Subgroups — C₂×#11720288 #13139412

Order 1728.

794 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	C₂²×C₄⋊(C₃⋊D₉)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3667	C₂	1	1	yes	maximal, characteristic, complemented
4	#11720288	C₂	1	4	yes	maximal, direct product factor
5	C₂×#63559	—	3	1	no	maximal
6	C₂×#63383	—	3	1	no	maximal
7	C₂³×C₃⋊D₉	C₄	1	2	yes	—
8	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₃⋊D₉)	—	2	1	no	—
10	C₂×C₄⋊(C₃⋊D₉)	—	2	1	no	—
11	C₂×C₄⋊(C₃⋊D₉)	—	2	1	no	—
12	C₂×C₄⋊(C₃⋊D₉)	—	2	1	no	—
13	C₂×C₄⋊(C₃⋊D₉)	C₄	1	2	yes	—
14	C₂×C₄⋊(C₃⋊D₉)	C₂²	1	2	yes	—
15	C₉×#208	—	2	1	no	—
16	C₉×#208	C₂²	1	2	yes	complemented
17	C₂×C₉×C₃⋊C₈	—	2	1	no	—
18	C₃×#3667	—	2	1	no	—
19	C₃×#3667	C₂²	1	2	yes	complemented
20	C₂×C₃×C₉⋊C₈	—	2	1	no	—
21	C₂²×C₄⋊(C₃⋊D₃)	—	3	1	no	—
22	C₂×C₃×#208	—	3	1	no	—
23	C₂×C₃×#208	D₃	1	1	yes	characteristic
24	C₂²×D₃₆	—	3	1	no	—
25	C₂²×D₃₆	—	6	1	no	—
26	#63559	—	3	4	no	—
27	C₂×C₉×M₁₆	—	3	1	no	—
28	C₂×#3667	D₃	1	1	yes	characteristic, complemented
29	#63383	—	3	4	no	—
30	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃⋊D₉	—	2	2	no	—
32	C₂²×C₃⋊D₉	—	2	2	no	—
33	C₂²×C₃⋊D₉	—	4	4	no	—
34	C₂²×C₃⋊D₉	C₂×C₄	1	4	yes	—
35	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
37	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
38	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
39	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
41	C₄⋊(C₃⋊D₉)	—	2	2	no	—
42	C₄⋊(C₃⋊D₉)	—	2	2	no	—
43	C₄⋊(C₃⋊D₉)	—	2	2	no	—
44	C₄⋊(C₃⋊D₉)	—	2	2	no	—
45	C₉×C₃⋊C₈	—	2	2	no	—
46	C₃×C₉⋊C₈	—	2	2	no	—
47	C₂×#823	—	9	1	no	—
48	C₂×#823	—	9	1	no	—
49	C₂³×C₃⋊D₃	—	3	2	no	—
50	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
51	C₂×C₄⋊(C₃⋊D₃)	—	3	2	no	—
52	C₂×C₄⋊(C₃⋊D₃)	—	3	2	no	—
53	C₂×C₄⋊(C₃⋊D₃)	—	6	1	no	—
54	C₂×C₄⋊(C₃⋊D₃)	—	6	1	no	—
55	C₂×C₄⋊(C₃⋊D₃)	—	6	1	no	—
56	C₂×C₄⋊(C₃⋊D₃)	—	6	1	no	—
57	C₂³×D₉	—	3	2	no	—
58	C₂³×D₉	—	6	2	no	—
59	C₃×#208	—	2	1	no	—
60	C₃×#208	—	3	2	no	—
61	C₃×#208	—	6	1	no	—
62	C₃×#208	C₂×D₃	1	2	yes	—
63	C₂×C₃×C₃⋊C₈	—	2	1	no	—
64	C₂×C₃×C₃⋊C₈	—	6	1	no	—
65	C₂²×C₄×C₉	—	2	1	no	—
66	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
67	C₂×D₃₆	—	3	2	no	—
68	C₂×D₃₆	—	3	2	no	—
69	C₂×D₃₆	—	6	2	no	—
70	C₂×D₃₆	—	6	2	no	—
71	C₂×D₃₆	—	6	2	no	—
72	C₂×D₃₆	—	6	2	no	—
73	C₂×D₃₆	—	6	2	no	—
74	C₂×D₃₆	—	6	2	no	—
75	C₂×D₃₆	—	6	1	no	—
76	C₂×D₃₆	—	6	1	no	—
77	C₂×D₃₆	—	6	1	no	—
78	C₂×D₃₆	—	6	1	no	—
79	C₉×M₁₆	—	3	2	no	—
80	C₉×M₁₆	—	6	1	no	—
81	C₂×C₈×C₉	—	6	1	no	—
82	#3667	—	2	1	no	—
83	#3667	C₂×D₃	1	2	yes	complemented
