Subgroups — C₂²×C₃×#64162 #72252821

Order 3456.

49864 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	C₂⁶×C₃³	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#638	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×#64162	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₃×#3757	C₂	1	3	yes	maximal, complemented
5	C₂²×C₃×#953	—	3	4	no	maximal
6	C₂²×#64162	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂⁵×C₃³	—	2	24	no	—
8	C₂⁵×C₃³	C₂²	1	3	yes	—
9	C₂⁵×C₃³	C₂²	1	12	yes	complemented
10	C₂⁴×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₃×#638	—	2	24	no	—
12	C₂²×C₃×#638	C₂²	1	36	yes	complemented
13	C₂³×C₃×C₃⋊Dic₃	C₂²	1	3	yes	complemented
14	C₃×#64162	C₂²	1	64	yes	direct product factor
15	C₂×C₃×#3757	C₂²	1	36	yes	complemented
16	C₂⁶×C₃²	—	2	4	no	—
17	C₂⁶×C₃²	D₃	1	4	yes	complemented
18	C₂⁶×C₃²	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂³×#638	C₂×C₃	1	3	yes	complemented
20	C₂³×C₃×#67	—	3	12	no	—
21	C₂×#64162	C₂×C₃	1	24	yes	direct product factor
22	C₂²×#3757	C₂×C₃	1	3	yes	complemented
23	C₂×C₃×#953	—	3	96	no	—
24	C₂²×C₃×#217	—	3	12	no	—
25	C₂⁴×C₃³	—	2	128	no	—
26	C₂⁴×C₃³	—	2	24	no	—
27	C₂⁴×C₃³	—	2	144	no	—
28	C₂⁴×C₃³	D₄	1	24	yes	complemented
29	C₂⁴×C₃³	C₂³	1	18	yes	—
30	C₂⁴×C₃³	C₂³	1	1	yes	characteristic
31	C₂⁴×C₃³	C₂³	1	16	yes	complemented
32	C₂³×C₃×C₃⋊D₃	—	2	12	no	—
33	C₂³×C₃×C₃⋊D₃	C₂³	1	6	yes	complemented
34	C₂×C₃×#638	—	2	144	no	—
35	C₂×C₃×#638	C₂³	1	48	yes	complemented
36	C₂²×C₃×C₃⋊Dic₃	—	2	12	no	—
37	C₂²×C₃×C₃⋊Dic₃	C₂³	1	18	yes	complemented
38	C₃×#3757	C₂³	1	48	yes	complemented
39	C₂²×C₃×#120	—	9	1	no	—
40	C₂²×#953	—	3	4	no	—
41	C₂⁵×C₃²	—	2	192	no	—
42	C₂⁵×C₃²	—	2	96	no	—
43	C₂⁵×C₃²	—	2	24	no	—
44	C₂⁵×C₃²	—	2	12	no	—
45	C₂⁵×C₃²	—	2	48	no	—
46	C₂⁵×C₃²	C₂×D₃	1	12	yes	—
47	C₂⁵×C₃²	C₂×D₃	1	48	yes	complemented
48	C₂⁵×C₃²	C₂²×C₃	1	3	yes	—
49	C₂⁵×C₃²	C₂²×C₃	1	12	yes	complemented
