Subgroups — C₃×#83898 #11860863

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic
2	C₃×#5827	C₂	1	2	yes	maximal, complemented
3	C₃×#5232	C₂	1	2	yes	maximal, complemented
4	C₃×Dic₃×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×#5164	C₂	1	4	yes	maximal, complemented
6	C₃×Dic₃×D₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2951	—	3	1	no	maximal
10	#83898	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃²×#41	C₂²	1	2	yes	—
12	C₃²×#135	C₄	1	8	yes	complemented
13	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃×Q₈×Dic₃	C₂²	1	4	yes	—
18	C₃×D₄×Dic₃	—	2	4	no	—
19	C₃×D₄×Dic₃	C₂²	1	4	yes	—
20	C₃×#926	—	2	2	no	—
21	C₃×#926	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Dic₃	—	2	2	no	—
23	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
24	C₂×C₃×#208	C₂²	1	1	yes	characteristic
25	C₃×#835	C₂²	1	4	yes	—
26	C₃×#832	C₂²	1	4	yes	—
27	C₃×#818	C₂²	1	2	yes	—
28	C₃×#818	C₂²	1	2	yes	—
29	C₃×#815	C₂²	1	2	yes	—
30	C₃×C₈×Dic₃	C₂²	1	2	yes	—
31	C₂×C₃×#135	—	2	1	no	—
32	C₂×C₃×#135	D₃	1	1	yes	characteristic
33	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
34	C₃×#520	—	3	2	no	—
35	#5827	C₂×C₃	1	2	yes	complemented
36	C₃×#440	—	3	4	no	—
37	C₃×C₄×Q₁₆	—	3	2	no	—
38	C₃×C₄×D₈	—	3	2	no	—
39	C₂×C₃×#107	—	3	1	no	—
40	C₃×#417	—	3	2	no	—
41	C₃×#405	—	3	1	no	—
42	#5232	C₂×C₃	1	2	yes	complemented
43	Dic₃×Q₁₆	C₂×C₃	1	2	yes	complemented
44	#5164	C₂×C₃	1	4	yes	complemented
45	Dic₃×D₈	C₂×C₃	1	2	yes	complemented
46	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
47	#5101	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃²×#41	—	2	4	no	—
49	C₃²×#41	C₂×C₄	1	8	yes	complemented
50	C₂×C₃²×Q₈	C₂³	1	2	yes	—
51	C₂×C₃²×D₄	—	2	2	no	—
52	C₂×C₃²×D₄	C₂³	1	2	yes	—
53	C₂²×C₃²×C₄	—	2	2	no	—
54	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
55	C₂²×C₃×Dic₃	—	2	2	no	—
56	C₂²×C₃×Dic₃	—	2	4	no	—
57	C₃²×Q₁₆	C₂×C₄	1	4	yes	complemented
58	C₃²×SD₁₆	C₂×C₄	1	8	yes	complemented
59	C₃²×D₈	C₂×C₄	1	4	yes	complemented
60	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
61	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
63	C₃×#217	—	2	4	no	—
64	C₃×#217	D₄	1	2	yes	—
65	C₃×C₄⋊Dic₃	—	2	2	no	—
66	C₃×C₄⋊Dic₃	—	2	4	no	—
67	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
68	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
69	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
70	C₃×C₄×Dic₃	—	2	4	no	—
71	C₃×C₄×Dic₃	C₂³	1	2	yes	—
72	C₃×#208	—	2	2	no	—
73	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
74	#2951	—	3	1	no	Sylow
75	C₂×C₃×#41	—	2	2	no	—
76	C₂×C₃×#41	C₂×D₃	1	2	yes	—
77	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
78	C₃×#135	—	2	8	no	—
79	C₃×#135	Dic₃	1	8	yes	complemented
80	C₃×#135	C₃×C₄	1	8	yes	complemented
81	C₂×C₃×Q₁₆	—	2	1	no	—
82	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×SD₁₆	—	2	2	no	—
85	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	—
86	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