84	C₂×C₉⋊C₈	—	2	1	no	—
85	C₂²×C₃×C₉	—	2	2	no	—
86	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃⋊D₉	—	2	4	no	—
90	C₂×C₃⋊D₉	—	4	4	no	—
91	C₂×C₃⋊D₉	—	4	4	no	—
92	C₂×C₃⋊D₉	—	4	4	no	—
93	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
96	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×D₁₂	—	9	1	no	—
98	C₂²×D₁₂	—	9	1	no	—
99	C₂²×D₁₂	—	18	1	no	—
100	C₂×C₃×M₁₆	—	3	1	no	—
101	C₂×C₃×M₁₆	—	9	1	no	—
102	C₂×#208	—	3	1	no	—
103	C₂×#208	D₉	1	1	yes	characteristic, complemented
104	#823	—	9	4	no	—
105	#823	—	9	4	no	—
106	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
107	C₂²×C₃⋊D₃	—	3	4	no	—
108	C₂²×C₃⋊D₃	—	6	2	no	—
109	C₂²×C₃⋊D₃	—	6	2	no	—
110	C₂²×C₃⋊D₃	—	12	4	no	—
111	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
112	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
113	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
114	C₂×C₃²×C₄	#67	1	1	yes	characteristic
115	C₂×C₃²×C₄	#67	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
117	C₄⋊(C₃⋊D₃)	—	6	2	no	—
118	C₄⋊(C₃⋊D₃)	—	6	2	no	—
119	C₄⋊(C₃⋊D₃)	—	6	2	no	—
120	C₄⋊(C₃⋊D₃)	—	6	2	no	—
121	C₂³×C₉	—	2	1	no	—
122	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
123	C₂²×D₉	—	3	4	no	—
124	C₂²×D₉	—	6	4	no	—
125	C₂²×D₉	—	6	4	no	—
126	C₂²×D₉	—	6	4	no	—
127	C₂²×D₉	—	6	2	no	—
128	C₂²×D₉	—	6	2	no	—
129	C₂²×D₉	—	12	8	no	—
130	C₂²×D₉	—	12	4	no	—
131	C₃×C₃⋊C₈	—	2	2	no	—
132	C₃×C₃⋊C₈	—	6	2	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
140	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
141	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
142	C₂×C₄×C₉	#67	1	1	yes	characteristic
143	C₂×C₄×C₉	#67	1	1	yes	characteristic
144	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
145	D₃₆	—	6	4	no	—
146	D₃₆	—	6	4	no	—
147	D₃₆	—	6	4	no	—
148	D₃₆	—	6	4	no	—
149	D₃₆	—	6	2	no	—
150	D₃₆	—	6	2	no	—
151	D₃₆	—	6	2	no	—
152	D₃₆	—	6	2	no	—
153	C₈×C₉	—	6	2	no	—
154	C₉⋊C₈	—	2	2	no	—
155	C₂×#100	—	27	1	no	Sylow
156	C₂×C₃×C₉	—	2	1	no	—
157	C₂×C₃×C₉	—	2	1	no	—
158	C₂×C₃×C₉	#100	1	2	yes	complemented
159	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₃⋊D₉	—	4	4	no	—
161	C₂³×D₃	—	9	2	no	—
162	C₂³×D₃	—	9	2	no	—
163	C₂³×D₃	—	18	2	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
166	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
167	C₂×D₁₂	—	9	2	no	—
168	C₂×D₁₂	—	9	2	no	—
169	C₂×D₁₂	—	9	2	no	—
170	C₂×D₁₂	—	9	2	no	—
171	C₂×D₁₂	—	18	2	no	—
172	C₂×D₁₂	—	18	2	no	—
173	C₂×D₁₂	—	18	2	no	—
174	C₂×D₁₂	—	18	2	no	—
175	C₂×D₁₂	—	18	2	no	—
