Subgroups — C₃×#83910 #11861201

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 477 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×#5819	C₂	1	2	yes	maximal, complemented
3	C₃×#5236	C₂	1	2	yes	maximal, complemented
4	C₃×#5197	C₂	1	4	yes	maximal, complemented
5	C₃×#5196	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2957	—	3	1	no	maximal
9	#83910	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃²×#41	C₂²	1	2	yes	—
11	C₃²×#135	C₄	1	2	yes	complemented
12	C₃²×#135	C₄	1	2	yes	complemented
13	C₃²×#135	C₂²	1	2	yes	—
14	C₃²×#135	C₂²	1	2	yes	—
15	C₂×C₃²×Q₁₆	C₄	1	1	yes	characteristic, complemented
16	C₂×C₃²×SD₁₆	C₄	1	2	yes	complemented
17	C₂×C₃²×D₈	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
19	C₃×#948	—	2	4	no	—
20	C₃×#948	C₂²	1	8	yes	complemented
21	C₃×#926	C₂²	1	1	yes	characteristic
22	C₂×C₃×#208	—	2	4	no	—
23	C₂×C₃×#208	C₂²	1	2	yes	—
24	C₂×C₃×#208	C₂²	1	1	yes	characteristic
25	C₃×#837	C₂²	1	8	yes	complemented
26	C₃×#819	C₂²	1	2	yes	complemented
27	C₃×#819	C₂²	1	2	yes	complemented
28	C₃×#815	C₂²	1	2	yes	complemented
29	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
30	C₂×C₃×#135	—	2	1	no	—
31	C₂×C₃×#135	D₃	1	1	yes	characteristic
32	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
33	C₃×#568	—	3	2	no	—
34	#5819	C₂×C₃	1	2	yes	complemented
35	C₃×#444	—	3	4	no	—
36	C₃×#443	—	3	4	no	—
37	C₂×C₃×#108	—	3	1	no	—
38	C₃×#421	—	3	2	no	—
39	C₃×#405	—	3	1	no	—
40	#5236	C₂×C₃	1	2	yes	complemented
41	#5197	C₂×C₃	1	4	yes	complemented
42	#5196	C₂×C₃	1	4	yes	complemented
43	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
44	#5101	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃²×#41	—	2	2	no	—
46	C₃²×#41	—	2	2	no	—
47	C₃²×#41	C₂×C₄	1	4	yes	—
48	C₃²×#41	C₂³	1	4	yes	—
49	C₂×C₃²×Q₈	C₂×C₄	1	2	yes	—
50	C₂×C₃²×D₄	—	2	2	no	—
51	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
52	C₂²×C₃²×C₄	—	2	2	no	—
53	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
54	C₃²×Q₁₆	C₂×C₄	1	2	yes	—
55	C₃²×Q₁₆	C₂×C₄	1	2	yes	—
56	C₃²×SD₁₆	C₂×C₄	1	4	yes	—
57	C₃²×SD₁₆	C₂×C₄	1	4	yes	—
58	C₃²×D₈	C₂×C₄	1	2	yes	—
59	C₃²×D₈	C₂×C₄	1	2	yes	—
60	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
66	C₃×#217	—	2	1	no	—
67	C₃×C₄⋊Dic₃	—	2	1	no	—
68	C₃×C₄×Dic₃	C₂³	1	2	yes	—
69	C₃×#208	—	2	2	no	—
70	C₃×#208	—	2	8	no	—
71	C₃×#208	D₄	1	2	yes	—
72	C₃×#208	D₄	1	2	yes	—
73	C₃×#208	C₂³	1	4	yes	—
74	C₂×C₃×C₃⋊C₈	—	2	2	no	—
75	C₂×C₃×C₃⋊C₈	—	2	8	no	—
76	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
77	#2957	—	3	1	no	Sylow
78	C₂×C₃×#41	—	2	2	no	—
79	C₂×C₃×#41	C₂×D₃	1	2	yes	—
80	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
81	C₃×#135	—	2	2	no	—
82	C₃×#135	—	2	2	no	—
83	C₃×#135	—	2	2	no	—
84	C₃×#135	—	2	2	no	—
85	C₃×#135	Dic₃	1	2	yes	complemented
86	C₃×#135	Dic₃	1	2	yes	complemented
87	C₃×#135	C₃×C₄	1	2	yes	complemented
88	C₃×#135	C₃×C₄	1	2	yes	complemented
89	C₃×#135	C₂×D₃	1	2	yes	—
90	C₃×#135	C₂×D₃	1	2	yes	—
91	C₃×#135	C₂²×C₃	1	2	yes	—
92	C₃×#135	C₂²×C₃	1	2	yes	—
93	C₂×C₃×Q₁₆	—	2	1	no	—
94	C₂×C₃×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
95	C₂×C₃×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
96	C₂×C₃×SD₁₆	—	2	2	no	—
97	C₂×C₃×SD₁₆	Dic₃	1	2	yes	complemented
