Subgroups — C₂×#11723634 #13178077

Order 1728.

4500 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6290	C₂	1	2	yes	maximal, complemented
4	C₂×#88864	C₂	1	1	yes	maximal, characteristic, complemented
5	#11723634	C₂	1	8	yes	maximal, direct product factor
6	C₂×#88803	C₂	1	2	yes	maximal, complemented
7	C₂×#64146	—	3	1	no	maximal
8	C₂×#63976	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₃⋊D₃	—	2	4	no	—
11	C₂³×C₃×C₃⋊D₃	—	2	8	no	—
12	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
13	C₂³×C₃×C₃⋊D₃	C₂²	1	4	yes	complemented
14	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
16	C₂×C₃²×#67	—	2	4	no	—
17	C₂×C₃²×#67	C₂²	1	4	yes	complemented
18	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×#6290	—	2	8	no	—
20	C₂×#6290	C₂²	1	8	yes	complemented
21	#88864	C₂²	1	4	yes	complemented
22	#88803	C₂²	1	8	yes	complemented
23	C₂⁴×C₃⋊D₃	D₃	1	1	yes	characteristic, complemented
24	C₂⁴×C₃×D₃	—	3	4	no	—
25	C₂²×C₃²×D₄	—	3	1	no	—
26	C₂²×#638	—	3	2	no	—
27	C₂²×C₃×#67	D₃	1	4	yes	complemented
28	C₂²×#625	—	3	8	no	—
29	C₂×#3757	—	3	1	no	—
30	C₂×#3757	—	3	4	no	—
31	C₂×#3757	—	6	4	no	—
32	#64146	—	3	8	no	—
33	C₂×#3752	—	3	2	no	—
34	#63976	—	3	32	no	—
35	C₂×(C₂×D₃)⋊Dic₃	—	3	8	no	—
36	C₂³×C₃³	—	2	4	no	—
37	C₂³×C₃³	D₄	1	4	yes	complemented
38	C₂³×C₃³	C₂³	1	2	yes	—
39	C₂³×C₃³	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₃⋊D₃	—	2	32	no	—
41	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
42	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
43	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
44	C₂²×C₃×C₃⋊D₃	—	2	16	no	—
45	C₂²×C₃×C₃⋊D₃	D₄	1	8	yes	complemented
46	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
47	C₂²×C₃²×D₃	—	2	4	no	—
48	C₂²×C₃²×D₃	—	2	2	no	—
49	C₂²×C₃²×D₃	C₂³	1	2	yes	complemented
50	C₂×C₃⋊(C₃⋊Dic₃)	—	2	4	no	—
51	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	4	yes	complemented
52	C₃²×#67	—	2	8	no	—
53	C₂×C₃²×Dic₃	—	2	2	no	—
54	C₂×C₃²×Dic₃	C₂³	1	2	yes	complemented
55	#6290	—	2	16	no	—
56	C₂×#953	—	9	1	no	—
57	C₂×#937	—	9	4	no	—
58	C₂⁴×C₃²	—	2	4	no	—
59	C₂⁴×C₃²	—	3	1	no	—
60	C₂⁴×C₃²	C₂×D₃	1	4	yes	—
61	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
62	C₂³×C₃⋊D₃	—	2	4	no	—
63	C₂³×C₃⋊D₃	—	2	8	no	—
64	C₂³×C₃⋊D₃	C₂×D₃	1	2	yes	—
65	C₂³×C₃⋊D₃	C₂×D₃	1	4	yes	complemented
66	C₂³×C₃×D₃	—	3	8	no	—
67	C₂³×C₃×D₃	—	3	16	no	—
68	C₂³×C₃×D₃	—	6	32	no	—