50	C₂⁴×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
51	C₂⁴×C₃×D₃	—	3	4	no	—
52	C₂²×#638	—	2	24	no	—
53	C₂²×#638	C₂²×C₃	1	36	yes	complemented
54	C₂³×C₃⋊Dic₃	C₂²×C₃	1	3	yes	complemented
55	C₂²×C₃×#67	—	3	144	no	—
56	C₂²×C₃×#67	—	6	96	no	—
57	C₂³×C₃×Dic₃	—	3	12	no	—
58	#64162	C₂²×C₃	1	64	yes	direct product factor
59	C₂×#3757	C₂²×C₃	1	36	yes	complemented
60	C₃×#953	—	3	256	no	—
61	C₂×C₃×#217	—	3	144	no	—
62	C₂³×C₃³	—	2	384	no	—
63	C₂³×C₃³	—	2	96	no	—
64	C₂³×C₃³	—	2	72	no	—
65	C₂³×C₃³	—	2	96	no	—
66	C₂³×C₃³	C₂×D₄	1	12	yes	—
67	C₂³×C₃³	C₂×D₄	1	72	yes	complemented
68	C₂³×C₃³	C₂⁴	1	12	yes	—
69	C₂³×C₃³	C₂⁴	1	3	yes	—
70	C₂²×C₃×C₃⋊D₃	—	2	36	no	—
71	C₂²×C₃×C₃⋊D₃	—	4	16	no	—
72	C₂²×C₃×C₃⋊D₃	C₂⁴	1	4	yes	complemented
73	C₃×#638	—	2	96	no	—
74	C₂×C₃×C₃⋊Dic₃	—	2	36	no	—
75	C₂×C₃×C₃⋊Dic₃	C₂⁴	1	12	yes	complemented
76	C₂⁶×C₃	—	2	4	no	—
77	C₂⁶×C₃	C₃×D₃	1	4	yes	complemented
78	C₂⁶×C₃	C₃⋊D₃	1	1	yes	characteristic, complemented
79	C₂³×C₃×D₄	—	9	3	no	—
80	C₂³×#67	—	3	12	no	—
81	C₂×C₃×#120	—	9	24	no	—
82	C₂²×C₃×C₂²⋊C₄	—	9	3	no	—
83	C₂×#953	—	3	96	no	—
84	C₂²×#217	—	3	12	no	—
85	C₂⁴×C₃²	—	2	1024	no	—
86	C₂⁴×C₃²	—	2	192	no	—
87	C₂⁴×C₃²	—	2	1152	no	—
88	C₂⁴×C₃²	—	2	512	no	—
89	C₂⁴×C₃²	—	2	128	no	—
90	C₂⁴×C₃²	—	2	96	no	—
91	C₂⁴×C₃²	—	2	72	no	—
92	C₂⁴×C₃²	—	2	4	no	—
93	C₂⁴×C₃²	—	2	64	no	—
94	C₂⁴×C₃²	—	2	96	no	—
95	C₂⁴×C₃²	—	2	576	no	—
96	C₂⁴×C₃²	—	2	24	no	—
97	C₂⁴×C₃²	—	2	144	no	—
98	C₂⁴×C₃²	#67	1	96	yes	complemented
99	C₂⁴×C₃²	C₃×D₄	1	24	yes	complemented
100	C₂⁴×C₃²	C₂²×D₃	1	72	yes	—
101	C₂⁴×C₃²	C₂²×D₃	1	4	yes	—
102	C₂⁴×C₃²	C₂²×D₃	1	64	yes	complemented
103	C₂⁴×C₃²	C₂³×C₃	1	18	yes	—
104	C₂⁴×C₃²	C₂³×C₃	1	1	yes	characteristic
105	C₂⁴×C₃²	C₂³×C₃	1	16	yes	complemented
106	C₂³×C₃⋊D₃	—	2	12	no	—
107	C₂³×C₃⋊D₃	C₂³×C₃	1	6	yes	complemented
108	C₂³×C₃×D₃	—	3	24	no	—
109	C₂³×C₃×D₃	—	6	48	no	—
110	C₂×#638	—	2	144	no	—
111	C₂×#638	C₂³×C₃	1	48	yes	complemented
112	C₂²×C₃⋊Dic₃	—	2	12	no	—
