Subgroups — C₂²×#89029 #13181652

Order 1728.

6284 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#638	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×#6290	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#89029	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×#3805	—	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	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
16	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	12	yes	complemented
17	C₂×C₃×#638	C₂²	1	12	yes	complemented
18	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
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×#6290	C₂²	1	12	yes	complemented
23	C₂×Dic₃×C₃⋊D₃	C₂²	1	12	yes	complemented
24	#89029	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	D₃	1	1	yes	characteristic, complemented
29	C₂³×C₃⋊Dic₃	—	3	1	no	—
30	C₂³×C₃⋊Dic₃	—	3	1	no	—
31	C₂³×C₃⋊Dic₃	—	3	4	no	—
32	C₂³×C₃⋊Dic₃	—	6	4	no	—
33	C₂×#3830	—	3	24	no	—
34	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
35	C₂²×#634	—	3	1	no	—
36	C₂²×C₃×#67	—	3	4	no	—
37	C₂²×C₃×#67	D₃	1	4	yes	complemented
38	C₂²×#627	—	3	4	no	—
39	C₂²×#625	—	3	4	no	—
40	C₂×#3805	—	3	96	no	—
41	C₂²×D₃×Dic₃	—	3	4	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	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	6	yes	—
51	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	6	yes	—
52	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	16	yes	complemented
53	C₃×#638	C₂³	1	16	yes	complemented
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	—
55	C₃²×#67	C₂³	1	16	yes	complemented
56	C₂×C₃²×Dic₃	C₂³	1	6	yes	—
57	#6293	C₂³	1	16	yes	complemented
58	#6290	C₂³	1	16	yes	complemented
59	Dic₃×C₃⋊D₃	C₂³	1	16	yes	complemented
60	D₃×C₃⋊Dic₃	C₂³	1	16	yes	complemented
61	C₂²×#237	—	9	4	no	—
62	C₂²×#237	—	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	C₂×D₃	1	1	yes	characteristic
68	C₂³×C₃×D₃	—	3	4	no	—
69	C₂³×C₃×D₃	C₂×D₃	1	4	yes	—
70	C₂×C₃²×D₄	—	3	12	no	—
71	C₂²×C₃²×C₄	—	3	1	no	—
72	C₂×#638	—	3	12	no	—
73	C₂×#638	C₂×D₃	1	12	yes	complemented
74	C₂²×C₃⋊Dic₃	—	3	1	no	—
75	C₂²×C₃⋊Dic₃	—	3	1	no	—
76	C₂²×C₃⋊Dic₃	—	3	12	no	—
77	C₂²×C₃⋊Dic₃	—	3	4	no	—
78	C₂²×C₃⋊Dic₃	—	3	48	no	—
79	C₂²×C₃⋊Dic₃	—	3	4	no	—
80	C₂²×C₃⋊Dic₃	—	3	12	no	—
81	C₂²×C₃⋊Dic₃	—	6	4	no	—
82	C₂²×C₃⋊Dic₃	—	6	4	no	—
83	C₂²×C₃⋊Dic₃	—	6	48	no	—
84	C₂²×C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic
85	#3830	—	3	64	no	—