69	C₂³×C₃×D₃	—	6	16	no	—
70	C₂³×C₃×D₃	C₂×D₃	1	4	yes	complemented
71	C₂×C₃²×D₄	—	3	4	no	—
72	C₂×C₃²×D₄	—	6	4	no	—
73	C₂²×C₃²×C₄	—	3	1	no	—
74	C₂×#638	—	3	8	no	—
75	C₂×#638	—	6	8	no	—
76	C₂²×C₃⋊Dic₃	—	3	2	no	—
77	C₂²×C₃⋊Dic₃	—	3	8	no	—
78	C₂²×C₃⋊Dic₃	—	6	8	no	—
79	C₂×C₃×#67	—	2	16	no	—
80	C₂×C₃×#67	C₂×D₃	1	16	yes	complemented
81	C₂²×C₃×Dic₃	C₂×D₃	1	4	yes	complemented
82	C₂×#625	—	3	32	no	—
83	C₂×#625	—	6	32	no	—
84	#3757	—	3	4	no	—
85	#3757	—	3	16	no	—
86	#3757	—	6	16	no	—
87	#3752	—	3	8	no	—
88	(C₂×D₃)⋊Dic₃	—	3	32	no	—
89	C₂²×C₃³	—	2	8	no	—
90	C₂²×C₃³	—	2	4	no	—
91	C₂²×C₃³	C₂×D₄	1	4	yes	—
92	C₂²×C₃³	C₂×D₄	1	2	yes	—
93	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
94	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
95	C₂×C₃×C₃⋊D₃	—	2	32	no	—
96	C₂×C₃×C₃⋊D₃	—	2	16	no	—
97	C₂×C₃×C₃⋊D₃	—	2	4	no	—
98	C₂×C₃×C₃⋊D₃	—	2	4	no	—
99	C₂×C₃×C₃⋊D₃	C₂×D₄	1	8	yes	complemented
100	C₂×C₃²×D₃	—	2	4	no	—
101	C₂×C₃²×D₃	—	2	2	no	—
102	C₂×C₃²×D₃	—	4	4	no	—
103	C₃⋊(C₃⋊Dic₃)	—	2	4	no	—
104	C₃²×Dic₃	—	2	2	no	—
105	C₂⁵×C₃	—	9	1	no	—
106	C₂⁴×D₃	—	3	4	no	—
107	C₂²×C₃×D₄	—	3	4	no	—
108	C₂²×#67	—	9	8	no	—
109	C₂²×#67	—	9	2	no	—
110	C₂²×#67	C₃⋊D₃	1	1	yes	characteristic, complemented
111	#953	—	9	8	no	—
112	C₂×#217	—	9	4	no	—
113	C₂×#217	—	9	1	no	—
114	C₂×#217	—	9	2	no	—
115	C₂×#217	—	18	4	no	—
116	#937	—	9	32	no	—
117	C₂×(C₂×D₃)⋊C₄	—	9	8	no	—
118	C₂³×C₃²	—	2	4	no	—
119	C₂³×C₃²	—	2	16	no	—
120	C₂³×C₃²	—	2	4	no	—
121	C₂³×C₃²	—	2	8	no	—
122	C₂³×C₃²	—	2	16	no	—
123	C₂³×C₃²	—	3	2	no	—
124	C₂³×C₃²	—	4	16	no	—
125	C₂³×C₃²	—	6	4	no	—
126	C₂³×C₃²	—	6	2	no	—
127	C₂³×C₃²	#67	1	16	yes	complemented
128	C₂³×C₃²	#67	1	4	yes	complemented
129	C₂³×C₃²	C₂²×D₃	1	8	yes	—
130	C₂³×C₃²	C₂²×D₃	1	4	yes	—
131	C₂³×C₃²	C₂²×D₃	1	2	yes	—
132	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
133	C₂²×C₃⋊D₃	—	2	32	no	—
134	C₂²×C₃⋊D₃	—	2	4	no	—
135	C₂²×C₃⋊D₃	—	2	4	no	—
136	C₂²×C₃⋊D₃	—	2	8	no	—
137	C₂²×C₃⋊D₃	—	2	16	no	—
138	C₂²×C₃⋊D₃	#67	1	8	yes	complemented
139	C₂²×C₃⋊D₃	C₂²×D₃	1	4	yes	—
140	C₂²×C₃×D₃	—	2	16	no	—
141	C₂²×C₃×D₃	—	2	8	no	—
142	C₂²×C₃×D₃	—	3	32	no	—
143	C₂²×C₃×D₃	—	3	16	no	—
144	C₂²×C₃×D₃	—	6	64	no	—
145	C₂²×C₃×D₃	—	6	128	no	—
146	C₂²×C₃×D₃	—	6	16	no	—
147	C₂²×C₃×D₃	—	6	16	no	—
148	C₂²×C₃×D₃	—	6	32	no	—
149	C₂²×C₃×D₃	C₂²×D₃	1	8	yes	complemented
150	C₃²×D₄	—	6	8	no	—
151	C₂×C₃²×C₄	—	3	2	no	—
152	C₂×C₃²×C₄	—	6	2	no	—