87	C₂×C₃×D₈	—	2	1	no	—
88	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
89	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×M₁₆	—	3	1	no	—
91	C₂²×C₃×C₈	—	2	1	no	—
92	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄×Q₈	—	3	4	no	—
95	C₃×C₄×D₄	—	3	4	no	—
96	C₃×C₄×D₄	—	6	4	no	—
97	C₃×#117	—	3	1	no	—
98	C₃×#117	—	6	2	no	—
99	C₂×C₃×C₄⋊C₄	—	3	2	no	—
100	C₂×C₃×C₄⋊C₄	—	6	2	no	—
101	Q₈×Dic₃	C₂²×C₃	1	4	yes	—
102	D₄×Dic₃	—	2	4	no	—
103	D₄×Dic₃	C₂²×C₃	1	4	yes	—
104	#926	—	2	2	no	—
105	#926	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄⋊Dic₃	—	2	2	no	—
107	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
108	C₂×#208	C₂²×C₃	1	1	yes	characteristic
109	C₃×#107	—	3	2	no	—
110	C₃×#107	—	3	2	no	—
111	C₃×#103	—	3	4	no	—
112	C₃×#102	—	3	4	no	—
113	C₃×#97	—	3	2	no	—
114	C₃×C₄×C₈	—	3	2	no	—
115	#835	C₂²×C₃	1	4	yes	—
116	#832	C₂²×C₃	1	4	yes	—
117	#818	C₂²×C₃	1	2	yes	—
118	#818	C₂²×C₃	1	2	yes	—
119	#815	C₂²×C₃	1	2	yes	—
120	C₈×Dic₃	C₂²×C₃	1	2	yes	—
121	C₂³×C₃²	—	2	2	no	—
122	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
123	C₃²×Q₈	—	2	2	no	—
124	C₃²×Q₈	C₂²×C₄	1	4	yes	—
125	C₃²×D₄	—	2	8	no	—
126	C₃²×D₄	—	2	2	no	—
127	C₃²×D₄	C₂²×C₄	1	4	yes	—
128	C₂×C₃²×C₄	—	2	2	no	—
129	C₂×C₃²×C₄	—	2	8	no	—
130	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	#41	1	2	yes	—
133	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
134	C₂×C₃×Dic₃	—	2	4	no	—
135	C₂×C₃×Dic₃	—	8	4	no	—
136	C₂×C₃×Dic₃	—	8	2	no	—
137	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
138	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
139	C₃²×C₈	C₂²×C₄	1	2	yes	—
140	C₃²×C₈	C₂²×C₄	1	2	yes	—
141	C₃×C₃⋊C₈	—	2	2	no	—
142	C₂×#135	C₃×D₃	1	1	yes	characteristic
143	#520	—	3	2	no	—
144	#440	—	3	4	no	—
145	C₄×Q₁₆	—	3	2	no	—
146	C₄×D₈	—	3	2	no	—
147	C₂×#107	—	3	1	no	—
148	#417	—	3	2	no	—
149	#405	—	3	1	no	—
150	C₃×#41	—	2	4	no	—
151	C₃×#41	—	2	4	no	—
152	C₃×#41	—	2	8	no	—
153	C₃×#41	—	4	4	no	—
154	C₃×#41	C₂×Dic₃	1	8	yes	complemented
155	C₃×#41	C₂×C₃×C₄	1	8	yes	complemented
156	C₂×C₃×Q₈	—	2	2	no	—
157	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
158	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	2	2	no	—
161	C₂×C₃×D₄	—	2	2	no	—
162	C₂×C₃×D₄	—	4	2	no	—
163	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
164	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	4	2	no	—
169	C₂²×C₃×C₄	—	6	4	no	—
170	C₂²×C₃×C₄	—	6	2	no	—
171	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂²×Dic₃	—	2	2	no	—
174	C₂²×Dic₃	—	2	4	no	—
175	C₃×Q₁₆	—	2	4	no	—
176	C₃×Q₁₆	C₂×Dic₃	1	4	yes	complemented
177	C₃×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
178	C₃×SD₁₆	—	2	8	no	—
179	C₃×SD₁₆	C₂×Dic₃	1	8	yes	complemented
180	C₃×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
181	C₃×D₈	—	2	4	no	—
182	C₃×D₈	C₂×Dic₃	1	4	yes	complemented
183	C₃×D₈	C₂×C₃×C₄	1	4	yes	complemented
184	C₃×M₁₆	—	6	2	no	—
185	C₂×C₃×C₈	—	2	4	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₂×C₃×C₈	—	2	1	no	—