86	C₂×C₄×C₃⋊D₃	—	3	12	no	—
87	C₂×#634	—	3	12	no	—
88	C₂×C₃×#67	—	3	48	no	—
89	C₂×C₃×#67	C₂×D₃	1	48	yes	complemented
90	C₂²×C₃×Dic₃	—	3	4	no	—
91	C₂²×C₃×Dic₃	C₂×D₃	1	4	yes	—
92	C₂×#627	—	3	48	no	—
93	C₂×#625	—	3	48	no	—
94	#3805	—	3	256	no	—
95	C₂×D₃×Dic₃	—	3	48	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	C₂²×C₃×D₄	—	9	1	no	—
111	C₂²×#67	—	3	4	no	—
112	C₂²×#67	—	9	4	no	—
113	C₂²×#67	—	9	1	no	—
114	C₂²×#67	C₃⋊D₃	1	1	yes	characteristic, complemented
115	C₂³×Dic₃	—	9	4	no	—
116	C₂³×Dic₃	—	9	4	no	—
117	C₂³×Dic₃	—	9	1	no	—
118	C₂³×Dic₃	—	9	1	no	—
119	C₂³×Dic₃	—	18	4	no	—
120	C₂×#237	—	9	96	no	—
121	C₂×#237	—	9	24	no	—
122	C₂²×C₄×D₃	—	9	4	no	—
123	C₂²×C₄×D₃	—	9	1	no	—
124	C₂²×Dic₆	—	9	4	no	—
125	C₂²×Dic₆	—	9	1	no	—
126	C₂³×C₃²	—	2	32	no	—
127	C₂³×C₃²	—	2	16	no	—
128	C₂³×C₃²	—	2	4	no	—
129	C₂³×C₃²	—	2	24	no	—
130	C₂³×C₃²	—	2	4	no	—
131	C₂³×C₃²	—	3	6	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	—	2	4	no	—
138	C₂²×C₃⋊D₃	C₂²×D₃	1	6	yes	—
139	C₂²×C₃×D₃	—	2	16	no	—
140	C₂²×C₃×D₃	—	3	24	no	—
141	C₂²×C₃×D₃	—	6	16	no	—
142	C₂²×C₃×D₃	C₂²×D₃	1	24	yes	—
143	C₃²×D₄	—	3	16	no	—
144	C₂×C₃²×C₄	—	3	6	no	—
145	#638	—	3	16	no	—
146	#638	C₂²×D₃	1	16	yes	complemented
147	C₂×C₃⋊Dic₃	—	3	6	no	—
148	C₂×C₃⋊Dic₃	—	3	6	no	—
149	C₂×C₃⋊Dic₃	—	3	16	no	—
150	C₂×C₃⋊Dic₃	—	3	16	no	—
151	C₂×C₃⋊Dic₃	—	3	24	no	—
152	C₂×C₃⋊Dic₃	—	3	24	no	—
153	C₂×C₃⋊Dic₃	—	3	64	no	—
154	C₂×C₃⋊Dic₃	—	6	24	no	—
155	C₂×C₃⋊Dic₃	—	6	24	no	—
156	C₂×C₃⋊Dic₃	—	6	64	no	—
157	C₂×C₃⋊Dic₃	C₂²×D₃	1	6	yes	—
158	C₄×C₃⋊D₃	—	3	16	no	—
159	#634	—	3	16	no	—
160	C₃×#67	—	3	64	no	—
161	C₃×#67	C₂²×D₃	1	64	yes	complemented
162	C₂×C₃×Dic₃	—	3	24	no	—
163	C₂×C₃×Dic₃	C₂²×D₃	1	24	yes	—
164	#627	—	3	64	no	—
165	#625	—	3	64	no	—
166	D₃×Dic₃	—	3	64	no	—
167	D₃×Dic₃	—	3	64	no	—
168	C₂²×#41	—	27	1	no	Sylow
169	C₂×C₃³	—	2	4	no	—
170	C₂×C₃³	C₂×#41	1	6	yes	complemented
171	C₂×C₃³	C₂⁵	1	1	yes	characteristic
172	C₃×C₃⋊D₃	—	2	4	no	—
173	C₃²×D₃	—	2	4	no	—
174	C₂⁴×C₃	—	2	4	no	—
175	C₂⁴×C₃	—	3	4	no	—
176	C₂⁴×C₃	—	9	1	no	—
177	C₂⁴×C₃	D₃²	1	4	yes	—
178	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
179	C₂³×D₃	—	3	4	no	—
180	C₂³×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic
181	C₂×C₃×D₄	—	3	48	no	—
182	C₂×C₃×D₄	—	9	12	no	—
183	C₂²×C₃×C₄	—	3	4	no	—
184	C₂²×C₃×C₄	—	9	1	no	—
185	C₂×#67	—	3	48	no	—
186	C₂×#67	—	9	48	no	—
187	C₂×#67	—	9	12	no	—
188	C₂×#67	C₂×C₃⋊D₃	1	12	yes	complemented
189	C₂²×Dic₃	—	3	4	no	—