153	#638	—	6	16	no	—
154	C₂×C₃⋊Dic₃	—	3	4	no	—
155	C₂×C₃⋊Dic₃	—	3	16	no	—
156	C₂×C₃⋊Dic₃	—	6	16	no	—
157	C₂×C₃⋊Dic₃	—	6	4	no	—
158	C₂×C₃⋊Dic₃	—	6	16	no	—
159	C₂×C₃⋊Dic₃	—	12	16	no	—
160	C₃×#67	—	2	32	no	—
161	C₂×C₃×Dic₃	—	2	8	no	—
162	C₂×C₃×Dic₃	C₂²×D₃	1	8	yes	complemented
163	#625	—	6	64	no	—
164	C₂×#120	—	27	1	no	Sylow
165	C₂×C₃³	—	2	4	no	—
166	C₂×C₃³	#120	1	4	yes	complemented
167	C₂×C₃³	C₂²×D₄	1	2	yes	—
168	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
169	C₃×C₃⋊D₃	—	2	8	no	—
170	C₃²×D₃	—	4	2	no	—
171	C₂⁴×C₃	—	2	4	no	—
172	C₂⁴×C₃	—	3	4	no	—
173	C₂⁴×C₃	—	9	2	no	—
174	C₂⁴×C₃	—	9	4	no	—
175	C₂⁴×C₃	—	18	8	no	—
176	C₂⁴×C₃	—	18	4	no	—
177	C₂⁴×C₃	D₃²	1	4	yes	—
178	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
179	C₂³×D₃	—	3	8	no	—
180	C₂³×D₃	—	3	16	no	—
181	C₂³×D₃	—	6	32	no	—
182	C₂³×D₃	—	6	16	no	—
183	C₂³×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
184	C₂×C₃×D₄	—	3	16	no	—
185	C₂×C₃×D₄	—	6	16	no	—
186	C₂²×C₃×C₄	—	3	4	no	—
187	C₂×#67	—	2	4	no	—
188	C₂×#67	—	9	32	no	—
189	C₂×#67	—	9	8	no	—
190	C₂×#67	—	18	8	no	—
191	C₂×#67	—	18	32	no	—
192	C₂×#67	C₂×C₃⋊D₃	1	4	yes	complemented
193	C₂²×Dic₃	—	9	8	no	—
194	C₂²×Dic₃	—	9	2	no	—
195	C₂²×Dic₃	—	18	8	no	—
196	C₂²×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
197	#217	—	9	16	no	—
198	#217	—	9	4	no	—
199	#217	—	9	8	no	—
200	#217	—	18	16	no	—
201	(C₂×D₃)⋊C₄	—	9	32	no	—
202	C₂²×C₃²	—	2	8	no	—
203	C₂²×C₃²	—	2	4	no	—
204	C₂²×C₃²	—	2	4	no	—
205	C₂²×C₃²	—	2	8	no	—
206	C₂²×C₃²	—	2	16	no	—
207	C₂²×C₃²	—	2	16	no	—
208	C₂²×C₃²	—	2	32	no	—
209	C₂²×C₃²	—	2	16	no	—
210	C₂²×C₃²	—	4	16	no	—
211	C₂²×C₃²	—	4	32	no	—
212	C₂²×C₃²	—	6	4	no	—
213	C₂²×C₃²	—	6	2	no	—
214	C₂²×C₃²	—	12	4	no	—
215	C₂²×C₃²	D₃×D₄	1	16	yes	—
216	C₂²×C₃²	C₂×#67	1	8	yes	—
217	C₂²×C₃²	C₂×#67	1	2	yes	—
218	C₂²×C₃²	C₂×#67	1	4	yes	—
219	C₂²×C₃²	C₂×#67	1	16	yes	complemented
220	C₂²×C₃²	C₂×#67	1	4	yes	complemented
221	C₂²×C₃²	C₂³×D₃	1	4	yes	—
222	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
223	C₂×C₃⋊D₃	—	2	32	no	—
224	C₂×C₃⋊D₃	—	2	16	no	—
225	C₂×C₃⋊D₃	—	2	4	no	—
226	C₂×C₃⋊D₃	—	2	4	no	—
227	C₂×C₃⋊D₃	C₂×#67	1	8	yes	complemented
228	C₂×C₃×D₃	—	2	16	no	—
229	C₂×C₃×D₃	—	2	8	no	—
230	C₂×C₃×D₃	—	3	32	no	—
231	C₂×C₃×D₃	—	4	16	no	—
232	C₂×C₃×D₃	—	6	128	no	—
233	C₂×C₃×D₃	—	6	64	no	—
234	C₂×C₃×D₃	—	6	16	no	—
235	C₂×C₃×D₃	—	6	16	no	—
236	C₃²×C₄	—	6	2	no	—
237	C₃⋊Dic₃	—	6	4	no	—