98	C₂×C₃×SD₁₆	C₃×C₄	1	2	yes	complemented
99	C₂×C₃×D₈	—	2	1	no	—
100	C₂×C₃×D₈	Dic₃	1	1	yes	characteristic, complemented
101	C₂×C₃×D₈	C₃×C₄	1	1	yes	characteristic, complemented
102	C₃×#131	—	3	8	no	—
103	C₃×#131	—	6	4	no	—
104	C₂×C₃×M₁₆	—	3	1	no	—
105	C₂×C₃×M₁₆	—	3	2	no	—
106	C₂×C₃×M₁₆	—	6	4	no	—
107	C₂²×C₃×C₈	—	2	1	no	—
108	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
110	C₃×#117	—	3	1	no	—
111	#948	—	2	4	no	—
112	#948	C₂²×C₃	1	8	yes	complemented
113	#926	C₂²×C₃	1	1	yes	characteristic
114	C₂×#208	—	2	4	no	—
115	C₂×#208	C₂²×C₃	1	2	yes	—
116	C₂×#208	C₂²×C₃	1	1	yes	characteristic
117	C₃×#108	—	3	2	no	—
118	C₃×#108	—	3	2	no	—
119	C₃×#104	—	3	8	no	—
120	C₃×#97	—	3	2	no	—
121	C₃×C₄×C₈	—	3	2	no	—
122	#837	C₂²×C₃	1	8	yes	complemented
123	#819	C₂²×C₃	1	2	yes	complemented
124	#819	C₂²×C₃	1	2	yes	complemented
125	#815	C₂²×C₃	1	2	yes	complemented
126	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
127	C₂³×C₃²	—	2	2	no	—
128	C₂³×C₃²	#41	1	1	yes	characteristic
129	C₃²×Q₈	—	2	2	no	—
130	C₃²×Q₈	C₂²×C₄	1	4	yes	—
131	C₃²×D₄	—	2	4	no	—
132	C₃²×D₄	—	2	4	no	—
133	C₃²×D₄	—	2	2	no	—
134	C₃²×D₄	C₂²×C₄	1	4	yes	—
135	C₂×C₃²×C₄	—	2	2	no	—
136	C₂×C₃²×C₄	—	2	4	no	—
137	C₂×C₃²×C₄	—	2	4	no	—
138	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃²×C₄	#41	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
144	C₂×C₃×Dic₃	—	2	2	no	—
145	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₃×C₃⋊C₈	—	2	4	no	—
150	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
151	C₂×#135	C₃×D₃	1	1	yes	characteristic
152	#568	—	3	2	no	—
153	#444	—	3	4	no	—
154	#443	—	3	4	no	—
155	C₂×#108	—	3	1	no	—
156	#421	—	3	2	no	—
157	#405	—	3	1	no	—
158	C₃×#41	—	2	2	no	—
159	C₃×#41	—	2	2	no	—
160	C₃×#41	—	2	2	no	—
161	C₃×#41	—	2	2	no	—
162	C₃×#41	—	2	4	no	—
163	C₃×#41	—	2	4	no	—
164	C₃×#41	—	4	2	no	—
165	C₃×#41	—	4	2	no	—
166	C₃×#41	C₂×Dic₃	1	4	yes	—
167	C₃×#41	C₂×C₃×C₄	1	4	yes	—
168	C₃×#41	C₂²×D₃	1	4	yes	—
169	C₃×#41	C₂³×C₃	1	4	yes	—
170	C₂×C₃×Q₈	—	2	2	no	—
171	C₂×C₃×Q₈	C₂×Dic₃	1	2	yes	—
172	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	—	2	2	no	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	4	2	no	—
177	C₂×C₃×D₄	C₂×Dic₃	1	2	yes	—
178	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	4	2	no	—
183	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₃×Q₁₆	—	2	2	no	—
186	C₃×Q₁₆	—	2	2	no	—
187	C₃×Q₁₆	C₂×Dic₃	1	2	yes	—
188	C₃×Q₁₆	C₂×Dic₃	1	2	yes	—
189	C₃×Q₁₆	C₂×C₃×C₄	1	2	yes	—
190	C₃×Q₁₆	C₂×C₃×C₄	1	2	yes	—
191	C₃×SD₁₆	—	2	4	no	—
192	C₃×SD₁₆	—	2	4	no	—
193	C₃×SD₁₆	C₂×Dic₃	1	4	yes	—
194	C₃×SD₁₆	C₂×Dic₃	1	4	yes	—
195	C₃×SD₁₆	C₂×C₃×C₄	1	4	yes	—
196	C₃×SD₁₆	C₂×C₃×C₄	1	4	yes	—
197	C₃×D₈	—	2	2	no	—
198	C₃×D₈	—	2	2	no	—
199	C₃×D₈	C₂×Dic₃	1	2	yes	—
200	C₃×D₈	C₂×Dic₃	1	2	yes	—
201	C₃×D₈	C₂×C₃×C₄	1	2	yes	—
202	C₃×D₈	C₂×C₃×C₄	1	2	yes	—
203	C₃×M₁₆	—	3	2	no	—
204	C₃×M₁₆	—	3	2	no	—
205	C₃×M₁₆	—	3	4	no	—
206	C₃×M₁₆	—	6	8	no	—
207	C₃×M₁₆	—	6	2	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	—	3	2	no	—
215	C₂×C₃×C₈	—	6	8	no	—
216	C₂×C₃×C₈	—	6	2	no	—
217	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
218	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
219	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
221	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
