Subgroups — C₃×#10592935 #13163277

Order 1728.

1580 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#64135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63664	C₂	1	4	yes	maximal, complemented
5	#10592935	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃×#5236	—	3	4	no	maximal
7	C₃³×#41	—	2	1	no	—
8	C₃³×#41	—	2	1	no	—
9	C₃³×#41	C₄	1	2	yes	complemented
10	C₃³×#41	C₂²	1	2	yes	—
11	C₂×C₃³×Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃³×D₄	—	2	1	no	—
13	C₂×C₃³×D₄	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₃³×C₄	—	2	1	no	—
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₃×#3757	—	2	1	no	—
17	C₃×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
18	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	complemented
19	C₃×#3748	—	2	1	no	—
20	C₃×#3748	C₂²	1	2	yes	complemented
21	C₂×C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
22	C₂×C₃²×#41	—	2	4	no	—
23	C₂×C₃²×#41	D₃	1	4	yes	—
24	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic
25	#64135	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×#926	—	3	4	no	—
28	C₂×C₃×#208	—	3	4	no	—
29	#63664	C₂×C₃	1	4	yes	complemented
30	C₃×#837	—	3	16	no	—
31	C₂³×C₃³	—	2	1	no	—
32	C₂³×C₃³	D₄	1	1	yes	characteristic
33	C₃³×Q₈	—	2	1	no	—
34	C₃³×Q₈	C₂×C₄	1	2	yes	—
35	C₃³×D₄	—	2	2	no	—
36	C₃³×D₄	—	2	2	no	—
37	C₃³×D₄	—	2	1	no	—
38	C₃³×D₄	C₂×C₄	1	2	yes	—
39	C₂×C₃³×C₄	—	2	1	no	—
40	C₂×C₃³×C₄	—	2	2	no	—
41	C₂×C₃³×C₄	—	2	2	no	—
42	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
45	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
46	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
47	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
49	C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
50	C₃×#421	—	9	1	no	—
51	#5236	—	3	4	no	—
52	C₃²×#41	—	2	8	no	—
53	C₃²×#41	—	2	8	no	—
54	C₃²×#41	—	2	8	no	—
55	C₃²×#41	—	2	8	no	—
56	C₃²×#41	—	2	4	no	—
57	C₃²×#41	—	2	4	no	—
58	C₃²×#41	—	2	1	no	—
59	C₃²×#41	—	2	1	no	—
60	C₃²×#41	Dic₃	1	8	yes	complemented
61	C₃²×#41	C₃×C₄	1	2	yes	complemented
62	C₃²×#41	C₂×D₃	1	8	yes	—
63	C₃²×#41	C₂²×C₃	1	2	yes	—
64	C₂×C₃²×Q₈	—	2	4	no	—
65	C₂×C₃²×Q₈	Dic₃	1	4	yes	complemented
66	C₂×C₃²×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
67	C₂×C₃²×D₄	—	2	8	no	—
68	C₂×C₃²×D₄	—	2	4	no	—
69	C₂×C₃²×D₄	—	2	4	no	—
70	C₂×C₃²×D₄	—	2	1	no	—
71	C₂×C₃²×D₄	Dic₃	1	4	yes	complemented
72	C₂×C₃²×D₄	C₃×C₄	1	1	yes	characteristic, complemented
73	C₂²×C₃²×C₄	—	2	8	no	—
74	C₂²×C₃²×C₄	—	2	4	no	—
75	C₂²×C₃²×C₄	—	2	4	no	—
76	C₂²×C₃²×C₄	—	2	1	no	—
77	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
78	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
79	#3757	—	2	1	no	—
80	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
81	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
