Subgroups — C₂²×#89028 #13181654

Order 1728.

6284 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×#6312	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#6293	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#6291	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6289	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#89028	C₂	1	24	yes	maximal, direct product factor
8	C₂²×D₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#3830	—	3	1	no	maximal
10	C₂²×#3804	—	3	4	no	maximal
11	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
12	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
13	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
14	C₂×#6312	C₂²	1	12	yes	complemented
15	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₃⋊Dic₃	C₂²	1	12	yes	complemented
19	C₂×C₃²×#67	C₂²	1	12	yes	complemented
20	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×#6293	C₂²	1	12	yes	complemented
22	C₂×#6291	C₂²	1	12	yes	complemented
23	C₂×#6289	C₂²	1	12	yes	complemented
24	#89028	C₂²	1	64	yes	direct product factor
25	C₂×D₃×C₃⋊Dic₃	C₂²	1	12	yes	complemented
26	C₂²×C₃²×D₄	—	3	1	no	—
27	C₂²×#638	—	3	1	no	—
28	C₂²×#638	—	3	1	no	—
29	C₂²×#638	—	3	4	no	—
30	C₂²×#638	—	6	4	no	—
31	C₂³×C₃⋊Dic₃	—	3	1	no	—
32	C₂³×C₃⋊Dic₃	D₃	1	1	yes	characteristic, complemented
33	C₂×#3830	—	3	24	no	—
34	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
35	C₂²×#634	—	3	1	no	—
36	C₂²×C₃×#67	D₃	1	4	yes	complemented
37	C₂³×C₃×Dic₃	—	3	4	no	—
38	C₂²×#627	—	3	4	no	—
39	C₂²×#626	—	3	4	no	—
40	C₂²×#624	—	3	4	no	—
41	C₂×#3804	—	3	96	no	—
42	C₂²×D₃×Dic₃	—	3	4	no	—
43	C₂³×C₃³	—	2	4	no	—
44	C₂³×C₃³	C₂³	1	6	yes	—
45	C₂³×C₃³	C₂³	1	1	yes	characteristic
46	C₂²×C₃⋊(C₃⋊D₃)	—	2	4	no	—
47	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	6	yes	—
48	C₂²×C₃²×D₃	—	2	4	no	—
49	C₂²×C₃²×D₃	C₂³	1	6	yes	—
50	#6312	C₂³	1	16	yes	complemented
51	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	6	yes	—
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	—
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	16	yes	complemented
55	C₃²×#67	C₂³	1	16	yes	complemented
56	C₂×C₃²×Dic₃	C₂³	1	6	yes	—
57	#6293	C₂³	1	16	yes	complemented
58	#6291	C₂³	1	16	yes	complemented
59	#6289	C₂³	1	16	yes	complemented
60	D₃×C₃⋊Dic₃	C₂³	1	16	yes	complemented