113	C₂²×C₃⋊Dic₃	C₂³×C₃	1	18	yes	complemented
114	C₂×C₃×#67	—	3	192	no	—
115	C₂×C₃×#67	—	6	576	no	—
116	C₂²×C₃×Dic₃	—	3	72	no	—
117	C₂²×C₃×Dic₃	—	6	48	no	—
118	#3757	C₂³×C₃	1	48	yes	complemented
119	C₃×#217	—	3	192	no	—
120	C₂²×#120	—	9	1	no	Sylow
121	C₂²×C₃³	—	2	128	no	—
122	C₂²×C₃³	—	2	144	no	—
123	C₂²×C₃³	—	2	24	no	—
124	C₂²×C₃³	#120	1	16	yes	complemented
125	C₂²×C₃³	C₂²×D₄	1	18	yes	—
126	C₂²×C₃³	C₂²×D₄	1	24	yes	complemented
127	C₂²×C₃³	C₂⁵	1	1	yes	characteristic
128	C₂×C₃×C₃⋊D₃	—	2	12	no	—
129	C₂×C₃×C₃⋊D₃	—	4	24	no	—
130	C₃×C₃⋊Dic₃	—	2	12	no	—
131	C₂⁵×C₃	—	2	192	no	—
132	C₂⁵×C₃	—	2	96	no	—
133	C₂⁵×C₃	—	2	24	no	—
134	C₂⁵×C₃	—	2	12	no	—
135	C₂⁵×C₃	—	2	48	no	—
136	C₂⁵×C₃	—	9	1	no	—
137	C₂⁵×C₃	C₂×C₃×D₃	1	12	yes	—
138	C₂⁵×C₃	C₂×C₃×D₃	1	48	yes	complemented
139	C₂⁵×C₃	C₂×C₃⋊D₃	1	3	yes	—
140	C₂⁵×C₃	C₂×C₃⋊D₃	1	12	yes	complemented
141	C₂⁴×D₃	—	3	4	no	—
142	C₂²×C₃×D₄	—	9	36	no	—
143	C₂²×C₃×D₄	—	18	24	no	—
144	C₂³×C₃×C₄	—	9	3	no	—
145	C₂²×#67	—	3	144	no	—
146	C₂²×#67	—	6	96	no	—
147	C₂³×Dic₃	—	3	12	no	—
148	C₃×#120	—	9	64	no	—
149	C₂×C₃×C₂²⋊C₄	—	9	36	no	—
150	#953	—	3	256	no	—
151	C₂×#217	—	3	144	no	—
152	C₂³×C₃²	—	2	3072	no	—
153	C₂³×C₃²	—	2	1536	no	—
154	C₂³×C₃²	—	2	384	no	—
155	C₂³×C₃²	—	2	768	no	—
156	C₂³×C₃²	—	2	576	no	—
157	C₂³×C₃²	—	2	768	no	—
158	C₂³×C₃²	—	2	384	no	—
159	C₂³×C₃²	—	2	96	no	—
160	C₂³×C₃²	—	2	288	no	—
161	C₂³×C₃²	—	2	384	no	—
162	C₂³×C₃²	—	2	72	no	—
163	C₂³×C₃²	—	2	96	no	—
164	C₂³×C₃²	—	2	48	no	—
165	C₂³×C₃²	—	2	12	no	—
166	C₂³×C₃²	—	2	48	no	—
167	C₂³×C₃²	—	2	288	no	—
168	C₂³×C₃²	C₂×#67	1	48	yes	—
169	C₂³×C₃²	C₂×#67	1	288	yes	complemented
170	C₂³×C₃²	C₂×C₃×D₄	1	12	yes	—
171	C₂³×C₃²	C₂×C₃×D₄	1	72	yes	complemented
172	C₂³×C₃²	C₂³×D₃	1	48	yes	—
173	C₂³×C₃²	C₂³×D₃	1	12	yes	—
174	C₂³×C₃²	C₂⁴×C₃	1	12	yes	—
175	C₂³×C₃²	C₂⁴×C₃	1	3	yes	—
176	C₂²×C₃⋊D₃	—	2	36	no	—
177	C₂²×C₃⋊D₃	—	4	16	no	—
178	C₂²×C₃⋊D₃	C₂⁴×C₃	1	4	yes	complemented