82	#3748	—	2	1	no	—
83	#3748	C₂²×C₃	1	2	yes	complemented
84	C₂×C₃⋊(C₃⋊C₈)	—	2	1	no	—
85	C₃×#217	—	6	4	no	—
86	C₃×C₄⋊Dic₃	—	6	4	no	—
87	C₃×C₄×Dic₃	—	3	8	no	—
88	C₃×#208	—	3	8	no	—
89	C₃×#208	—	6	4	no	—
90	C₂×C₃×C₃⋊C₈	—	6	4	no	—
91	C₂²×C₃³	—	2	2	no	—
92	C₂²×C₃³	—	4	1	no	—
93	C₂²×C₃³	—	4	2	no	—
94	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
97	C₃³×C₄	—	2	2	no	—
98	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
99	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
100	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
102	C₃×C₃⋊Dic₃	—	4	2	no	—
103	C₂×C₃×#41	—	2	4	no	—
104	C₂×C₃×#41	C₃×D₃	1	4	yes	—
105	C₂×C₃×#41	C₃⋊D₃	1	1	yes	characteristic
106	C₂×C₃×M₁₆	—	9	1	no	—
107	C₃×#117	—	9	1	no	—
108	#926	—	3	4	no	—
109	C₂×#208	—	3	4	no	—
110	C₃×#104	—	9	4	no	—
111	#837	—	3	16	no	—
112	C₂³×C₃²	—	2	8	no	—
113	C₂³×C₃²	—	2	4	no	—
114	C₂³×C₃²	—	2	1	no	—
115	C₂³×C₃²	—	2	4	no	—
116	C₂³×C₃²	#67	1	4	yes	—
117	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
118	C₃²×Q₈	—	2	8	no	—
119	C₃²×Q₈	—	2	4	no	—
120	C₃²×Q₈	—	2	1	no	—
121	C₃²×Q₈	—	2	8	no	—
122	C₃²×Q₈	C₂×Dic₃	1	8	yes	—
123	C₃²×Q₈	C₂×C₃×C₄	1	2	yes	—
124	C₃²×D₄	—	2	16	no	—
125	C₃²×D₄	—	2	16	no	—
126	C₃²×D₄	—	2	8	no	—
127	C₃²×D₄	—	2	8	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₃²×D₄	—	2	8	no	—
130	C₃²×D₄	—	2	2	no	—
131	C₃²×D₄	—	2	4	no	—
132	C₃²×D₄	—	2	1	no	—
133	C₃²×D₄	—	2	8	no	—
134	C₃²×D₄	C₂×Dic₃	1	8	yes	—
135	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
136	C₂×C₃²×C₄	—	2	8	no	—
137	C₂×C₃²×C₄	—	2	16	no	—
138	C₂×C₃²×C₄	—	2	16	no	—
139	C₂×C₃²×C₄	—	2	4	no	—
140	C₂×C₃²×C₄	—	2	1	no	—
141	C₂×C₃²×C₄	—	2	8	no	—
142	C₂×C₃²×C₄	—	2	2	no	—
143	C₂×C₃²×C₄	—	2	8	no	—
144	C₂×C₃²×C₄	—	2	2	no	—
145	C₂×C₃²×C₄	—	2	4	no	—
146	C₂×C₃²×C₄	—	2	4	no	—
147	C₂×C₃²×C₄	—	2	4	no	—
148	C₂×C₃²×C₄	—	2	4	no	—
149	C₂×C₃²×C₄	—	2	4	no	—
150	C₂×C₃²×C₄	—	2	4	no	—
151	C₂×C₃²×C₄	C₂×Dic₃	1	4	yes	—
152	C₂×C₃²×C₄	C₂×Dic₃	1	4	yes	—
153	C₂×C₃²×C₄	#67	1	4	yes	—
154	C₂×C₃²×C₄	#67	1	4	yes	—
155	C₂×C₃²×C₄	#67	1	4	yes	—
156	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
159	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
160	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
161	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
162	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₃⋊Dic₃	—	2	2	no	—
164	C₂×C₃×Dic₃	—	6	8	no	—
165	C₃⋊(C₃⋊C₈)	—	2	2	no	—
166	C₃×C₃⋊C₈	—	6	8	no	—
167	#421	—	9	1	no	Sylow
168	C₂×C₃³	—	2	1	no	—
169	C₂×C₃³	—	2	1	no	—
170	C₂×C₃³	—	2	1	no	—
171	C₂×C₃³	—	4	2	no	—
172	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₃×#41	—	2	8	no	—
174	C₃×#41	—	2	8	no	—
175	C₃×#41	—	2	4	no	—
176	C₃×#41	—	2	4	no	—
177	C₃×#41	—	2	1	no	—
178	C₃×#41	—	2	1	no	—
179	C₃×#41	—	2	8	no	—
180	C₃×#41	—	2	8	no	—
181	C₃×#41	C₃×Dic₃	1	8	yes	complemented