176	C₂×D₁₂	—	18	2	no	—
177	C₂×D₁₂	—	18	1	no	—
178	C₂×D₁₂	—	18	1	no	—
179	C₂×D₁₂	—	18	1	no	—
180	C₂×D₁₂	—	18	1	no	—
181	C₂×D₁₂	—	18	1	no	—
182	C₂×D₁₂	—	18	1	no	—
183	C₂×D₁₂	—	18	1	no	—
184	C₂×D₁₂	—	18	1	no	—
185	C₃×M₁₆	—	3	2	no	—
186	C₃×M₁₆	—	6	1	no	—
187	C₃×M₁₆	—	9	2	no	—
188	C₃×M₁₆	—	18	1	no	—
189	C₂×C₃×C₈	—	6	1	no	—
190	C₂×C₃×C₈	—	18	1	no	—
191	#208	—	2	1	no	—
192	#208	—	3	2	no	—
193	#208	—	6	1	no	—
194	#208	C₂×D₉	1	2	yes	complemented
195	C₂×C₃⋊C₈	—	2	1	no	—
196	C₂×C₃⋊C₈	—	6	1	no	—
197	C₂²×C₃²	—	2	2	no	—
198	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
199	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
200	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
201	C₂×C₃⋊D₃	—	6	4	no	—
202	C₂×C₃⋊D₃	—	12	4	no	—
203	C₂×C₃⋊D₃	—	12	4	no	—
204	C₂×C₃⋊D₃	—	12	4	no	—
205	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
206	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
207	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
208	C₃²×C₄	C₂×#67	1	1	yes	characteristic
209	C₂²×C₉	—	2	4	no	—
210	C₂²×C₉	—	2	2	no	—
211	C₂²×C₉	—	2	1	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	2	1	no	—
214	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
215	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
216	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
217	C₂×D₉	—	6	8	no	—
218	C₂×D₉	—	6	4	no	—
219	C₂×D₉	—	12	8	no	—
220	C₂×D₉	—	12	4	no	—
221	C₂×D₉	—	12	8	no	—
222	C₂×D₉	—	12	8	no	—
223	C₂×D₉	—	12	4	no	—
224	C₂×D₉	—	12	4	no	—
225	C₄×C₉	—	2	1	no	—
226	C₄×C₉	—	2	1	no	—
227	C₄×C₉	—	2	1	no	—
228	C₄×C₉	—	2	1	no	—
229	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
230	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
231	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
232	C₄×C₉	C₂×#67	1	1	yes	characteristic
233	C₂²×D₄	—	27	1	no	—
234	C₂×M₁₆	—	3	1	no	—
235	C₂×M₁₆	—	9	1	no	—
236	#100	—	27	4	no	—
237	C₃×C₉	C₂×#100	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₃	—	2	1	no	—
239	C₂³×C₃	C₄×D₉	1	1	yes	characteristic
240	C₂³×C₃	#624	1	1	yes	characteristic
241	C₂²×D₃	—	9	4	no	—
242	C₂²×D₃	—	9	4	no	—
243	C₂²×D₃	—	18	4	no	—
244	C₂²×D₃	—	18	4	no	—
245	C₂²×D₃	—	18	4	no	—
246	C₂²×D₃	—	18	2	no	—
247	C₂²×D₃	—	18	2	no	—
248	C₂²×D₃	—	18	2	no	—
249	C₂²×D₃	—	18	2	no	—
250	C₂²×D₃	—	36	8	no	—
251	C₂²×D₃	—	36	4	no	—
252	C₂²×D₃	—	36	4	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
260	C₂×C₃×C₄	D₃₆	1	1	yes	characteristic
261	C₂×C₃×C₄	D₃₆	1	1	yes	characteristic
262	C₂×C₃×C₄	#611	1	1	yes	characteristic