179	C₂²×C₃×D₃	—	3	16	no	—
180	C₂²×C₃×D₃	—	6	144	no	—
181	C₂²×C₃×D₃	—	12	64	no	—
182	#638	—	2	96	no	—
183	C₂×C₃⋊Dic₃	—	2	36	no	—
184	C₂×C₃⋊Dic₃	C₂⁴×C₃	1	12	yes	complemented
185	C₃×#67	—	6	384	no	—
186	C₂×C₃×Dic₃	—	3	48	no	—
187	C₂×C₃×Dic₃	—	6	144	no	—
188	C₂⁶	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
189	C₂³×D₄	—	9	3	no	—
190	C₂×#120	—	9	24	no	—
191	C₂²×C₂²⋊C₄	—	9	3	no	—
192	C₂×C₃³	—	2	24	no	—
193	C₂×C₃³	C₂×#120	1	12	yes	complemented
194	C₂×C₃³	C₂³×D₄	1	3	yes	—
195	C₃×C₃⋊D₃	—	4	4	no	—
196	C₂⁴×C₃	—	2	1024	no	—
197	C₂⁴×C₃	—	2	512	no	—
198	C₂⁴×C₃	—	2	128	no	—
199	C₂⁴×C₃	—	2	192	no	—
200	C₂⁴×C₃	—	2	1152	no	—
201	C₂⁴×C₃	—	2	96	no	—
202	C₂⁴×C₃	—	2	576	no	—
203	C₂⁴×C₃	—	2	24	no	—
204	C₂⁴×C₃	—	2	144	no	—
205	C₂⁴×C₃	—	2	96	no	—
206	C₂⁴×C₃	—	2	72	no	—
207	C₂⁴×C₃	—	2	4	no	—
208	C₂⁴×C₃	—	2	64	no	—
209	C₂⁴×C₃	—	9	6	no	—
210	C₂⁴×C₃	—	18	12	no	—
211	C₂⁴×C₃	C₃×#67	1	96	yes	complemented
212	C₂⁴×C₃	#638	1	24	yes	complemented
213	C₂⁴×C₃	C₂²×C₃×D₃	1	72	yes	—
214	C₂⁴×C₃	C₂²×C₃×D₃	1	4	yes	—
215	C₂⁴×C₃	C₂²×C₃×D₃	1	64	yes	complemented
216	C₂⁴×C₃	C₂²×C₃⋊D₃	1	18	yes	—
217	C₂⁴×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
218	C₂⁴×C₃	C₂²×C₃⋊D₃	1	16	yes	complemented
219	C₂³×D₃	—	3	24	no	—
220	C₂³×D₃	—	6	48	no	—
221	C₂×C₃×D₄	—	9	48	no	—
222	C₂×C₃×D₄	—	18	144	no	—
223	C₂²×C₃×C₄	—	9	18	no	—
224	C₂²×C₃×C₄	—	18	12	no	—
225	C₂×#67	—	3	192	no	—
226	C₂×#67	—	6	576	no	—
227	C₂²×Dic₃	—	3	72	no	—
228	C₂²×Dic₃	—	6	48	no	—
229	C₃×C₂²⋊C₄	—	9	48	no	—
230	#217	—	3	192	no	—
231	C₂²×C₃²	—	2	1024	no	—
232	C₂²×C₃²	—	2	512	no	—
233	C₂²×C₃²	—	2	128	no	—
234	C₂²×C₃²	—	2	1152	no	—
235	C₂²×C₃²	—	2	192	no	—
236	C₂²×C₃²	—	2	96	no	—
237	C₂²×C₃²	—	2	24	no	—
238	C₂²×C₃²	—	2	576	no	—
239	C₂²×C₃²	—	2	144	no	—
240	C₂²×C₃²	—	2	64	no	—
241	C₂²×C₃²	—	2	72	no	—
242	C₂²×C₃²	—	2	96	no	—
243	C₂²×C₃²	—	2	4	no	—
244	C₂²×C₃²	#953	1	64	yes	complemented
245	C₂²×C₃²	C₃×#120	1	16	yes	complemented