188	C₂×C₃×C₈	—	3	2	no	—
189	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	complemented
190	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
191	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
192	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
195	C₃×C₄⋊C₄	—	3	1	no	—
196	C₃×C₄⋊C₄	—	3	1	no	—
197	C₃×C₄⋊C₄	—	3	4	no	—
198	C₃×C₄⋊C₄	—	6	4	no	—
199	C₃×C₄⋊C₄	—	6	2	no	—
200	C₃×C₂²⋊C₄	—	3	2	no	—
201	C₃×C₂²⋊C₄	—	6	4	no	—
202	C₃×C₄²	—	3	2	no	—
203	C₃×C₄²	—	6	4	no	—
204	#217	—	2	4	no	—
205	#217	C₃×D₄	1	2	yes	—
206	C₄⋊Dic₃	—	2	2	no	—
207	C₄⋊Dic₃	—	2	4	no	—
208	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
209	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
210	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
211	C₄×Dic₃	—	2	4	no	—
212	C₄×Dic₃	C₂³×C₃	1	2	yes	—
213	#208	—	2	2	no	—
214	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
215	C₂²×C₃²	—	2	1	no	—
216	C₂²×C₃²	—	2	1	no	—
217	C₂²×C₃²	—	2	4	no	—
218	C₂²×C₃²	—	4	2	no	—
219	C₂²×C₃²	—	4	2	no	—
220	C₂²×C₃²	C₄×D₄	1	2	yes	—
221	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
222	C₃²×C₄	—	2	4	no	—
223	C₃²×C₄	C₄×D₄	1	2	yes	—
224	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
225	C₃²×C₄	C₂×#41	1	1	yes	characteristic
226	C₃×Dic₃	—	2	2	no	—
227	C₃×Dic₃	—	2	2	no	—
228	C₃×Dic₃	—	4	4	no	—
229	C₂×#41	C₂×C₃×D₃	1	2	yes	—
230	#135	C₃×Dic₃	1	8	yes	complemented
231	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	—
233	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
234	C₂×M₁₆	—	3	1	no	—
235	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
236	C₄×Q₈	—	3	4	no	—
237	C₄×D₄	—	3	4	no	—
238	C₄×D₄	—	6	4	no	—
239	#117	—	3	1	no	—
240	#117	—	6	2	no	—
241	C₂×C₄⋊C₄	—	3	2	no	—
242	C₂×C₄⋊C₄	—	6	2	no	—
243	#107	—	3	2	no	—
244	#107	—	3	2	no	—
245	#103	—	3	4	no	—
246	#102	—	3	4	no	—
247	#97	—	3	2	no	—
248	C₄×C₈	—	3	2	no	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	4	2	no	—
253	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
254	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
255	C₃×Q₈	—	2	2	no	—
256	C₃×Q₈	—	2	2	no	—
257	C₃×Q₈	—	2	4	no	—
258	C₃×Q₈	—	4	2	no	—
259	C₃×Q₈	C₂²×Dic₃	1	4	yes	—
260	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
261	C₃×D₄	—	2	8	no	—
262	C₃×D₄	—	2	8	no	—
263	C₃×D₄	—	2	2	no	—
264	C₃×D₄	—	2	2	no	—
265	C₃×D₄	—	2	4	no	—
266	C₃×D₄	—	4	2	no	—
267	C₃×D₄	—	4	8	no	—
268	C₃×D₄	C₂²×Dic₃	1	4	yes	—
269	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	2	8	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	3	2	no	—
279	C₂×C₃×C₄	—	3	2	no	—
280	C₂×C₃×C₄	—	4	8	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	—	6	4	no	—
283	C₂×C₃×C₄	—	24	4	no	—
284	C₂×C₃×C₄	—	24	2	no	—
285	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	#237	1	2	yes	—
287	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
288	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