61	C₂²×#237	—	9	4	no	—
62	C₂²×#235	—	9	1	no	—
63	C₂⁴×C₃²	—	2	4	no	—
64	C₂⁴×C₃²	—	3	1	no	—
65	C₂⁴×C₃²	C₂×D₃	1	4	yes	—
66	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
67	C₂³×C₃⋊D₃	—	3	1	no	—
68	C₂³×C₃⋊D₃	—	3	4	no	—
69	C₂³×C₃⋊D₃	—	6	4	no	—
70	C₂³×C₃×D₃	C₂×D₃	1	4	yes	—
71	C₂×C₃²×D₄	—	3	12	no	—
72	C₂²×C₃²×C₄	—	3	1	no	—
73	C₂×#638	—	3	12	no	—
74	C₂×#638	—	3	48	no	—
75	C₂×#638	—	3	12	no	—
76	C₂×#638	—	6	48	no	—
77	C₂²×C₃⋊Dic₃	—	3	1	no	—
78	C₂²×C₃⋊Dic₃	—	3	4	no	—
79	C₂²×C₃⋊Dic₃	—	3	12	no	—
80	C₂²×C₃⋊Dic₃	—	6	4	no	—
81	C₂²×C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₃⋊Dic₃	C₂×D₃	1	12	yes	complemented
84	#3830	—	3	64	no	—
85	C₂×C₄×C₃⋊D₃	—	3	12	no	—
86	C₂×#634	—	3	12	no	—
87	C₂×C₃×#67	C₂×D₃	1	48	yes	complemented
88	C₂²×C₃×Dic₃	—	3	4	no	—
89	C₂²×C₃×Dic₃	—	3	48	no	—
90	C₂²×C₃×Dic₃	—	3	4	no	—
91	C₂²×C₃×Dic₃	C₂×D₃	1	4	yes	—
92	C₂×#627	—	3	48	no	—
93	C₂×#626	—	3	48	no	—
94	C₂×#624	—	3	48	no	—
95	#3804	—	3	256	no	—
96	C₂×D₃×Dic₃	—	3	48	no	—
97	C₂²×C₃³	—	2	12	no	—
98	C₂²×C₃³	#41	1	4	yes	complemented
99	C₂²×C₃³	C₂⁴	1	4	yes	—
100	C₂²×C₃³	C₂⁴	1	3	yes	—
101	C₂×C₃⋊(C₃⋊D₃)	—	2	12	no	—
102	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	4	yes	—
103	C₂×C₃²×D₃	—	2	12	no	—
104	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
105	C₃⋊(C₃⋊Dic₃)	C₂⁴	1	4	yes	—
106	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	—
107	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	—
108	C₃²×Dic₃	C₂⁴	1	4	yes	—
109	C₂²×C₃×D₄	—	3	4	no	—
110	C₂³×C₃×C₄	—	9	1	no	—
111	C₂²×#67	—	9	4	no	—
112	C₂²×#67	—	9	4	no	—
113	C₂²×#67	—	9	1	no	—
114	C₂²×#67	—	18	4	no	—
115	C₂²×#67	C₃⋊D₃	1	1	yes	characteristic, complemented
116	C₂³×Dic₃	—	3	4	no	—
117	C₂³×Dic₃	—	9	4	no	—
118	C₂×#237	—	9	96	no	—
119	C₂×#235	—	9	24	no	—
120	C₂²×D₁₂	—	9	1	no	—
121	C₂²×C₄×D₃	—	9	4	no	—
122	C₂²×C₄×D₃	—	9	1	no	—
123	C₂²×C₄×D₃	—	9	1	no	—
124	C₂²×Dic₆	—	9	4	no	—
125	C₂²×Dic₆	—	9	1	no	—
126	C₂³×C₃²	—	2	4	no	—
127	C₂³×C₃²	—	2	4	no	—
128	C₂³×C₃²	—	2	24	no	—
129	C₂³×C₃²	—	2	16	no	—
130	C₂³×C₃²	—	3	6	no	—
131	C₂³×C₃²	—	4	16	no	—
132	C₂³×C₃²	—	6	4	no	—
133	C₂³×C₃²	C₂²×D₃	1	24	yes	—
134	C₂³×C₃²	C₂²×D₃	1	4	yes	—
135	C₂³×C₃²	C₂²×D₃	1	6	yes	—
136	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
137	C₂²×C₃⋊D₃	—	3	6	no	—
138	C₂²×C₃⋊D₃	—	3	24	no	—
139	C₂²×C₃⋊D₃	—	6	24	no	—
