—	4	2	no	—
303	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
304	C₂×C₉	C₃×H(5,𝔽₂)	1	2	yes	—
305	D₉	—	4	4	no	—
306	C₂⁴	—	9	2	no	—
307	#41	—	2	4	no	—
308	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
309	C₂×D₄	—	9	8	no	—
310	C₂×D₄	—	9	2	no	—
311	C₂×D₄	—	9	2	no	—
312	C₂×D₄	—	18	4	no	—
313	C₂×D₄	C₂×C₃×D₉	1	2	yes	—
314	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
315	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₃×D₉	1	2	yes	complemented
317	C₄⋊C₄	—	9	2	no	—
318	C₂²⋊C₄	—	9	2	no	—
319	C₂²⋊C₄	—	9	8	no	—
320	C₄²	—	9	2	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	4	no	—
324	C₂²×C₃	—	2	4	no	—
325	C₂²×C₃	—	2	2	no	—
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	4	2	no	—
331	C₂²×C₃	—	4	4	no	—
332	C₂²×C₃	—	18	8	no	—
333	C₂²×C₃	—	18	4	no	—
334	C₂²×C₃	—	36	8	no	—
335	C₂²×C₃	C₂×#611	1	2	yes	—
336	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
337	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
338	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
339	C₂×D₃	—	6	8	no	—
340	C₂×D₃	—	6	4	no	—
341	C₂×D₃	—	12	8	no	—
342	C₃×C₄	—	2	4	no	—
343	C₃×C₄	—	2	2	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	18	4	no	—
348	C₃×C₄	C₂×#611	1	2	yes	—
349	C₃×C₄	C₂×#611	1	2	yes	—
350	C₃×C₄	C₂×C₃×#67	1	2	yes	—
351	C₃×C₄	C₂×C₃×#67	1	2	yes	—
352	Dic₃	—	6	4	no	—
353	C₃²	#5830	1	1	yes	characteristic
354	C₉	—	2	1	no	—
355	C₉	C₃×#535	1	1	yes	characteristic, complemented
356	C₂³	—	9	4	no	—
357	C₂³	—	18	4	no	—
358	C₂³	—	36	4	no	—
359	C₂³	C₂²×C₃×D₉	1	2	yes	—
360	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	18	4	no	—
365	D₄	—	18	4	no	—
366	D₄	—	36	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	9	4	no	—
369	C₂×C₄	C₃×#611	1	4	yes	complemented
370	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
371	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	4	2	no	—
378	C₂×C₃	—	4	4	no	—
379	C₂×C₃	—	4	2	no	—
380	C₂×C₃	—	4	2	no	—
381	C₂×C₃	—	36	4	no	—
382	C₂×C₃	#63715	1	2	yes	—
383	C₂×C₃	C₂²×#611	1	1	yes	characteristic
384	C₂×C₃	C₃×#1009	1	2	yes	—
385	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
386	D₃	—	12	4	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	18	8	no	—
391	C₂²	—	18	4	no	—
392	C₂²	—	36	8	no	—
393	C₂²	C₂×C₃×#611	1	2	yes	—
394	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	18	4	no	—
397	C₄	C₂×C₃×#611	1	2	yes	—
398	C₄	C₂×C₃×#611	1	2	yes	—
399	C₃	—	2	1	no	—
400	C₃	#10589932	1	1	yes	characteristic, direct product factor
401	C₃	C₃×#5830	1	1	yes	characteristic
402	C₂	—	2	2	no	—
403	C₂	—	4	2	no	—
404	C₂	—	36	4	no	—
405	C₂	C₃×#63715	1	2	yes	—
406	C₂	C₂²×C₃×#611	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	C₂×C₃×C₉×#41	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₂×C₃×#41	D₉
hypocenter	C₉	C₃×#535
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂²×C₃×D₃₆	C₂	semidirect
3. C₃×#63509	C₂	semidirect
4. C₃×#63502	C₂	semidirect
5. C₃×#63499	C₂	semidirect
6. C₃×#63492	C₂	semidirect
7. C₃×#63488	C₂	semidirect
9. #10589932	C₃	direct (N × H)
12. C₂×C₃×Q₈×C₉	C₂²	semidirect
14. C₂×C₃×D₄×C₉	C₂²	semidirect
16. C₂²×C₃×C₄×C₉	C₂²	semidirect
17. C₂×C₃×#611	C₂²	semidirect
22. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
23. C₃×C₄⋊Dic₉	C₂²	semidirect
24. C₃×C₄×Dic₉	C₂²	semidirect
33. C₂×C₉×#41	C₂×C₃	semidirect
34. C₂²×D₃₆	C₂×C₃	semidirect
35. #63509	C₂×C₃	semidirect
36. #63502	C₂×C₃	semidirect
37. #63499	C₂×C₃	semidirect
38. #63492	C₂×C₃	semidirect
39. #63488	C₂×C₃	semidirect
49. C₂×C₃×C₄×C₉	D₄	semidirect
78. C₂×Q₈×C₉	C₂²×C₃	semidirect
82. C₂×D₄×C₉	C₂²×C₃	semidirect
86. C₂²×C₄×C₉	C₂²×C₃	semidirect
87. C₂×#611	C₂²×C₃	semidirect
92. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
93. C₄⋊Dic₉	C₂²×C₃	semidirect
94. C₄×Dic₉	C₂²×C₃	semidirect
108. C₂×C₃×#41	D₉	semidirect
158. C₂×C₄×C₉	C₃×D₄	semidirect
178. C₂×C₃×Q₈	C₂×D₉	semidirect
187. C₂×C₃×D₄	C₂×D₉	semidirect
193. C₂²×C₃×C₄	C₂×D₉	semidirect
240. C₂×#41	C₃×D₉	semidirect
247. C₃×C₉	#535	semidirect
280. C₂×C₃×C₄	#611	semidirect
308. C₂×Q₈	C₂×C₃×D₉	semidirect
314. C₂×D₄	C₂×C₃×D₉	semidirect
316. C₂²×C₄	C₂×C₃×D₉	semidirect
355. C₉	C₃×#535	semidirect
369. C₂×C₄	C₃×#611	semidirect
400. C₃	#10589932	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×C₉×#41	2
C₂²×C₃×D₃₆	2
C₃×#63509	2
C₃×#63502	2
C₃×#63499	2
C₃×#63492	2
C₃×#63488	2
C₃×#5830	3
#10589932	3

Subgroups — C3×#10589932 #13153695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589932 #13153695