246	C₂²×C₃²	C₂²×#67	1	72	yes	—
247	C₂²×C₃²	C₂²×#67	1	96	yes	complemented
248	C₂²×C₃²	C₂²×C₃×D₄	1	18	yes	—
249	C₂²×C₃²	C₂²×C₃×D₄	1	24	yes	complemented
250	C₂²×C₃²	C₂⁴×D₃	1	4	yes	—
251	C₂²×C₃²	C₂⁵×C₃	1	1	yes	characteristic
252	C₂×C₃⋊D₃	—	2	12	no	—
253	C₂×C₃⋊D₃	—	4	24	no	—
254	C₂×C₃×D₃	—	6	48	no	—
255	C₂×C₃×D₃	—	12	96	no	—
256	C₃⋊Dic₃	—	2	12	no	—
257	C₃×Dic₃	—	6	48	no	—
258	C₂⁵	—	2	24	no	—
259	C₂⁵	—	9	1	no	—
260	C₂⁵	C₂×C₃×C₃⋊D₃	1	3	yes	—
261	C₂⁵	C₂×C₃×C₃⋊D₃	1	12	yes	complemented
262	C₂²×D₄	—	9	36	no	—
263	C₂²×D₄	—	18	24	no	—
264	C₂³×C₄	—	9	3	no	—
265	#120	—	9	64	no	—
266	C₂×C₂²⋊C₄	—	9	36	no	—
267	C₃³	C₂²×#120	1	1	yes	characteristic, complemented, Sylow
268	C₂³×C₃	—	2	3072	no	—
269	C₂³×C₃	—	2	1536	no	—
270	C₂³×C₃	—	2	384	no	—
271	C₂³×C₃	—	2	576	no	—
272	C₂³×C₃	—	2	768	no	—
273	C₂³×C₃	—	2	768	no	—
274	C₂³×C₃	—	2	384	no	—
275	C₂³×C₃	—	2	288	no	—
276	C₂³×C₃	—	2	384	no	—
277	C₂³×C₃	—	2	72	no	—
278	C₂³×C₃	—	2	96	no	—
279	C₂³×C₃	—	2	96	no	—
280	C₂³×C₃	—	2	48	no	—
281	C₂³×C₃	—	2	12	no	—
282	C₂³×C₃	—	2	48	no	—
283	C₂³×C₃	—	2	288	no	—
284	C₂³×C₃	—	9	4	no	—
285	C₂³×C₃	—	18	36	no	—
286	C₂³×C₃	—	36	16	no	—
287	C₂³×C₃	C₂×C₃×#67	1	48	yes	—
288	C₂³×C₃	C₂×C₃×#67	1	288	yes	complemented
289	C₂³×C₃	C₂×#638	1	12	yes	—
290	C₂³×C₃	C₂×#638	1	72	yes	complemented
291	C₂³×C₃	C₂³×C₃×D₃	1	48	yes	—
292	C₂³×C₃	C₂³×C₃×D₃	1	12	yes	—
293	C₂³×C₃	C₂³×C₃⋊D₃	1	12	yes	—
294	C₂³×C₃	C₂³×C₃⋊D₃	1	3	yes	—
295	C₂²×D₃	—	3	16	no	—
296	C₂²×D₃	—	6	144	no	—
297	C₂²×D₃	—	12	64	no	—
298	C₃×D₄	—	18	96	no	—
299	C₂×C₃×C₄	—	9	12	no	—
300	C₂×C₃×C₄	—	18	36	no	—
301	#67	—	6	384	no	—
302	C₂×Dic₃	—	3	48	no	—
303	C₂×Dic₃	—	6	144	no	—
304	C₂×C₃²	—	2	192	no	—
305	C₂×C₃²	—	2	96	no	—
306	C₂×C₃²	—	2	24	no	—
307	C₂×C₃²	—	2	48	no	—
308	C₂×C₃²	—	2	12	no	—
309	C₂×C₃²	C₂×#953	1	48	yes	complemented
310	C₂×C₃²	C₂×C₃×#120	1	12	yes	complemented
311	C₂×C₃²	C₂³×#67	1	12	yes	—
312	C₂×C₃²	C₂³×C₃×D₄	1	3	yes	—
313	C₃⋊D₃	—	4	4	no	—