182	C₃×#41	C₃⋊Dic₃	1	2	yes	complemented
183	C₃×#41	C₂×C₃×D₃	1	8	yes	—
184	C₃×#41	C₂×C₃⋊D₃	1	2	yes	—
185	C₂×C₃×Q₈	—	2	4	no	—
186	C₂×C₃×Q₈	C₃×Dic₃	1	4	yes	complemented
187	C₂×C₃×Q₈	C₃⋊Dic₃	1	1	yes	characteristic, complemented
188	C₂×C₃×D₄	—	2	8	no	—
189	C₂×C₃×D₄	—	2	4	no	—
190	C₂×C₃×D₄	—	2	1	no	—
191	C₂×C₃×D₄	—	2	4	no	—
192	C₂×C₃×D₄	C₃×Dic₃	1	4	yes	complemented
193	C₂×C₃×D₄	C₃⋊Dic₃	1	1	yes	characteristic, complemented
194	C₂²×C₃×C₄	—	2	8	no	—
195	C₂²×C₃×C₄	—	2	4	no	—
196	C₂²×C₃×C₄	—	2	1	no	—
197	C₂²×C₃×C₄	—	2	4	no	—
198	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
199	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
200	C₃×M₁₆	—	9	2	no	—
201	C₃×M₁₆	—	18	1	no	—
202	C₂×C₃×C₈	—	18	1	no	—
203	C₃×C₄⋊C₄	—	18	1	no	—
204	C₃×C₂²⋊C₄	—	18	1	no	—
205	C₃×C₄²	—	9	2	no	—
206	#217	—	6	4	no	—
207	C₄⋊Dic₃	—	6	4	no	—
208	C₄×Dic₃	—	3	8	no	—
209	#208	—	3	8	no	—
210	#208	—	6	4	no	—
211	C₂×C₃⋊C₈	—	6	4	no	—
212	C₂²×C₃²	—	2	16	no	—
213	C₂²×C₃²	—	2	8	no	—
214	C₂²×C₃²	—	2	2	no	—
215	C₂²×C₃²	—	2	4	no	—
216	C₂²×C₃²	—	2	4	no	—
217	C₂²×C₃²	—	2	4	no	—
218	C₂²×C₃²	—	4	4	no	—
219	C₂²×C₃²	—	4	1	no	—
220	C₂²×C₃²	—	4	8	no	—
221	C₂²×C₃²	—	4	16	no	—
222	C₂²×C₃²	—	4	8	no	—
223	C₂²×C₃²	—	4	2	no	—
224	C₂²×C₃²	#217	1	4	yes	—
225	C₂²×C₃²	#217	1	4	yes	—
226	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₃²	C₂×#67	1	4	yes	—
229	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
230	C₃²×C₄	—	2	16	no	—
231	C₃²×C₄	—	2	8	no	—
232	C₃²×C₄	—	2	2	no	—
233	C₃²×C₄	—	2	4	no	—
234	C₃²×C₄	—	2	4	no	—
235	C₃²×C₄	—	2	4	no	—
236	C₃²×C₄	—	2	4	no	—
237	C₃²×C₄	#217	1	4	yes	—
238	C₃²×C₄	#217	1	4	yes	—
239	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
240	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
241	C₃²×C₄	C₂²×Dic₃	1	4	yes	—
242	C₃²×C₄	C₂×#67	1	4	yes	—
243	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
245	C₃⋊Dic₃	—	4	2	no	—
246	C₃×Dic₃	—	12	8	no	—
247	C₂×#41	C₃×C₃⋊D₃	1	1	yes	characteristic
248	C₂×M₁₆	—	9	1	no	—
249	#117	—	9	1	no	—
250	#104	—	9	4	no	—
251	C₃³	#421	1	1	yes	characteristic, complemented, Sylow
252	C₂³×C₃	—	2	8	no	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	C₃×#67	1	4	yes	—
257	C₂³×C₃	#638	1	1	yes	characteristic
258	C₃×Q₈	—	2	8	no	—
259	C₃×Q₈	—	2	4	no	—
260	C₃×Q₈	—	2	1	no	—
261	C₃×Q₈	—	2	8	no	—
262	C₃×Q₈	C₂×C₃×Dic₃	1	8	yes	—
263	C₃×Q₈	C₂×C₃⋊Dic₃	1	2	yes	—
264	C₃×D₄	—	2	16	no	—
265	C₃×D₄	—	2	16	no	—
266	C₃×D₄	—	2	8	no	—
267	C₃×D₄	—	2	8	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	2	8	no	—
270	C₃×D₄	—	2	2	no	—
271	C₃×D₄	—	2	4	no	—
272	C₃×D₄	—	2	1	no	—
273	C₃×D₄	—	2	8	no	—
274	C₃×D₄	C₂×C₃×Dic₃	1	8	yes	—
275	C₃×D₄	C₂×C₃⋊Dic₃	1	2	yes	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	16	no	—