222	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
223	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
224	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
225	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
226	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
227	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
228	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
229	C₃×C₄⋊C₄	—	6	1	no	—
230	C₃×C₂²⋊C₄	—	6	1	no	—
231	C₃×C₄²	—	3	2	no	—
232	#217	—	2	1	no	—
233	C₄⋊Dic₃	—	2	1	no	—
234	C₄×Dic₃	C₂³×C₃	1	2	yes	—
235	#208	—	2	2	no	—
236	#208	—	2	8	no	—
237	#208	C₃×D₄	1	2	yes	—
238	#208	C₃×D₄	1	2	yes	—
239	#208	C₂³×C₃	1	4	yes	—
240	C₂×C₃⋊C₈	—	2	2	no	—
241	C₂×C₃⋊C₈	—	2	8	no	—
242	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
243	C₂²×C₃²	—	2	4	no	—
244	C₂²×C₃²	—	4	1	no	—
245	C₂²×C₃²	—	8	2	no	—
246	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
247	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
248	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
249	C₃²×C₄	—	2	4	no	—
250	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
251	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
252	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
253	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
254	C₃×Dic₃	—	4	2	no	—
255	C₂×#41	C₂×C₃×D₃	1	2	yes	—
256	#135	C₃×Dic₃	1	2	yes	complemented
257	#135	C₃×Dic₃	1	2	yes	complemented
258	#135	C₂×C₃×D₃	1	2	yes	—
259	#135	C₂×C₃×D₃	1	2	yes	—
260	C₂×Q₁₆	C₃×Dic₃	1	1	yes	characteristic, complemented
261	C₂×SD₁₆	C₃×Dic₃	1	2	yes	complemented
262	C₂×D₈	C₃×Dic₃	1	1	yes	characteristic, complemented
263	#131	—	3	8	no	—
264	#131	—	6	4	no	—
265	C₂×M₁₆	—	3	1	no	—
266	C₂×M₁₆	—	3	2	no	—
267	C₂×M₁₆	—	6	4	no	—
268	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
269	#117	—	3	1	no	—
270	#108	—	3	2	no	—
271	#108	—	3	2	no	—
272	#104	—	3	8	no	—
273	#97	—	3	2	no	—
274	C₄×C₈	—	3	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	1	no	—
278	C₂³×C₃	—	4	2	no	—
279	C₂³×C₃	#237	1	1	yes	characteristic
280	C₂³×C₃	C₃×#41	1	1	yes	characteristic
281	C₃×Q₈	—	2	2	no	—
282	C₃×Q₈	—	2	2	no	—
283	C₃×Q₈	—	2	4	no	—
284	C₃×Q₈	—	4	2	no	—
285	C₃×Q₈	C₂²×Dic₃	1	4	yes	—
286	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
287	C₃×D₄	—	2	4	no	—
288	C₃×D₄	—	2	4	no	—
289	C₃×D₄	—	2	4	no	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	2	2	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	—	2	4	no	—
294	C₃×D₄	—	4	2	no	—
295	C₃×D₄	—	4	4	no	—
296	C₃×D₄	—	4	4	no	—
297	C₃×D₄	C₂²×Dic₃	1	4	yes	—
298	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	—	2	4	no	—
304	C₂×C₃×C₄	—	2	4	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	4	4	no	—
312	C₂×C₃×C₄	—	4	4	no	—
313	C₂×C₃×C₄	—	4	2	no	—
314	C₂×C₃×C₄	—	6	2	no	—
315	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
316	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
317	C₂×C₃×C₄	#237	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
327	C₂×Dic₃	—	2	2	no	—
328	C₃×C₈	—	2	1	no	—
329	C₃×C₈	—	2	1	no	—
330	C₃×C₈	—	2	1	no	—
331	C₃×C₈	—	2	1	no	—
332	C₃×C₈	—	3	4	no	—
333	C₃×C₈	—	6	4	no	—
334	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