190	C₂²×Dic₃	—	9	48	no	—
191	C₂²×Dic₃	—	9	4	no	—
192	C₂²×Dic₃	—	9	4	no	—
193	C₂²×Dic₃	—	9	48	no	—
194	C₂²×Dic₃	—	9	1	no	—
195	C₂²×Dic₃	—	9	1	no	—
196	C₂²×Dic₃	—	9	12	no	—
197	C₂²×Dic₃	—	9	12	no	—
198	C₂²×Dic₃	—	18	48	no	—
199	C₂²×Dic₃	—	18	4	no	—
200	C₂²×Dic₃	—	18	4	no	—
201	C₂²×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic
202	#237	—	9	256	no	—
203	#237	—	9	64	no	—
204	C₂×C₄×D₃	—	9	48	no	—
205	C₂×C₄×D₃	—	9	12	no	—
206	C₂×Dic₆	—	9	48	no	—
207	C₂×Dic₆	—	9	12	no	—
208	C₂²×C₃²	—	2	96	no	—
209	C₂²×C₃²	—	2	48	no	—
210	C₂²×C₃²	—	2	12	no	—
211	C₂²×C₃²	—	2	16	no	—
212	C₂²×C₃²	—	2	12	no	—
213	C₂²×C₃²	—	2	16	no	—
214	C₂²×C₃²	—	3	4	no	—
215	C₂²×C₃²	—	6	12	no	—
216	C₂²×C₃²	#237	1	16	yes	complemented
217	C₂²×C₃²	#237	1	4	yes	complemented
218	C₂²×C₃²	C₂³×D₃	1	16	yes	—
219	C₂²×C₃²	C₂³×D₃	1	12	yes	—
220	C₂²×C₃²	C₂³×D₃	1	4	yes	—
221	C₂²×C₃²	C₂³×D₃	1	3	yes	—
222	C₂×C₃⋊D₃	—	2	12	no	—
223	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	—
224	C₂×C₃×D₃	—	2	48	no	—
225	C₂×C₃×D₃	—	3	16	no	—
226	C₂×C₃×D₃	—	6	48	no	—
227	C₂×C₃×D₃	C₂³×D₃	1	16	yes	—
228	C₃²×C₄	—	3	4	no	—
229	C₃⋊Dic₃	—	3	4	no	—
230	C₃⋊Dic₃	—	3	4	no	—
231	C₃⋊Dic₃	—	3	16	no	—
232	C₃⋊Dic₃	—	3	16	no	—
233	C₃⋊Dic₃	—	6	16	no	—
234	C₃⋊Dic₃	—	6	16	no	—
235	C₃⋊Dic₃	C₂³×D₃	1	4	yes	—
236	C₃×Dic₃	—	3	16	no	—
237	C₃×Dic₃	C₂³×D₃	1	16	yes	—
238	C₂×#41	—	27	24	no	—
239	C₂²×Q₈	—	27	1	no	—
240	C₂²×D₄	—	3	1	no	—
241	C₂²×D₄	—	9	1	no	—
242	C₂²×D₄	—	27	1	no	—
243	C₂³×C₄	—	27	1	no	—
244	C₂³×C₄	—	27	1	no	—
245	C₂³×C₄	—	27	1	no	—
246	C₃³	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₃	—	2	32	no	—
248	C₂³×C₃	—	2	16	no	—
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	2	24	no	—
251	C₂³×C₃	—	2	4	no	—
252	C₂³×C₃	—	3	24	no	—
253	C₂³×C₃	—	6	16	no	—
254	C₂³×C₃	—	9	6	no	—
255	C₂³×C₃	—	18	4	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	—	3	24	no	—
262	C₂²×D₃	—	6	16	no	—
263	C₂²×D₃	C₂²×C₃⋊D₃	1	6	yes	—
264	C₃×D₄	—	3	64	no	—
265	C₃×D₄	—	9	16	no	—
266	C₂×C₃×C₄	—	3	24	no	—
267	C₂×C₃×C₄	—	9	6	no	—
268	#67	—	3	64	no	—
269	#67	—	9	64	no	—
270	#67	—	9	16	no	—
271	#67	C₂²×C₃⋊D₃	1	16	yes	complemented
272	C₂×Dic₃	—	3	24	no	—
273	C₂×Dic₃	—	9	64	no	—
274	C₂×Dic₃	—	9	24	no	—
275	C₂×Dic₃	—	9	24	no	—
276	C₂×Dic₃	—	9	64	no	—
277	C₂×Dic₃	—	9	6	no	—
278	C₂×Dic₃	—	9	6	no	—
279	C₂×Dic₃	—	9	16	no	—
280	C₂×Dic₃	—	9	16	no	—
281	C₂×Dic₃	—	18	24	no	—
282	C₂×Dic₃	—	18	24	no	—
283	C₂×Dic₃	—	18	64	no	—
284	C₂×Dic₃	C₂²×C₃⋊D₃	1	6	yes	—