278	C₂×C₃×C₄	—	2	16	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	8	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	8	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	18	2	no	—
292	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
293	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
294	C₂×C₃×C₄	C₃×#67	1	4	yes	—
295	C₂×C₃×C₄	C₃×#67	1	4	yes	—
296	C₂×C₃×C₄	C₃×#67	1	4	yes	—
297	C₂×C₃×C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
299	C₂×C₃×C₄	#638	1	1	yes	characteristic
300	C₂×C₃×C₄	#638	1	1	yes	characteristic
301	C₂×C₃×C₄	#638	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
303	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
304	C₂×Dic₃	—	6	8	no	—
305	C₃×C₈	—	18	2	no	—
306	C₃⋊C₈	—	6	8	no	—
307	C₂×C₃²	—	2	8	no	—
308	C₂×C₃²	—	2	4	no	—
309	C₂×C₃²	—	2	1	no	—
310	C₂×C₃²	—	2	1	no	—
311	C₂×C₃²	—	2	1	no	—
312	C₂×C₃²	—	2	4	no	—
313	C₂×C₃²	—	2	4	no	—
314	C₂×C₃²	—	2	4	no	—
315	C₂×C₃²	—	4	4	no	—
316	C₂×C₃²	—	4	4	no	—
317	C₂×C₃²	—	4	16	no	—
318	C₂×C₃²	—	4	8	no	—
319	C₂×C₃²	—	4	2	no	—
320	C₂×C₃²	C₂×#217	1	4	yes	—
321	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
322	#41	—	2	1	no	—
323	#41	—	2	1	no	—
324	#41	C₃×C₃⋊Dic₃	1	2	yes	complemented
325	#41	C₂×C₃×C₃⋊D₃	1	2	yes	—
326	C₂×Q₈	C₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
331	M₁₆	—	9	2	no	—
332	M₁₆	—	18	1	no	—
333	C₂×C₈	—	18	1	no	—
334	C₄⋊C₄	—	18	1	no	—
335	C₂²⋊C₄	—	18	1	no	—
336	C₄²	—	9	2	no	—
337	C₂²×C₃	—	2	16	no	—
338	C₂²×C₃	—	2	8	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	4	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	4	no	—
343	C₂²×C₃	—	4	4	no	—
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	—	4	8	no	—
346	C₂²×C₃	—	4	16	no	—
347	C₂²×C₃	—	4	8	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	C₃×#217	1	4	yes	—
350	C₂²×C₃	C₃×#217	1	4	yes	—
351	C₂²×C₃	#3757	1	1	yes	characteristic
352	C₂²×C₃	#3757	1	1	yes	characteristic
353	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
354	C₂²×C₃	C₂×#638	1	1	yes	characteristic
355	C₃×C₄	—	2	16	no	—
356	C₃×C₄	—	2	8	no	—
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	2	4	no	—
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	36	2	no	—
363	C₃×C₄	C₃×#217	1	4	yes	—
364	C₃×C₄	C₃×#217	1	4	yes	—
365	C₃×C₄	#3757	1	1	yes	characteristic
366	C₃×C₄	#3757	1	1	yes	characteristic
367	C₃×C₄	C₂²×C₃×Dic₃	1	4	yes	—
368	C₃×C₄	C₂×C₃×#67	1	4	yes	—
369	C₃×C₄	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
370	C₃×C₄	C₂×#638	1	1	yes	characteristic
371	Dic₃	—	12	8	no	—
372	C₃²	—	2	4	no	—
373	C₃²	#5236	1	4	yes	complemented
374	C₃²	C₃×#421	1	1	yes	characteristic, complemented
375	C₂³	—	2	1	no	—
376	C₂³	C₃×#638	1	1	yes	characteristic
377	Q₈	—	2	1	no	—
378	Q₈	C₂×C₃×C₃⋊Dic₃	1	2	yes	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	C₂×C₃×C₃⋊Dic₃	1	2	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	18	2	no	—