238	C₃⋊Dic₃	—	6	16	no	—
239	C₃⋊Dic₃	—	12	16	no	—
240	C₃×Dic₃	—	2	8	no	—
241	C₂⁵	—	9	1	no	—
242	C₂²×D₄	—	3	1	no	—
243	C₂²×D₄	—	27	2	no	—
244	#120	—	27	8	no	—
245	C₂×C₂²⋊C₄	—	27	2	no	—
246	C₂×C₂²⋊C₄	—	27	1	no	—
247	C₃³	C₂×#120	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	16	no	—
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	2	16	no	—
251	C₂³×C₃	—	2	8	no	—
252	C₂³×C₃	—	2	4	no	—
253	C₂³×C₃	—	3	8	no	—
254	C₂³×C₃	—	4	16	no	—
255	C₂³×C₃	—	6	8	no	—
256	C₂³×C₃	—	6	16	no	—
257	C₂³×C₃	—	9	4	no	—
258	C₂³×C₃	—	9	8	no	—
259	C₂³×C₃	—	18	16	no	—
260	C₂³×C₃	—	18	32	no	—
261	C₂³×C₃	—	18	4	no	—
262	C₂³×C₃	—	18	4	no	—
263	C₂³×C₃	—	18	8	no	—
264	C₂³×C₃	#625	1	16	yes	complemented
265	C₂³×C₃	#638	1	4	yes	complemented
266	C₂³×C₃	C₂×D₃²	1	8	yes	—
267	C₂³×C₃	C₂×D₃²	1	4	yes	—
268	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
269	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
270	C₂²×D₃	—	2	4	no	—
271	C₂²×D₃	—	2	2	no	—
272	C₂²×D₃	—	3	16	no	—
273	C₂²×D₃	—	3	32	no	—
274	C₂²×D₃	—	6	64	no	—
275	C₂²×D₃	—	6	128	no	—
276	C₂²×D₃	—	6	16	no	—
277	C₂²×D₃	—	6	32	no	—
278	C₂²×D₃	—	6	16	no	—
279	C₂²×D₃	C₂²×C₃⋊D₃	1	2	yes	complemented
280	C₃×D₄	—	6	32	no	—
281	C₂×C₃×C₄	—	3	8	no	—
282	C₂×C₃×C₄	—	6	8	no	—
283	#67	—	2	8	no	—
284	#67	—	18	16	no	—
285	#67	—	18	64	no	—
286	C₂×Dic₃	—	2	2	no	—
287	C₂×Dic₃	—	9	16	no	—
288	C₂×Dic₃	—	9	4	no	—
289	C₂×Dic₃	—	18	16	no	—
290	C₂×Dic₃	—	18	16	no	—
291	C₂×Dic₃	—	18	4	no	—
292	C₂×Dic₃	—	36	16	no	—
293	C₂×Dic₃	C₂²×C₃⋊D₃	1	2	yes	complemented
294	C₂×C₃²	—	2	4	no	—
295	C₂×C₃²	—	2	4	no	—
296	C₂×C₃²	—	2	8	no	—
297	C₂×C₃²	—	2	16	no	—
298	C₂×C₃²	—	2	16	no	—
299	C₂×C₃²	—	4	16	no	—
300	C₂×C₃²	—	12	2	no	—
301	C₂×C₃²	#937	1	16	yes	complemented
302	C₂×C₃²	#953	1	4	yes	complemented
303	C₂×C₃²	C₂×D₃×D₄	1	8	yes	—
304	C₂×C₃²	C₂²×#67	1	4	yes	—
305	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
306	C₂×C₃²	C₂²×#67	1	2	yes	—
307	C₃⋊D₃	—	2	8	no	—
308	C₃×D₃	—	4	8	no	—
309	C₃×D₃	—	6	32	no	—
310	C₂⁴	—	3	1	no	—
311	C₂⁴	—	9	2	no	—
312	C₂⁴	—	9	4	no	—
313	C₂⁴	—	18	8	no	—
314	C₂⁴	—	18	4	no	—
315	C₂⁴	D₃×C₃⋊D₃	1	1	yes	characteristic
316	C₂×D₄	—	3	4	no	—
317	C₂×D₄	—	6	4	no	—
318	C₂×D₄	—	27	8	no	—
319	C₂×D₄	—	54	8	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	—	27	2	no	—
322	C₂²⋊C₄	—	27	8	no	—
323	C₂²⋊C₄	—	27	4	no	—
324	C₂²×C₃	—	2	16	no	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	8	no	—