140	C₂²×C₃⋊D₃	—	6	4	no	—
141	C₂²×C₃⋊D₃	—	6	16	no	—
142	C₂²×C₃⋊D₃	—	12	16	no	—
143	C₂²×C₃×D₃	—	2	16	no	—
144	C₂²×C₃×D₃	C₂²×D₃	1	24	yes	—
145	C₃²×D₄	—	3	16	no	—
146	C₂×C₃²×C₄	—	3	6	no	—
147	#638	—	3	16	no	—
148	#638	—	3	16	no	—
149	#638	—	3	64	no	—
150	#638	—	6	64	no	—
151	C₂×C₃⋊Dic₃	—	3	6	no	—
152	C₂×C₃⋊Dic₃	—	3	16	no	—
153	C₂×C₃⋊Dic₃	—	3	24	no	—
154	C₂×C₃⋊Dic₃	—	6	24	no	—
155	C₂×C₃⋊Dic₃	C₂²×D₃	1	6	yes	—
156	C₂×C₃⋊Dic₃	C₂²×D₃	1	6	yes	—
157	C₂×C₃⋊Dic₃	C₂²×D₃	1	16	yes	complemented
158	C₄×C₃⋊D₃	—	3	16	no	—
159	#634	—	3	16	no	—
160	C₃×#67	C₂²×D₃	1	64	yes	complemented
161	C₂×C₃×Dic₃	—	3	24	no	—
162	C₂×C₃×Dic₃	—	3	24	no	—
163	C₂×C₃×Dic₃	—	3	64	no	—
164	C₂×C₃×Dic₃	C₂²×D₃	1	24	yes	—
165	#627	—	3	64	no	—
166	#626	—	3	64	no	—
167	#624	—	3	64	no	—
168	D₃×Dic₃	—	3	64	no	—
169	C₂²×#41	—	27	1	no	Sylow
170	C₂×C₃³	—	2	4	no	—
171	C₂×C₃³	C₂×#41	1	6	yes	complemented
172	C₂×C₃³	C₂⁵	1	1	yes	characteristic
173	C₃⋊(C₃⋊D₃)	—	2	4	no	—
174	C₃²×D₃	—	2	4	no	—
175	C₂⁴×C₃	—	2	4	no	—
176	C₂⁴×C₃	—	3	4	no	—
177	C₂⁴×C₃	D₃²	1	4	yes	—
178	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
179	C₂³×D₃	—	9	4	no	—
180	C₂³×D₃	—	9	1	no	—
181	C₂³×D₃	—	18	4	no	—
182	C₂³×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic
183	C₂×C₃×D₄	—	3	48	no	—
184	C₂²×C₃×C₄	—	3	4	no	—
185	C₂²×C₃×C₄	—	9	1	no	—
186	C₂²×C₃×C₄	—	9	1	no	—
187	C₂²×C₃×C₄	—	9	12	no	—
188	C₂×#67	—	9	48	no	—
189	C₂×#67	—	9	48	no	—
190	C₂×#67	—	9	12	no	—
191	C₂×#67	—	18	48	no	—
192	C₂×#67	C₂×C₃⋊D₃	1	12	yes	complemented
193	C₂²×Dic₃	—	3	4	no	—
194	C₂²×Dic₃	—	3	4	no	—
195	C₂²×Dic₃	—	3	48	no	—
196	C₂²×Dic₃	—	9	48	no	—
197	C₂²×Dic₃	—	9	4	no	—
198	C₂²×Dic₃	—	9	1	no	—
199	C₂²×Dic₃	—	18	4	no	—
200	C₂²×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic
201	#237	—	9	256	no	—
202	#235	—	9	64	no	—
203	C₂×D₁₂	—	9	12	no	—
204	C₂×C₄×D₃	—	9	48	no	—
205	C₂×C₄×D₃	—	9	12	no	—
206	C₂×C₄×D₃	—	9	12	no	—
207	C₂×Dic₆	—	9	48	no	—
208	C₂×Dic₆	—	9	12	no	—
209	C₂²×C₃²	—	2	12	no	—
210	C₂²×C₃²	—	2	12	no	—
211	C₂²×C₃²	—	2	16	no	—
212	C₂²×C₃²	—	2	16	no	—
213	C₂²×C₃²	—	2	48	no	—
214	C₂²×C₃²	—	3	4	no	—
215	C₂²×C₃²	—	4	48	no	—
216	C₂²×C₃²	—	6	12	no	—
217	C₂²×C₃²	#235	1	4	yes	complemented
218	C₂²×C₃²	#237	1	16	yes	complemented
219	C₂²×C₃²	C₂³×D₃	1	16	yes	—
220	C₂²×C₃²	C₂³×D₃	1	12	yes	—
221	C₂²×C₃²	C₂³×D₃	1	4	yes	—