387	C₂×C₄	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic
389	C₂×C₄	C₃×#638	1	1	yes	characteristic
390	C₂×C₄	C₃×#638	1	1	yes	characteristic
391	C₂×C₄	C₃×#638	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
393	C₈	—	18	2	no	—
394	C₂×C₃	—	2	8	no	—
395	C₂×C₃	—	2	4	no	—
396	C₂×C₃	—	2	4	no	—
397	C₂×C₃	—	2	4	no	—
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	2	4	no	—
402	C₂×C₃	—	4	4	no	—
403	C₂×C₃	—	4	4	no	—
404	C₂×C₃	—	4	16	no	—
405	C₂×C₃	—	4	8	no	—
406	C₂×C₃	—	4	2	no	—
407	C₂×C₃	C₂×C₃×#217	1	4	yes	—
408	C₂×C₃	C₂×#3757	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₃×#3757	1	1	yes	characteristic
413	C₂²	C₃×#3757	1	1	yes	characteristic
414	C₂²	C₂×C₃×#638	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	36	2	no	—
417	C₄	C₃×#3757	1	1	yes	characteristic
418	C₄	C₃×#3757	1	1	yes	characteristic
419	C₄	C₂²×C₃×C₃⋊Dic₃	1	1	yes	characteristic
420	C₄	C₂×C₃×#638	1	1	yes	characteristic
421	C₃	—	2	4	no	—
422	C₃	C₃×#5236	1	4	yes	complemented
423	C₃	#10592935	1	1	yes	characteristic, direct product factor
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	4	2	no	—
428	C₂	C₂×C₃×#3757	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×#638
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting, prime radical	C₂×C₃³×#41	C₂
socle	C₂×C₃³	C₂×C₂²⋊C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×#41	C₃⋊D₃
hypocenter	C₃²	C₃×#421
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
2. C₃×#64135	C₂	semidirect
3. C₂×C₃×#3748	C₂	semidirect
4. C₃×#63664	C₂	semidirect
5. #10592935	C₃	direct (N × H)
9. C₃³×#41	C₄	semidirect
11. C₂×C₃³×Q₈	C₄	semidirect
13. C₂×C₃³×D₄	C₄	semidirect
18. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
20. C₃×#3748	C₂²	semidirect
25. #64135	C₂×C₃	semidirect
26. C₂×#3748	C₂×C₃	semidirect
29. #63664	C₂×C₃	semidirect
60. C₃²×#41	Dic₃	semidirect
61. C₃²×#41	C₃×C₄	semidirect
65. C₂×C₃²×Q₈	Dic₃	semidirect
66. C₂×C₃²×Q₈	C₃×C₄	semidirect
71. C₂×C₃²×D₄	Dic₃	semidirect
72. C₂×C₃²×D₄	C₃×C₄	semidirect
81. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
83. #3748	C₂²×C₃	semidirect
181. C₃×#41	C₃×Dic₃	semidirect
182. C₃×#41	C₃⋊Dic₃	semidirect
186. C₂×C₃×Q₈	C₃×Dic₃	semidirect
187. C₂×C₃×Q₈	C₃⋊Dic₃	semidirect
192. C₂×C₃×D₄	C₃×Dic₃	semidirect
193. C₂×C₃×D₄	C₃⋊Dic₃	semidirect
251. C₃³	#421	semidirect
324. #41	C₃×C₃⋊Dic₃	semidirect
326. C₂×Q₈	C₃×C₃⋊Dic₃	semidirect
328. C₂×D₄	C₃×C₃⋊Dic₃	semidirect
373. C₃²	#5236	semidirect
374. C₃²	C₃×#421	semidirect
422. C₃	C₃×#5236	semidirect
423. C₃	#10592935	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×#41	2
C₃×#64135	2
C₂×C₃×#3748	2
C₃×#63664	2
#10592935	3
C₃×#5236	3

Subgroups — C3×#10592935 #13163277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10592935 #13163277