314	C₃×D₃	—	12	16	no	—
315	C₂⁴	—	2	128	no	—
316	C₂⁴	—	2	24	no	—
317	C₂⁴	—	2	144	no	—
318	C₂⁴	—	9	6	no	—
319	C₂⁴	—	18	12	no	—
320	C₂⁴	C₃×#638	1	24	yes	complemented
321	C₂⁴	C₂²×C₃×C₃⋊D₃	1	18	yes	—
322	C₂⁴	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
323	C₂⁴	C₂²×C₃×C₃⋊D₃	1	16	yes	complemented
324	C₂×D₄	—	9	48	no	—
325	C₂×D₄	—	18	144	no	—
326	C₂²×C₄	—	9	18	no	—
327	C₂²×C₄	—	18	12	no	—
328	C₂²⋊C₄	—	9	48	no	—
329	C₂²×C₃	—	2	1024	no	—
330	C₂²×C₃	—	2	128	no	—
331	C₂²×C₃	—	2	512	no	—
332	C₂²×C₃	—	2	192	no	—
333	C₂²×C₃	—	2	1152	no	—
334	C₂²×C₃	—	2	576	no	—
335	C₂²×C₃	—	2	96	no	—
336	C₂²×C₃	—	2	24	no	—
337	C₂²×C₃	—	2	144	no	—
338	C₂²×C₃	—	2	72	no	—
339	C₂²×C₃	—	2	96	no	—
340	C₂²×C₃	—	2	64	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	18	12	no	—
343	C₂²×C₃	—	36	24	no	—
344	C₂²×C₃	C₃×#953	1	64	yes	complemented
345	C₂²×C₃	#64162	1	16	yes	direct product factor
346	C₂²×C₃	C₂²×C₃×#67	1	72	yes	—
347	C₂²×C₃	C₂²×C₃×#67	1	96	yes	complemented
348	C₂²×C₃	C₂²×#638	1	18	yes	—
349	C₂²×C₃	C₂²×#638	1	24	yes	complemented
350	C₂²×C₃	C₂⁴×C₃×D₃	1	4	yes	—
351	C₂²×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
352	C₂×D₃	—	6	48	no	—
353	C₂×D₃	—	12	96	no	—
354	C₃×C₄	—	18	12	no	—
355	Dic₃	—	6	48	no	—
356	C₃²	—	2	4	no	—
357	C₃²	C₂²×#953	1	4	yes	complemented
358	C₃²	C₂²×C₃×#120	1	1	yes	characteristic, complemented
359	C₂³	—	2	384	no	—
360	C₂³	—	2	72	no	—
361	C₂³	—	2	96	no	—
362	C₂³	—	2	96	no	—
363	C₂³	—	9	4	no	—
364	C₂³	—	18	36	no	—
365	C₂³	—	36	16	no	—
366	C₂³	C₂×C₃×#638	1	12	yes	—
367	C₂³	C₂×C₃×#638	1	72	yes	complemented
368	C₂³	C₂³×C₃×C₃⋊D₃	1	12	yes	—
369	C₂³	C₂³×C₃×C₃⋊D₃	1	3	yes	—
370	D₄	—	18	96	no	—
371	C₂×C₄	—	9	12	no	—
372	C₂×C₄	—	18	36	no	—
373	C₂×C₃	—	2	192	no	—
374	C₂×C₃	—	2	24	no	—
375	C₂×C₃	—	2	96	no	—
376	C₂×C₃	—	2	12	no	—
377	C₂×C₃	—	2	48	no	—
378	C₂×C₃	—	36	4	no	—
379	C₂×C₃	C₂×C₃×#953	1	48	yes	complemented