289	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₃×#41	1	2	yes	—
291	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
293	C₂×Dic₃	—	2	4	no	—
294	C₂×Dic₃	—	8	4	no	—
295	C₂×Dic₃	—	8	2	no	—
296	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
297	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
298	C₃×C₈	—	2	2	no	—
299	C₃×C₈	—	2	2	no	—
300	C₃×C₈	—	6	2	no	—
301	C₃×C₈	C₂²×Dic₃	1	2	yes	—
302	C₃×C₈	C₂²×Dic₃	1	2	yes	—
303	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
304	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
305	C₃⋊C₈	—	2	2	no	—
306	C₂×C₃²	—	2	2	no	—
307	C₂×C₃²	—	4	4	no	—
308	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂×C₃²	#576	1	1	yes	characteristic
310	C₂×C₃²	#578	1	1	yes	characteristic
311	#41	—	2	4	no	—
312	#41	C₂×C₃×Dic₃	1	8	yes	complemented
313	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	6	4	no	—
318	C₂²×C₄	—	6	2	no	—
319	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
320	Q₁₆	C₂×C₃×Dic₃	1	4	yes	complemented
321	SD₁₆	C₂×C₃×Dic₃	1	8	yes	complemented
322	D₈	C₂×C₃×Dic₃	1	4	yes	complemented
323	M₁₆	—	6	2	no	—
324	C₂×C₈	—	3	2	no	—
325	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	complemented
326	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
328	C₄⋊C₄	—	3	1	no	—
329	C₄⋊C₄	—	3	1	no	—
330	C₄⋊C₄	—	3	4	no	—
331	C₄⋊C₄	—	6	4	no	—
332	C₄⋊C₄	—	6	2	no	—
333	C₂²⋊C₄	—	3	2	no	—
334	C₂²⋊C₄	—	6	4	no	—
335	C₄²	—	3	2	no	—
336	C₄²	—	6	4	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	1	no	—
340	C₂²×C₃	—	2	1	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	4	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	4	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	8	2	no	—
353	C₂²×C₃	—	8	2	no	—
354	C₂²×C₃	D₄×Dic₃	1	2	yes	—
355	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
356	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
357	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	4	4	no	—
364	C₃×C₄	—	6	2	no	—
365	C₃×C₄	—	6	2	no	—
366	C₃×C₄	—	12	4	no	—
367	C₃×C₄	D₄×Dic₃	1	2	yes	—
368	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
369	C₃×C₄	C₂×#237	1	1	yes	characteristic
370	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
371	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
372	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
373	Dic₃	—	2	2	no	—
374	Dic₃	—	2	2	no	—
375	Dic₃	—	4	4	no	—
376	C₃²	#2951	1	1	yes	characteristic, complemented, Sylow
377	C₂³	—	2	2	no	—
378	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	C₂²×C₃×Dic₃	1	4	yes	—
381	D₄	—	2	8	no	—
382	D₄	—	2	2	no	—
383	D₄	C₂²×C₃×Dic₃	1	4	yes	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	3	2	no	—
387	C₂×C₄	—	3	2	no	—
388	C₂×C₄	—	6	4	no	—
389	C₂×C₄	—	24	4	no	—
390	C₂×C₄	—	24	2	no	—
391	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
392	C₂×C₄	C₃×#237	1	2	yes	—
393	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
394	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
395	C₈	—	6	2	no	—