222	C₂²×C₃²	C₂³×D₃	1	3	yes	—
223	C₂×C₃⋊D₃	—	3	4	no	—
224	C₂×C₃⋊D₃	—	3	16	no	—
225	C₂×C₃⋊D₃	—	6	16	no	—
226	C₂×C₃⋊D₃	—	6	12	no	—
227	C₂×C₃⋊D₃	—	6	48	no	—
228	C₂×C₃⋊D₃	—	12	48	no	—
229	C₂×C₃×D₃	—	2	48	no	—
230	C₂×C₃×D₃	C₂³×D₃	1	16	yes	—
231	C₃²×C₄	—	3	4	no	—
232	C₃⋊Dic₃	—	3	4	no	—
233	C₃⋊Dic₃	—	3	16	no	—
234	C₃⋊Dic₃	—	6	16	no	—
235	C₃⋊Dic₃	C₂³×D₃	1	4	yes	—
236	C₃⋊Dic₃	C₂³×D₃	1	4	yes	—
237	C₃×Dic₃	—	3	16	no	—
238	C₃×Dic₃	—	3	16	no	—
239	C₃×Dic₃	C₂³×D₃	1	16	yes	—
240	C₂×#41	—	27	24	no	—
241	C₂²×Q₈	—	27	1	no	—
242	C₂²×D₄	—	3	1	no	—
243	C₂²×D₄	—	27	1	no	—
244	C₂²×D₄	—	27	1	no	—
245	C₂³×C₄	—	9	1	no	—
246	C₂³×C₄	—	27	1	no	—
247	C₂³×C₄	—	27	1	no	—
248	C₃³	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₃	—	2	16	no	—
250	C₂³×C₃	—	2	4	no	—
251	C₂³×C₃	—	2	24	no	—
252	C₂³×C₃	—	2	4	no	—
253	C₂³×C₃	—	3	24	no	—
254	C₂³×C₃	—	4	16	no	—
255	C₂³×C₃	—	6	16	no	—
256	C₂³×C₃	C₂×D₃²	1	24	yes	—
257	C₂³×C₃	C₂×D₃²	1	4	yes	—
258	C₂³×C₃	C₂²×C₃⋊D₃	1	6	yes	—
259	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
260	C₂²×D₃	—	2	4	no	—
261	C₂²×D₃	—	9	24	no	—
262	C₂²×D₃	—	9	6	no	—
263	C₂²×D₃	—	18	24	no	—
264	C₂²×D₃	—	18	16	no	—
265	C₂²×D₃	—	18	4	no	—
266	C₂²×D₃	—	36	16	no	—
267	C₂²×D₃	C₂²×C₃⋊D₃	1	6	yes	—
268	C₃×D₄	—	3	64	no	—
269	C₂×C₃×C₄	—	3	24	no	—
270	C₂×C₃×C₄	—	9	6	no	—
271	C₂×C₃×C₄	—	9	6	no	—
272	C₂×C₃×C₄	—	9	16	no	—
273	#67	—	9	64	no	—
274	#67	—	9	64	no	—
275	#67	—	9	16	no	—
276	#67	—	18	64	no	—
277	#67	C₂²×C₃⋊D₃	1	16	yes	complemented
278	C₂×Dic₃	—	3	24	no	—
279	C₂×Dic₃	—	3	24	no	—
280	C₂×Dic₃	—	3	64	no	—
281	C₂×Dic₃	—	9	64	no	—
282	C₂×Dic₃	—	9	24	no	—
283	C₂×Dic₃	—	9	6	no	—
284	C₂×Dic₃	—	18	24	no	—
285	C₂×Dic₃	C₂²×C₃⋊D₃	1	6	yes	—
286	D₁₂	—	9	16	no	—
287	C₄×D₃	—	9	64	no	—
288	C₄×D₃	—	9	16	no	—
289	C₄×D₃	—	9	16	no	—
290	Dic₆	—	9	64	no	—
291	Dic₆	—	9	16	no	—
292	C₂×C₃²	—	2	4	no	—
293	C₂×C₃²	—	2	24	no	—
294	C₂×C₃²	—	2	4	no	—
295	C₂×C₃²	—	2	16	no	—
296	C₂×C₃²	—	4	16	no	—
297	C₂×C₃²	—	6	4	no	—
298	C₂×C₃²	C₂×#235	1	6	yes	complemented
299	C₂×C₃²	C₂×#237	1	24	yes	complemented
300	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
301	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
302	C₃⋊D₃	—	6	4	no	—
303	C₃⋊D₃	—	6	16	no	—
304	C₃⋊D₃	—	12	16	no	—
305	C₃×D₃	—	2	16	no	—
306	C₂⁴	—	3	1	no	—
307	C₂⁴	—	27	1	no	—
308	C₂⁴	D₃×C₃⋊D₃	1	1	yes	characteristic