380	C₂×C₃	C₂×#64162	1	12	yes	direct product factor
381	C₂×C₃	C₂³×C₃×#67	1	12	yes	—
382	C₂×C₃	C₂³×#638	1	3	yes	—
383	D₃	—	12	16	no	—
384	C₂²	—	2	128	no	—
385	C₂²	—	2	24	no	—
386	C₂²	—	2	144	no	—
387	C₂²	—	18	12	no	—
388	C₂²	—	36	24	no	—
389	C₂²	C₃×#64162	1	16	yes	direct product factor
390	C₂²	C₂²×C₃×#638	1	18	yes	—
391	C₂²	C₂²×C₃×#638	1	24	yes	complemented
392	C₂²	C₂⁴×C₃×C₃⋊D₃	1	1	yes	characteristic
393	C₄	—	18	12	no	—
394	C₃	—	2	4	no	—
395	C₃	C₂²×#64162	1	1	yes	characteristic, direct product factor
396	C₃	C₂²×C₃×#953	1	4	yes	complemented
397	C₂	—	2	24	no	—
398	C₂	—	36	4	no	—
399	C₂	C₂×C₃×#64162	1	12	yes	direct product factor
400	C₂	C₂³×C₃×#638	1	3	yes	—

	subgroup	G/H
center	C₂⁴×C₃	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×C₃⋊D₃
Fitting	C₂⁶×C₃³	C₂
socle	C₂⁴×C₃³	C₂³
hypercenter	C₂⁶×C₃	C₃⋊D₃
hypocenter	C₃²	C₂²×C₃×#120
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂⁶×C₃

Complements

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

N	H ≅ G/N	type
1. C₂⁶×C₃³	C₂	semidirect
2. C₂³×C₃×#638	C₂	semidirect
3. C₂×C₃×#64162	C₂	direct (N × H)
4. C₂²×C₃×#3757	C₂	semidirect
6. C₂²×#64162	C₃	direct (N × H)
9. C₂⁵×C₃³	C₂²	semidirect
10. C₂⁴×C₃×C₃⋊D₃	C₂²	semidirect
12. C₂²×C₃×#638	C₂²	semidirect
13. C₂³×C₃×C₃⋊Dic₃	C₂²	semidirect
14. C₃×#64162	C₂²	direct (N × H)
15. C₂×C₃×#3757	C₂²	semidirect
17. C₂⁶×C₃²	D₃	semidirect
18. C₂⁶×C₃²	C₂×C₃	semidirect
19. C₂³×#638	C₂×C₃	semidirect
21. C₂×#64162	C₂×C₃	direct (N × H)
22. C₂²×#3757	C₂×C₃	semidirect
28. C₂⁴×C₃³	D₄	semidirect
31. C₂⁴×C₃³	C₂³	semidirect
33. C₂³×C₃×C₃⋊D₃	C₂³	semidirect
35. C₂×C₃×#638	C₂³	semidirect
37. C₂²×C₃×C₃⋊Dic₃	C₂³	semidirect
38. C₃×#3757	C₂³	semidirect
47. C₂⁵×C₃²	C₂×D₃	semidirect
49. C₂⁵×C₃²	C₂²×C₃	semidirect
50. C₂⁴×C₃⋊D₃	C₂²×C₃	semidirect
53. C₂²×#638	C₂²×C₃	semidirect
54. C₂³×C₃⋊Dic₃	C₂²×C₃	semidirect
58. #64162	C₂²×C₃	direct (N × H)
59. C₂×#3757	C₂²×C₃	semidirect
67. C₂³×C₃³	C₂×D₄	semidirect