285	C₄×D₃	—	9	64	no	—
286	C₄×D₃	—	9	16	no	—
287	Dic₆	—	9	64	no	—
288	Dic₆	—	9	16	no	—
289	C₂×C₃²	—	2	32	no	—
290	C₂×C₃²	—	2	16	no	—
291	C₂×C₃²	—	2	4	no	—
292	C₂×C₃²	—	2	24	no	—
293	C₂×C₃²	—	2	4	no	—
294	C₂×C₃²	—	6	4	no	—
295	C₂×C₃²	C₂×#237	1	24	yes	complemented
296	C₂×C₃²	C₂×#237	1	6	yes	complemented
297	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
298	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
299	C₃⋊D₃	—	2	4	no	—
300	C₃×D₃	—	2	16	no	—
301	C₃×D₃	—	6	16	no	—
302	C₂⁴	—	3	1	no	—
303	C₂⁴	—	9	1	no	—
304	C₂⁴	D₃×C₃⋊D₃	1	1	yes	characteristic
305	#41	—	27	64	no	—
306	C₂×Q₈	—	27	12	no	—
307	C₂×D₄	—	3	12	no	—
308	C₂×D₄	—	9	12	no	—
309	C₂×D₄	—	27	12	no	—
310	C₂²×C₄	—	3	1	no	—
311	C₂²×C₄	—	9	1	no	—
312	C₂²×C₄	—	27	12	no	—
313	C₂²×C₄	—	27	12	no	—
314	C₂²×C₄	—	27	12	no	—
315	C₂²×C₄	—	27	1	no	—
316	C₂²×C₄	—	27	1	no	—
317	C₂²×C₃	—	2	96	no	—
318	C₂²×C₃	—	2	48	no	—
319	C₂²×C₃	—	2	12	no	—
320	C₂²×C₃	—	2	16	no	—
321	C₂²×C₃	—	2	12	no	—
322	C₂²×C₃	—	2	16	no	—
323	C₂²×C₃	—	3	16	no	—
324	C₂²×C₃	—	6	48	no	—
325	C₂²×C₃	—	9	4	no	—
326	C₂²×C₃	—	18	12	no	—
327	C₂²×C₃	#3805	1	16	yes	complemented
328	C₂²×C₃	#3830	1	4	yes	complemented
329	C₂²×C₃	C₂²×D₃²	1	16	yes	—
330	C₂²×C₃	C₂²×D₃²	1	12	yes	—
331	C₂²×C₃	C₂³×C₃⋊D₃	1	4	yes	—
332	C₂²×C₃	C₂³×C₃⋊D₃	1	3	yes	—
333	C₂×D₃	—	2	12	no	—
334	C₂×D₃	—	3	16	no	—
335	C₂×D₃	—	6	48	no	—
336	C₂×D₃	C₂³×C₃⋊D₃	1	4	yes	—
337	C₃×C₄	—	3	16	no	—
338	C₃×C₄	—	9	4	no	—
339	Dic₃	—	3	16	no	—
340	Dic₃	—	9	16	no	—
341	Dic₃	—	9	16	no	—
342	Dic₃	—	9	4	no	—
343	Dic₃	—	9	4	no	—
344	Dic₃	—	18	16	no	—
345	Dic₃	—	18	16	no	—
346	Dic₃	C₂³×C₃⋊D₃	1	4	yes	—
347	C₃²	—	2	4	no	—
348	C₃²	C₂²×#237	1	4	yes	complemented
349	C₃²	C₂²×#237	1	1	yes	characteristic, complemented
350	C₂³	—	2	4	no	—
351	C₂³	—	3	6	no	—
352	C₂³	—	6	4	no	—
353	C₂³	—	9	6	no	—
354	C₂³	—	18	4	no	—
355	C₂³	C₂×D₃×C₃⋊D₃	1	6	yes	—
356	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
357	Q₈	—	27	16	no	—
358	D₄	—	3	16	no	—
359	D₄	—	9	16	no	—
360	D₄	—	27	16	no	—
361	C₂×C₄	—	3	6	no	—
362	C₂×C₄	—	9	6	no	—
363	C₂×C₄	—	27	16	no	—
364	C₂×C₄	—	27	16	no	—
365	C₂×C₄	—	27	6	no	—
366	C₂×C₄	—	27	6	no	—
367	C₂×C₄	—	27	16	no	—
368	C₂×C₃	—	2	32	no	—
369	C₂×C₃	—	2	16	no	—
370	C₂×C₃	—	2	4	no	—
371	C₂×C₃	—	2	24	no	—
372	C₂×C₃	—	2	4	no	—
373	C₂×C₃	—	6	16	no	—
374	C₂×C₃	—	18	4	no	—
375	C₂×C₃	C₂×#3805	1	24	yes	complemented
376	C₂×C₃	C₂×#3830	1	6	yes	complemented
377	C₂×C₃	C₂³×D₃²	1	4	yes	—