309	#41	—	27	64	no	—
310	C₂×Q₈	—	27	12	no	—
311	C₂×D₄	—	3	12	no	—
312	C₂×D₄	—	27	12	no	—
313	C₂×D₄	—	27	12	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	9	12	no	—
316	C₂²×C₄	—	9	1	no	—
317	C₂²×C₄	—	9	1	no	—
318	C₂²×C₄	—	27	12	no	—
319	C₂²×C₄	—	27	12	no	—
320	C₂²×C₄	—	27	1	no	—
321	C₂²×C₃	—	2	48	no	—
322	C₂²×C₃	—	2	12	no	—
323	C₂²×C₃	—	2	12	no	—
324	C₂²×C₃	—	2	16	no	—
325	C₂²×C₃	—	2	16	no	—
326	C₂²×C₃	—	3	16	no	—
327	C₂²×C₃	—	4	48	no	—
328	C₂²×C₃	—	6	48	no	—
329	C₂²×C₃	#3804	1	16	yes	complemented
330	C₂²×C₃	#3830	1	4	yes	complemented
331	C₂²×C₃	C₂²×D₃²	1	16	yes	—
332	C₂²×C₃	C₂²×D₃²	1	12	yes	—
333	C₂²×C₃	C₂³×C₃⋊D₃	1	4	yes	—
334	C₂²×C₃	C₂³×C₃⋊D₃	1	3	yes	—
335	C₂×D₃	—	2	12	no	—
336	C₂×D₃	—	9	16	no	—
337	C₂×D₃	—	9	4	no	—
338	C₂×D₃	—	18	16	no	—
339	C₂×D₃	—	18	48	no	—
340	C₂×D₃	—	18	12	no	—
341	C₂×D₃	—	36	48	no	—
342	C₂×D₃	C₂³×C₃⋊D₃	1	4	yes	—
343	C₃×C₄	—	3	16	no	—
344	C₃×C₄	—	9	4	no	—
345	C₃×C₄	—	9	4	no	—
346	Dic₃	—	3	16	no	—
347	Dic₃	—	3	16	no	—
348	Dic₃	—	9	16	no	—
349	Dic₃	—	9	4	no	—
350	Dic₃	—	18	16	no	—
351	Dic₃	C₂³×C₃⋊D₃	1	4	yes	—
352	C₃²	—	2	4	no	—
353	C₃²	C₂²×#235	1	1	yes	characteristic, complemented
354	C₃²	C₂²×#237	1	4	yes	complemented
355	C₂³	—	2	4	no	—
356	C₂³	—	3	6	no	—
357	C₂³	—	6	4	no	—
358	C₂³	—	27	6	no	—
359	C₂³	—	54	4	no	—
360	C₂³	C₂×D₃×C₃⋊D₃	1	6	yes	—
361	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
362	Q₈	—	27	16	no	—
363	D₄	—	3	16	no	—
364	D₄	—	27	16	no	—
365	D₄	—	27	16	no	—
366	C₂×C₄	—	3	6	no	—
367	C₂×C₄	—	9	6	no	—
368	C₂×C₄	—	9	6	no	—
369	C₂×C₄	—	9	16	no	—
370	C₂×C₄	—	27	16	no	—
371	C₂×C₄	—	27	16	no	—
372	C₂×C₄	—	27	6	no	—
373	C₂×C₃	—	2	16	no	—
374	C₂×C₃	—	2	4	no	—
375	C₂×C₃	—	2	24	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	4	16	no	—
378	C₂×C₃	—	6	16	no	—
379	C₂×C₃	C₂×#3804	1	24	yes	complemented
380	C₂×C₃	C₂×#3830	1	6	yes	complemented
381	C₂×C₃	C₂³×D₃²	1	4	yes	—
382	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
383	D₃	—	2	4	no	—
384	D₃	—	18	16	no	—
385	D₃	—	18	4	no	—
386	D₃	—	36	16	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	3	4	no	—
389	C₂²	—	6	12	no	—
390	C₂²	—	27	4	no	—
391	C₂²	—	54	12	no	—
392	C₂²	#89028	1	4	yes	direct product factor
393	C₂²	C₂²×D₃×C₃⋊D₃	1	4	yes	—
394	C₂²	C₂²×D₃×C₃⋊D₃	1	3	yes	—
395	C₄	—	3	4	no	—
396	C₄	—	9	4	no	—
397	C₄	—	9	4	no	—