396	C₈	C₂²×C₃×Dic₃	1	2	yes	—
397	C₈	C₂²×C₃×Dic₃	1	2	yes	—
398	C₂×C₃	—	2	2	no	—
399	C₂×C₃	—	2	2	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	2	1	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	4	2	no	—
404	C₂×C₃	—	4	4	no	—
405	C₂×C₃	—	4	4	no	—
406	C₂×C₃	—	8	4	no	—
407	C₂×C₃	#5769	1	1	yes	characteristic
408	C₂×C₃	#5771	1	1	yes	characteristic
409	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
410	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
411	C₂×C₃	C₃×#576	1	1	yes	characteristic
412	C₂×C₃	C₃×#578	1	1	yes	characteristic
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	C₃×D₄×Dic₃	1	2	yes	—
419	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
420	C₄	—	2	4	no	—
421	C₄	—	6	2	no	—
422	C₄	—	6	2	no	—
423	C₄	—	12	4	no	—
424	C₄	C₃×D₄×Dic₃	1	2	yes	—
425	C₄	C₂×C₃×#237	1	1	yes	characteristic
426	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
427	C₃	—	2	1	no	—
428	C₃	#83898	1	1	yes	characteristic, direct product factor
429	C₃	C₃×#2951	1	1	yes	characteristic, complemented
430	C₂	—	2	2	no	—
431	C₂	—	4	4	no	—
432	C₂	C₃×#5769	1	1	yes	characteristic
433	C₂	C₃×#5771	1	1	yes	characteristic
434	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting, prime radical	C₂×C₃²×#135	C₂
socle	C₂²×C₃²	C₂²×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#135	D₃
hypocenter	C₃	C₃×#2951
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
2. C₃×#5827	C₂	semidirect
3. C₃×#5232	C₂	semidirect
4. C₃×Dic₃×Q₁₆	C₂	semidirect
5. C₃×#5164	C₂	semidirect
6. C₃×Dic₃×D₈	C₂	semidirect
7. C₂×C₃×#818	C₂	semidirect
8. C₃×#5101	C₂	semidirect
10. #83898	C₃	direct (N × H)
12. C₃²×#135	C₄	semidirect
35. #5827	C₂×C₃	semidirect
42. #5232	C₂×C₃	semidirect
43. Dic₃×Q₁₆	C₂×C₃	semidirect
44. #5164	C₂×C₃	semidirect
45. Dic₃×D₈	C₂×C₃	semidirect
46. C₂×#818	C₂×C₃	semidirect
47. #5101	C₂×C₃	semidirect
49. C₃²×#41	C₂×C₄	semidirect
57. C₃²×Q₁₆	C₂×C₄	semidirect
58. C₃²×SD₁₆	C₂×C₄	semidirect
59. C₃²×D₈	C₂×C₄	semidirect
60. C₂×C₃²×C₈	C₂×C₄	semidirect
79. C₃×#135	Dic₃	semidirect
80. C₃×#135	C₃×C₄	semidirect
154. C₃×#41	C₂×Dic₃	semidirect
155. C₃×#41	C₂×C₃×C₄	semidirect
176. C₃×Q₁₆	C₂×Dic₃	semidirect
177. C₃×Q₁₆	C₂×C₃×C₄	semidirect
179. C₃×SD₁₆	C₂×Dic₃	semidirect
180. C₃×SD₁₆	C₂×C₃×C₄	semidirect
182. C₃×D₈	C₂×Dic₃	semidirect
183. C₃×D₈	C₂×C₃×C₄	semidirect
189. C₂×C₃×C₈	C₂×Dic₃	semidirect
190. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
230. #135	C₃×Dic₃	semidirect
312. #41	C₂×C₃×Dic₃	semidirect
320. Q₁₆	C₂×C₃×Dic₃	semidirect
321. SD₁₆	C₂×C₃×Dic₃	semidirect
322. D₈	C₂×C₃×Dic₃	semidirect
325. C₂×C₈	C₂×C₃×Dic₃	semidirect
376. C₃²	#2951	semidirect
428. C₃	#83898	direct (N × H)
429. C₃	C₃×#2951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#135	2
C₃×#5827	2
C₃×#5232	2
C₃×Dic₃×Q₁₆	2
C₃×#5164	2
C₃×Dic₃×D₈	2
C₂×C₃×#818	2
C₃×#5101	2
C₃×#2951	3
#83898	3

Subgroups — C3×#83898 #11860863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83898 #11860863