263	C₂×C₃×C₄	#611	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
265	C₂×C₃×C₄	#624	1	1	yes	characteristic
266	C₂×C₃×C₄	#626	1	1	yes	characteristic
267	C₂×C₃×C₄	#626	1	1	yes	characteristic
268	C₂×C₃×C₄	#626	1	1	yes	characteristic
269	C₂×C₃×C₄	#626	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
271	D₁₂	—	18	4	no	—
272	D₁₂	—	18	4	no	—
273	D₁₂	—	18	4	no	—
274	D₁₂	—	18	4	no	—
275	D₁₂	—	18	2	no	—
276	D₁₂	—	18	2	no	—
277	D₁₂	—	18	2	no	—
278	D₁₂	—	18	2	no	—
279	D₁₂	—	18	2	no	—
280	D₁₂	—	18	2	no	—
281	D₁₂	—	18	2	no	—
282	D₁₂	—	18	2	no	—
283	C₃×C₈	—	6	2	no	—
284	C₃×C₈	—	18	2	no	—
285	C₃⋊C₈	—	2	2	no	—
286	C₃⋊C₈	—	6	2	no	—
287	C₂×C₃²	—	2	1	no	—
288	C₂×C₃²	—	2	1	no	—
289	C₂×C₃²	#823	1	2	yes	—
290	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
291	C₃⋊D₃	—	12	4	no	—
292	C₂×C₉	—	2	2	no	—
293	C₂×C₉	—	2	2	no	—
294	C₂×C₉	—	2	1	no	—
295	C₂×C₉	—	2	1	no	—
296	C₂×C₉	—	2	2	no	—
297	C₂×C₉	—	2	1	no	—
298	C₂×C₉	#823	1	2	yes	complemented
299	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
300	D₉	—	12	8	no	—
301	D₉	—	12	4	no	—
302	C₂⁴	—	27	2	no	—
303	C₂×D₄	—	27	2	no	—
304	C₂×D₄	—	27	2	no	—
305	C₂×D₄	—	54	1	no	—
306	C₂×D₄	—	54	1	no	—
307	C₂×D₄	—	54	1	no	—
308	C₂×D₄	—	54	1	no	—
309	C₂²×C₄	D₃×D₉	1	1	yes	characteristic
310	M₁₆	—	3	2	no	—
311	M₁₆	—	6	1	no	—
312	M₁₆	—	9	2	no	—
313	M₁₆	—	18	1	no	—
314	C₂×C₈	—	6	1	no	—
315	C₂×C₈	—	18	1	no	—
316	C₂²×C₃	—	2	4	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	(C₂×D₉)⋊C₄	1	1	yes	characteristic
323	C₂²×C₃	(C₂×D₉)⋊C₄	1	1	yes	characteristic
324	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
325	C₂²×C₃	#3722	1	1	yes	characteristic
326	C₂²×C₃	#3722	1	1	yes	characteristic
327	C₂²×C₃	C₂×#624	1	1	yes	characteristic
328	C₂×D₃	—	18	8	no	—
329	C₂×D₃	—	18	4	no	—
330	C₂×D₃	—	18	4	no	—
331	C₂×D₃	—	36	4	no	—
332	C₂×D₃	—	36	8	no	—
333	C₂×D₃	—	36	8	no	—
334	C₂×D₃	—	36	4	no	—
335	C₂×D₃	—	36	8	no	—
336	C₂×D₃	—	36	4	no	—
337	C₂×D₃	—	36	4	no	—
338	C₂×D₃	—	36	4	no	—
339	C₂×D₃	—	36	4	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	(C₂×D₉)⋊C₄	1	1	yes	characteristic
345	C₃×C₄	(C₂×D₉)⋊C₄	1	1	yes	characteristic
346	C₃×C₄	C₂×D₃₆	1	1	yes	characteristic
347	C₃×C₄	C₂×#611	1	1	yes	characteristic
348	C₃×C₄	#3722	1	1	yes	characteristic
349	C₃×C₄	#3722	1	1	yes	characteristic
350	C₃×C₄	C₂×#626	1	1	yes	characteristic
351	C₃×C₄	C₂×#626	1	1	yes	characteristic
352	C₃²	C₂×#823	1	1	yes	characteristic
353	C₉	—	2	1	no	—
354	C₉	C₂×#823	1	1	yes	characteristic, complemented
355	C₂³	—	27	4	no	—
356	C₂³	—	54	2	no	—