335	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
336	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
337	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
338	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
340	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
341	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
342	C₃⋊C₈	—	2	4	no	—
343	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
344	C₂×C₃²	—	2	1	no	—
345	C₂×C₃²	—	2	1	no	—
346	C₂×C₃²	—	2	1	no	—
347	C₂×C₃²	—	4	4	no	—
348	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
349	#41	—	2	2	no	—
350	#41	—	2	2	no	—
351	#41	C₂×C₃×Dic₃	1	4	yes	—
352	#41	C₂²×C₃×D₃	1	4	yes	—
353	C₂×Q₈	C₂×C₃×Dic₃	1	2	yes	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	C₂×C₃×Dic₃	1	2	yes	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
358	Q₁₆	C₂×C₃×Dic₃	1	2	yes	—
359	Q₁₆	C₂×C₃×Dic₃	1	2	yes	—
360	SD₁₆	C₂×C₃×Dic₃	1	4	yes	—
361	SD₁₆	C₂×C₃×Dic₃	1	4	yes	—
362	D₈	C₂×C₃×Dic₃	1	2	yes	—
363	D₈	C₂×C₃×Dic₃	1	2	yes	—
364	M₁₆	—	3	2	no	—
365	M₁₆	—	3	2	no	—
366	M₁₆	—	3	4	no	—
367	M₁₆	—	6	8	no	—
368	M₁₆	—	6	2	no	—
369	C₂×C₈	—	3	2	no	—
370	C₂×C₈	—	6	8	no	—
371	C₂×C₈	—	6	2	no	—
372	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
373	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
374	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
375	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
376	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
377	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
378	C₄⋊C₄	—	6	1	no	—
379	C₂²⋊C₄	—	6	1	no	—
380	C₄²	—	3	2	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	4	no	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	4	4	no	—
387	C₂²×C₃	—	4	1	no	—
388	C₂²×C₃	—	4	1	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	—	8	2	no	—
391	C₂²×C₃	—	8	2	no	—
392	C₂²×C₃	—	8	4	no	—
393	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
394	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
395	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
396	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
397	C₂²×C₃	C₂×#237	1	1	yes	characteristic
398	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
399	C₃×C₄	—	2	4	no	—
400	C₃×C₄	—	2	4	no	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	4	4	no	—
406	C₃×C₄	—	12	2	no	—
407	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
408	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
409	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
410	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
411	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
412	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
413	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
414	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
415	Dic₃	—	4	2	no	—
416	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
417	C₂³	—	2	2	no	—
418	C₂³	C₃×#237	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	C₂²×C₃×Dic₃	1	4	yes	—
421	D₄	—	2	4	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	2	no	—
424	D₄	C₂²×C₃×Dic₃	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
430	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