327	C₂²×C₃	—	2	32	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	2	16	no	—
331	C₂²×C₃	—	2	16	no	—
332	C₂²×C₃	—	4	16	no	—
333	C₂²×C₃	—	4	32	no	—
334	C₂²×C₃	—	6	8	no	—
335	C₂²×C₃	—	6	16	no	—
336	C₂²×C₃	—	9	8	no	—
337	C₂²×C₃	—	12	16	no	—
338	C₂²×C₃	—	18	32	no	—
339	C₂²×C₃	—	18	4	no	—
340	C₂²×C₃	—	18	4	no	—
341	C₂²×C₃	—	18	16	no	—
342	C₂²×C₃	C₂×#625	1	8	yes	—
343	C₂²×C₃	C₂×#625	1	16	yes	complemented
344	C₂²×C₃	D₃×#67	1	16	yes	—
345	C₂²×C₃	D₄×C₃⋊D₃	1	4	yes	—
346	C₂²×C₃	C₂×#638	1	2	yes	—
347	C₂²×C₃	C₂×#638	1	4	yes	complemented
348	C₂²×C₃	C₂²×D₃²	1	4	yes	—
349	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
350	C₂×D₃	—	2	4	no	—
351	C₂×D₃	—	2	2	no	—
352	C₂×D₃	—	3	32	no	—
353	C₂×D₃	—	4	4	no	—
354	C₂×D₃	—	6	128	no	—
355	C₂×D₃	—	6	16	no	—
356	C₂×D₃	—	6	16	no	—
357	C₂×D₃	—	6	64	no	—
358	C₃×C₄	—	6	8	no	—
359	Dic₃	—	2	2	no	—
360	Dic₃	—	18	16	no	—
361	Dic₃	—	18	4	no	—
362	Dic₃	—	36	16	no	—
363	C₃²	—	2	4	no	—
364	C₃²	C₂×#937	1	4	yes	complemented
365	C₃²	C₂×#953	1	1	yes	characteristic, complemented
366	C₂³	—	2	4	no	—
367	C₂³	—	3	2	no	—
368	C₂³	—	6	2	no	—
369	C₂³	—	6	4	no	—
370	C₂³	—	9	4	no	—
371	C₂³	—	9	8	no	—
372	C₂³	—	18	16	no	—
373	C₂³	—	18	32	no	—
374	C₂³	—	18	4	no	—
375	C₂³	—	18	8	no	—
376	C₂³	—	18	4	no	—
377	C₂³	#6290	1	4	yes	complemented
378	C₂³	C₂×D₃×C₃⋊D₃	1	2	yes	—
379	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
380	D₄	—	6	8	no	—
381	D₄	—	54	16	no	—
382	C₂×C₄	—	3	2	no	—
383	C₂×C₄	—	6	2	no	—
384	C₂×C₄	—	27	4	no	—
385	C₂×C₄	—	54	4	no	—
386	C₂×C₃	—	2	4	no	—
387	C₂×C₃	—	2	16	no	—
388	C₂×C₃	—	2	4	no	—
389	C₂×C₃	—	2	8	no	—
390	C₂×C₃	—	2	16	no	—
391	C₂×C₃	—	4	16	no	—
392	C₂×C₃	—	12	8	no	—
393	C₂×C₃	—	18	8	no	—
394	C₂×C₃	#63976	1	16	yes	complemented
395	C₂×C₃	#64146	1	4	yes	complemented
396	C₂×C₃	C₂²×#625	1	4	yes	—
397	C₂×C₃	C₂×D₃×#67	1	8	yes	—
398	C₂×C₃	C₂×D₄×C₃⋊D₃	1	2	yes	—
399	C₂×C₃	C₂²×#638	1	1	yes	characteristic
400	D₃	—	4	2	no	—
401	D₃	—	6	32	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	6	2	no	—
405	C₂²	—	6	4	no	—
406	C₂²	—	9	8	no	—
407	C₂²	—	12	4	no	—
408	C₂²	—	18	32	no	—
409	C₂²	—	18	4	no	—
410	C₂²	—	18	4	no	—
411	C₂²	—	18	16	no	—
412	C₂²	C₂×#6290	1	2	yes	—
413	C₂²	C₂×#6290	1	4	yes	complemented
414	C₂²	C₃⋊D₃×#67	1	4	yes	—
415	C₂²	C₂²×D₃×C₃⋊D₃	1	1	yes	characteristic
416	C₄	—	6	2	no	—
417	C₄	—	54	4	no	—
418	C₃	—	2	4	no	—
419	C₃	C₂×#63976	1	4	yes	complemented