357	C₂³	—	54	2	no	—
358	C₂³	—	108	4	no	—
359	C₂³	(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
360	D₄	—	54	2	no	—
361	D₄	—	54	2	no	—
362	D₄	—	54	2	no	—
363	D₄	—	54	2	no	—
364	C₂×C₄	(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
365	C₂×C₄	#6192	1	1	yes	characteristic
366	C₂×C₄	#6192	1	1	yes	characteristic
367	C₂×C₄	#6195	1	1	yes	characteristic
368	C₂×C₄	#6195	1	1	yes	characteristic
369	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
370	C₈	—	6	2	no	—
371	C₈	—	18	2	no	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	2	no	—
380	C₂×C₃	#63383	1	2	yes	complemented
381	C₂×C₃	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
382	C₂×C₃	#63559	1	2	yes	—
383	C₂×C₃	C₂×#3722	1	1	yes	characteristic
384	D₃	—	36	8	no	—
385	D₃	—	36	4	no	—
386	D₃	—	36	4	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	54	4	no	—
389	C₂²	—	108	4	no	—
390	C₂²	—	108	4	no	—
391	C₂²	—	108	4	no	—
392	C₂²	#88445	1	1	yes	characteristic
393	C₂²	#88445	1	1	yes	characteristic
394	C₂²	C₂×(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
395	C₄	#88445	1	1	yes	characteristic
396	C₄	#88445	1	1	yes	characteristic
397	C₄	C₂×#6192	1	1	yes	characteristic
398	C₄	C₂×#6195	1	1	yes	characteristic
399	C₃	—	2	1	no	—
400	C₃	C₂×#63383	1	1	yes	characteristic, complemented
401	C₃	C₂×#63559	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	108	4	no	—
405	C₂	#11720288	1	2	yes	direct product factor
406	C₂	C₂×#88445	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88445
commutator	C₂²×C₃×C₉	C₂²×C₄
Frattini	C₂×C₃×C₄	C₂×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂²×C₃²	(C₂×D₃)⋊C₄
prime radical	C₂²×C₄⋊(C₃⋊D₉)	C₂
cosocle	C₂×C₃×C₄×C₉	C₂³
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	C₂×#100
LCS	G ▷ C₂²×C₃×C₉ ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×#208	C₂	semidirect
3. C₂×C₃×#3667	C₂	semidirect
4. #11720288	C₂	direct (N × H)
16. C₉×#208	C₂²	semidirect
19. C₃×#3667	C₂²	semidirect
28. C₂×#3667	D₃	semidirect
83. #3667	C₂×D₃	semidirect
103. C₂×#208	D₉	semidirect
158. C₂×C₃×C₉	#100	semidirect
194. #208	C₂×D₉	semidirect
237. C₃×C₉	C₂×#100	semidirect
298. C₂×C₉	#823	semidirect
354. C₉	C₂×#823	semidirect
380. C₂×C₃	#63383	semidirect
400. C₃	C₂×#63383	semidirect
405. C₂	#11720288	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₃⋊D₉)	2
C₂×C₉×#208	2
C₂×C₃×#3667	2
#11720288	2
C₂×#63559	3
C₂×#63383	3

Subgroups — C2×#11720288 #13139412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11720288 #13139412