398	C₄	—	27	4	no	—
399	C₃	—	2	4	no	—
400	C₃	C₂²×#3804	1	4	yes	complemented
401	C₃	C₂²×#3830	1	1	yes	characteristic, complemented
402	C₂	—	2	4	no	—
403	C₂	—	6	4	no	—
404	C₂	—	54	4	no	—
405	C₂	C₂×#89028	1	6	yes	direct product factor
406	C₂	C₂³×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×C₃⋊D₃
commutator, cosocle	C₂×C₃³	C₂⁵
Frattini	C₂	C₂³×D₃×C₃⋊D₃
Fitting	C₂⁴×C₃³	C₂²
socle	C₂³×C₃³	C₂³
hypercenter	C₂⁴	D₃×C₃⋊D₃
hypocenter	C₃³	C₂²×#41
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂²×#6312	C₂	semidirect
2. C₂³×C₃×C₃⋊Dic₃	C₂	semidirect
3. C₂²×C₃²×#67	C₂	semidirect
4. C₂²×#6293	C₂	semidirect
5. C₂²×#6291	C₂	semidirect
6. C₂²×#6289	C₂	semidirect
7. C₂×#89028	C₂	direct (N × H)
8. C₂²×D₃×C₃⋊Dic₃	C₂	semidirect
14. C₂×#6312	C₂²	semidirect
18. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
19. C₂×C₃²×#67	C₂²	semidirect
21. C₂×#6293	C₂²	semidirect
22. C₂×#6291	C₂²	semidirect
23. C₂×#6289	C₂²	semidirect
24. #89028	C₂²	direct (N × H)
25. C₂×D₃×C₃⋊Dic₃	C₂²	semidirect
32. C₂³×C₃⋊Dic₃	D₃	semidirect
36. C₂²×C₃×#67	D₃	semidirect
50. #6312	C₂³	semidirect
54. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
55. C₃²×#67	C₂³	semidirect
57. #6293	C₂³	semidirect
58. #6291	C₂³	semidirect
59. #6289	C₂³	semidirect
60. D₃×C₃⋊Dic₃	C₂³	semidirect
83. C₂²×C₃⋊Dic₃	C₂×D₃	semidirect
87. C₂×C₃×#67	C₂×D₃	semidirect
98. C₂²×C₃³	#41	semidirect
115. C₂²×#67	C₃⋊D₃	semidirect
157. C₂×C₃⋊Dic₃	C₂²×D₃	semidirect
160. C₃×#67	C₂²×D₃	semidirect
171. C₂×C₃³	C₂×#41	semidirect
192. C₂×#67	C₂×C₃⋊D₃	semidirect
217. C₂²×C₃²	#235	semidirect
218. C₂²×C₃²	#237	semidirect
248. C₃³	C₂²×#41	semidirect
277. #67	C₂²×C₃⋊D₃	semidirect
298. C₂×C₃²	C₂×#235	semidirect
299. C₂×C₃²	C₂×#237	semidirect
329. C₂²×C₃	#3804	semidirect
330. C₂²×C₃	#3830	semidirect
353. C₃²	C₂²×#235	semidirect
354. C₃²	C₂²×#237	semidirect
379. C₂×C₃	C₂×#3804	semidirect
380. C₂×C₃	C₂×#3830	semidirect
392. C₂²	#89028	direct (N × H)
400. C₃	C₂²×#3804	semidirect
401. C₃	C₂²×#3830	semidirect
405. C₂	C₂×#89028	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×#6312	2
C₂³×C₃×C₃⋊Dic₃	2
C₂²×C₃²×#67	2
C₂²×#6293	2
C₂²×#6291	2
C₂²×#6289	2
C₂×#89028	2
C₂²×D₃×C₃⋊Dic₃	2
C₂²×#3830	3
C₂²×#3804	3

Subgroups — C22×#89028 #13181654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#89028 #13181654