72. C₂²×C₃×C₃⋊D₃	C₂⁴	semidirect
75. C₂×C₃×C₃⋊Dic₃	C₂⁴	semidirect
77. C₂⁶×C₃	C₃×D₃	semidirect
78. C₂⁶×C₃	C₃⋊D₃	semidirect
98. C₂⁴×C₃²	#67	semidirect
99. C₂⁴×C₃²	C₃×D₄	semidirect
102. C₂⁴×C₃²	C₂²×D₃	semidirect
105. C₂⁴×C₃²	C₂³×C₃	semidirect
107. C₂³×C₃⋊D₃	C₂³×C₃	semidirect
111. C₂×#638	C₂³×C₃	semidirect
113. C₂²×C₃⋊Dic₃	C₂³×C₃	semidirect
118. #3757	C₂³×C₃	semidirect
124. C₂²×C₃³	#120	semidirect
126. C₂²×C₃³	C₂²×D₄	semidirect
138. C₂⁵×C₃	C₂×C₃×D₃	semidirect
140. C₂⁵×C₃	C₂×C₃⋊D₃	semidirect
169. C₂³×C₃²	C₂×#67	semidirect
171. C₂³×C₃²	C₂×C₃×D₄	semidirect
178. C₂²×C₃⋊D₃	C₂⁴×C₃	semidirect
184. C₂×C₃⋊Dic₃	C₂⁴×C₃	semidirect
188. C₂⁶	C₃×C₃⋊D₃	semidirect
193. C₂×C₃³	C₂×#120	semidirect
211. C₂⁴×C₃	C₃×#67	semidirect
212. C₂⁴×C₃	#638	semidirect
215. C₂⁴×C₃	C₂²×C₃×D₃	semidirect
218. C₂⁴×C₃	C₂²×C₃⋊D₃	semidirect
244. C₂²×C₃²	#953	semidirect
245. C₂²×C₃²	C₃×#120	semidirect
247. C₂²×C₃²	C₂²×#67	semidirect
249. C₂²×C₃²	C₂²×C₃×D₄	semidirect
261. C₂⁵	C₂×C₃×C₃⋊D₃	semidirect
267. C₃³	C₂²×#120	semidirect
288. C₂³×C₃	C₂×C₃×#67	semidirect
290. C₂³×C₃	C₂×#638	semidirect
309. C₂×C₃²	C₂×#953	semidirect
310. C₂×C₃²	C₂×C₃×#120	semidirect
320. C₂⁴	C₃×#638	semidirect
323. C₂⁴	C₂²×C₃×C₃⋊D₃	semidirect
344. C₂²×C₃	C₃×#953	semidirect
345. C₂²×C₃	#64162	direct (N × H)
347. C₂²×C₃	C₂²×C₃×#67	semidirect
349. C₂²×C₃	C₂²×#638	semidirect
357. C₃²	C₂²×#953	semidirect
358. C₃²	C₂²×C₃×#120	semidirect
367. C₂³	C₂×C₃×#638	semidirect
379. C₂×C₃	C₂×C₃×#953	semidirect
380. C₂×C₃	C₂×#64162	direct (N × H)
389. C₂²	C₃×#64162	direct (N × H)
391. C₂²	C₂²×C₃×#638	semidirect
395. C₃	C₂²×#64162	direct (N × H)
396. C₃	C₂²×C₃×#953	semidirect
399. C₂	C₂×C₃×#64162	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×C₃³	2
C₂³×C₃×#638	2
C₂×C₃×#64162	2
C₂²×C₃×#3757	2
C₂²×C₃×#953	3
C₂²×#64162	3

Subgroups — C22×C3×#64162 #72252821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#64162 #72252821