378	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
379	D₃	—	2	4	no	—
380	D₃	—	6	16	no	—
381	C₂²	—	2	12	no	—
382	C₂²	—	3	4	no	—
383	C₂²	—	6	12	no	—
384	C₂²	—	9	4	no	—
385	C₂²	—	18	12	no	—
386	C₂²	#89029	1	4	yes	direct product factor
387	C₂²	C₂²×D₃×C₃⋊D₃	1	4	yes	—
388	C₂²	C₂²×D₃×C₃⋊D₃	1	3	yes	—
389	C₄	—	3	4	no	—
390	C₄	—	9	4	no	—
391	C₄	—	27	4	no	—
392	C₄	—	27	4	no	—
393	C₃	—	2	4	no	—
394	C₃	C₂²×#3805	1	4	yes	complemented
395	C₃	C₂²×#3830	1	1	yes	characteristic, complemented
396	C₂	—	2	4	no	—
397	C₂	—	6	4	no	—
398	C₂	—	18	4	no	—
399	C₂	C₂×#89029	1	6	yes	direct product factor
400	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. C₂³×C₃⋊(C₃⋊Dic₃)	C₂	semidirect
2. C₂²×C₃×#638	C₂	semidirect
3. C₂²×C₃²×#67	C₂	semidirect
4. C₂²×#6293	C₂	semidirect
5. C₂²×#6290	C₂	semidirect
6. C₂²×Dic₃×C₃⋊D₃	C₂	semidirect
7. C₂×#89029	C₂	direct (N × H)
8. C₂²×D₃×C₃⋊Dic₃	C₂	semidirect
16. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
17. C₂×C₃×#638	C₂²	semidirect
19. C₂×C₃²×#67	C₂²	semidirect
21. C₂×#6293	C₂²	semidirect
22. C₂×#6290	C₂²	semidirect
23. C₂×Dic₃×C₃⋊D₃	C₂²	semidirect
24. #89029	C₂²	direct (N × H)
25. C₂×D₃×C₃⋊Dic₃	C₂²	semidirect
28. C₂²×#638	D₃	semidirect
37. C₂²×C₃×#67	D₃	semidirect
52. C₂×C₃⋊(C₃⋊Dic₃)	C₂³	semidirect
53. C₃×#638	C₂³	semidirect
55. C₃²×#67	C₂³	semidirect
57. #6293	C₂³	semidirect
58. #6290	C₂³	semidirect
59. Dic₃×C₃⋊D₃	C₂³	semidirect
60. D₃×C₃⋊Dic₃	C₂³	semidirect
73. C₂×#638	C₂×D₃	semidirect
89. C₂×C₃×#67	C₂×D₃	semidirect
98. C₂²×C₃³	#41	semidirect
114. C₂²×#67	C₃⋊D₃	semidirect
146. #638	C₂²×D₃	semidirect
161. C₃×#67	C₂²×D₃	semidirect
170. C₂×C₃³	C₂×#41	semidirect
188. C₂×#67	C₂×C₃⋊D₃	semidirect
216. C₂²×C₃²	#237	semidirect
217. C₂²×C₃²	#237	semidirect
246. C₃³	C₂²×#41	semidirect
271. #67	C₂²×C₃⋊D₃	semidirect
295. C₂×C₃²	C₂×#237	semidirect
296. C₂×C₃²	C₂×#237	semidirect
327. C₂²×C₃	#3805	semidirect
328. C₂²×C₃	#3830	semidirect
348. C₃²	C₂²×#237	semidirect
349. C₃²	C₂²×#237	semidirect
375. C₂×C₃	C₂×#3805	semidirect
376. C₂×C₃	C₂×#3830	semidirect
386. C₂²	#89029	direct (N × H)
394. C₃	C₂²×#3805	semidirect
395. C₃	C₂²×#3830	semidirect
399. C₂	C₂×#89029	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃⋊(C₃⋊Dic₃)	2
C₂²×C₃×#638	2
C₂²×C₃²×#67	2
C₂²×#6293	2
C₂²×#6290	2
C₂²×Dic₃×C₃⋊D₃	2
C₂×#89029	2
C₂²×D₃×C₃⋊Dic₃	2
C₂²×#3830	3
C₂²×#3805	3

Subgroups — C22×#89029 #13181652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#89029 #13181652