420	C₃	C₂×#64146	1	1	yes	characteristic, complemented
421	C₂	—	2	4	no	—
422	C₂	—	12	2	no	—
423	C₂	—	18	8	no	—
424	C₂	#11723634	1	4	yes	direct product factor
425	C₂	C₂²×#6290	1	1	yes	characteristic
426	C₂	C₂×C₃⋊D₃×#67	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₃⋊D₃	C₂	semidirect
2. C₂²×C₃²×#67	C₂	semidirect
3. C₂²×#6290	C₂	semidirect
4. C₂×#88864	C₂	semidirect
5. #11723634	C₂	direct (N × H)
6. C₂×#88803	C₂	semidirect
13. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
14. C₂³×C₃²×D₃	C₂²	semidirect
15. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
17. C₂×C₃²×#67	C₂²	semidirect
18. C₂²×C₃²×Dic₃	C₂²	semidirect
20. C₂×#6290	C₂²	semidirect
21. #88864	C₂²	semidirect
22. #88803	C₂²	semidirect
23. C₂⁴×C₃⋊D₃	D₃	semidirect
27. C₂²×C₃×#67	D₃	semidirect
37. C₂³×C₃³	D₄	semidirect
45. C₂²×C₃×C₃⋊D₃	D₄	semidirect
49. C₂²×C₃²×D₃	C₂³	semidirect
51. C₂×C₃⋊(C₃⋊Dic₃)	C₂³	semidirect
54. C₂×C₃²×Dic₃	C₂³	semidirect
65. C₂³×C₃⋊D₃	C₂×D₃	semidirect
70. C₂³×C₃×D₃	C₂×D₃	semidirect
80. C₂×C₃×#67	C₂×D₃	semidirect
81. C₂²×C₃×Dic₃	C₂×D₃	semidirect
93. C₂²×C₃³	C₂×D₄	semidirect
99. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
110. C₂²×#67	C₃⋊D₃	semidirect
127. C₂³×C₃²	#67	semidirect
128. C₂³×C₃²	#67	semidirect
138. C₂²×C₃⋊D₃	#67	semidirect
149. C₂²×C₃×D₃	C₂²×D₃	semidirect
162. C₂×C₃×Dic₃	C₂²×D₃	semidirect
166. C₂×C₃³	#120	semidirect
183. C₂³×D₃	C₂×C₃⋊D₃	semidirect
192. C₂×#67	C₂×C₃⋊D₃	semidirect
196. C₂²×Dic₃	C₂×C₃⋊D₃	semidirect
219. C₂²×C₃²	C₂×#67	semidirect
220. C₂²×C₃²	C₂×#67	semidirect
227. C₂×C₃⋊D₃	C₂×#67	semidirect
247. C₃³	C₂×#120	semidirect
264. C₂³×C₃	#625	semidirect
265. C₂³×C₃	#638	semidirect
279. C₂²×D₃	C₂²×C₃⋊D₃	semidirect
293. C₂×Dic₃	C₂²×C₃⋊D₃	semidirect
301. C₂×C₃²	#937	semidirect
302. C₂×C₃²	#953	semidirect
343. C₂²×C₃	C₂×#625	semidirect
347. C₂²×C₃	C₂×#638	semidirect
364. C₃²	C₂×#937	semidirect
365. C₃²	C₂×#953	semidirect
377. C₂³	#6290	semidirect
394. C₂×C₃	#63976	semidirect
395. C₂×C₃	#64146	semidirect
413. C₂²	C₂×#6290	semidirect
419. C₃	C₂×#63976	semidirect
420. C₃	C₂×#64146	semidirect
424. C₂	#11723634	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₃⋊D₃	2
C₂²×C₃²×#67	2
C₂²×#6290	2
C₂×#88864	2
#11723634	2
C₂×#88803	2
C₂×#64146	3
C₂×#63976	3

Subgroups — C2×#11723634 #13178077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11723634 #13178077