431	C₂×C₄	C₃×#237	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
434	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
435	C₈	—	3	4	no	—
436	C₈	—	6	4	no	—
437	C₈	C₂²×C₃×Dic₃	1	1	yes	characteristic
438	C₈	C₂²×C₃×Dic₃	1	1	yes	characteristic
439	C₈	C₂²×C₃×Dic₃	1	1	yes	characteristic
440	C₈	C₂²×C₃×Dic₃	1	1	yes	characteristic
441	C₂×C₃	—	2	2	no	—
442	C₂×C₃	—	2	1	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	2	1	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	4	1	no	—
450	C₂×C₃	—	4	1	no	—
451	C₂×C₃	—	4	4	no	—
452	C₂×C₃	—	4	4	no	—
453	C₂×C₃	—	8	4	no	—
454	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
455	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
456	C₂²	—	2	4	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	8	2	no	—
459	C₂²	C₃×D₄×Dic₃	1	1	yes	characteristic
460	C₂²	C₃×D₄×Dic₃	1	1	yes	characteristic
461	C₂²	C₂×C₃×#237	1	1	yes	characteristic
462	C₄	—	2	4	no	—
463	C₄	—	12	2	no	—
464	C₄	C₃×D₄×Dic₃	1	1	yes	characteristic
465	C₄	C₃×D₄×Dic₃	1	1	yes	characteristic
466	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
467	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
468	C₃	—	2	1	no	—
469	C₃	#83910	1	1	yes	characteristic, direct product factor
470	C₃	C₃×#2957	1	1	yes	characteristic, complemented
471	C₂	—	2	1	no	—
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	4	4	no	—
475	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting, prime radical	C₂×C₃²×#135	C₂
socle	C₂×C₃²	C₂×C₄×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#135	D₃
hypocenter	C₃	C₃×#2957
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
2. C₃×#5819	C₂	semidirect
3. C₃×#5236	C₂	semidirect
4. C₃×#5197	C₂	semidirect
5. C₃×#5196	C₂	semidirect
6. C₂×C₃×#819	C₂	semidirect
7. C₃×#5101	C₂	semidirect
9. #83910	C₃	direct (N × H)
11. C₃²×#135	C₄	semidirect
12. C₃²×#135	C₄	semidirect
15. C₂×C₃²×Q₁₆	C₄	semidirect
16. C₂×C₃²×SD₁₆	C₄	semidirect
17. C₂×C₃²×D₈	C₄	semidirect
20. C₃×#948	C₂²	semidirect
25. C₃×#837	C₂²	semidirect
26. C₃×#819	C₂²	semidirect
27. C₃×#819	C₂²	semidirect
28. C₃×#815	C₂²	semidirect
29. C₃×C₈×Dic₃	C₂²	semidirect
34. #5819	C₂×C₃	semidirect
40. #5236	C₂×C₃	semidirect
41. #5197	C₂×C₃	semidirect
42. #5196	C₂×C₃	semidirect
43. C₂×#819	C₂×C₃	semidirect
44. #5101	C₂×C₃	semidirect
85. C₃×#135	Dic₃	semidirect
86. C₃×#135	Dic₃	semidirect
87. C₃×#135	C₃×C₄	semidirect
88. C₃×#135	C₃×C₄	semidirect
94. C₂×C₃×Q₁₆	Dic₃	semidirect
95. C₂×C₃×Q₁₆	C₃×C₄	semidirect
97. C₂×C₃×SD₁₆	Dic₃	semidirect
98. C₂×C₃×SD₁₆	C₃×C₄	semidirect
100. C₂×C₃×D₈	Dic₃	semidirect
101. C₂×C₃×D₈	C₃×C₄	semidirect
112. #948	C₂²×C₃	semidirect
122. #837	C₂²×C₃	semidirect
123. #819	C₂²×C₃	semidirect
124. #819	C₂²×C₃	semidirect
125. #815	C₂²×C₃	semidirect
126. C₈×Dic₃	C₂²×C₃	semidirect
256. #135	C₃×Dic₃	semidirect
257. #135	C₃×Dic₃	semidirect
260. C₂×Q₁₆	C₃×Dic₃	semidirect
261. C₂×SD₁₆	C₃×Dic₃	semidirect
262. C₂×D₈	C₃×Dic₃	semidirect
416. C₃²	#2957	semidirect
469. C₃	#83910	direct (N × H)
470. C₃	C₃×#2957	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×#5819	2
C₃×#5236	2
C₃×#5197	2
C₃×#5196	2
C₂×C₃×#819	2
C₃×#5101	2
C₃×#2957	3
#83910	3

Subgroups — C3×#83910 #11861201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83910 #11861201