Subgroups — C₃×Dic₃×#135 #11859980

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 421 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×Dic₃×#41	C₂	1	2	yes	maximal, complemented
3	C₃×#5233	C₂	1	2	yes	maximal, complemented
4	C₃×Dic₃×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×Dic₃×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₃×Dic₃×D₈	C₂	1	2	yes	maximal, complemented
7	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×#135	—	3	1	no	maximal
10	Dic₃×#135	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	2	yes	—
22	C₂×C₃×C₄×Dic₃	—	2	2	no	—
23	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₃⋊C₈	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×#817	C₂²	1	2	yes	—
29	C₃×C₈×Dic₃	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×C₄×#41	—	3	2	no	—
35	Dic₃×#41	C₂×C₃	1	2	yes	complemented
36	C₃×C₄×Q₁₆	—	3	2	no	—
37	C₃×C₄×SD₁₆	—	3	4	no	—
38	C₃×C₄×D₈	—	3	2	no	—
39	C₃×#427	—	3	1	no	—
40	C₃×#416	—	3	2	no	—
41	C₂×C₃×C₄×C₈	—	3	1	no	—
42	#5233	C₂×C₃	1	2	yes	complemented
43	Dic₃×Q₁₆	C₂×C₃	1	2	yes	complemented
44	Dic₃×SD₁₆	C₂×C₃	1	4	yes	complemented
45	Dic₃×D₈	C₂×C₃	1	2	yes	complemented
46	#5106	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×C₈×Dic₃	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	4	no	—
56	C₂²×C₃×Dic₃	D₄	1	2	yes	—
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	2	no	—
64	C₃×#217	—	2	4	no	—
65	C₃×C₄⋊Dic₃	—	2	4	no	—
66	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
67	C₃×C₄×Dic₃	—	2	2	no	—
68	C₃×C₄×Dic₃	—	2	4	no	—
69	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
70	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
71	C₃×C₄×Dic₃	C₂³	1	2	yes	—
72	C₂×C₃×C₃⋊C₈	—	2	2	no	—
73	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
74	C₄×#135	—	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	direct product factor
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	C₂²×C₃×C₈	—	2	1	no	—
91	C₂²×C₃×C₈	—	3	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	2	no	—
98	C₃×#117	—	6	2	no	—
99	C₂×C₃×C₄²	—	3	1	no	—
100	C₂×C₃×C₄²	—	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	2	yes	—
106	C₂×C₄×Dic₃	—	2	2	no	—
107	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
109	C₃×#107	—	3	2	no	—
110	C₃×#106	—	3	2	no	—
111	C₃×#103	—	3	4	no	—
112	C₃×#102	—	3	4	no	—
113	C₃×C₄×C₈	—	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	#817	C₂²×C₃	1	2	yes	—
119	C₈×Dic₃	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	—	2	4	no	—
136	C₂×C₃×Dic₃	—	4	8	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	C₄×#41	—	3	2	no	—
144	C₄×Q₁₆	—	3	2	no	—
145	C₄×SD₁₆	—	3	4	no	—
146	C₄×D₈	—	3	2	no	—
147	#427	—	3	1	no	—
148	#416	—	3	2	no	—
149	C₂×C₄×C₈	—	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	—	3	2	no	—
169	C₂²×C₃×C₄	—	4	2	no	—
170	C₂²×C₃×C₄	—	6	4	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	4	no	—
174	C₂²×Dic₃	C₃×D₄	1	2	yes	—
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	C₂×C₃×C₈	—	2	4	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₂×C₃×C₈	—	3	2	no	—
188	C₂×C₃×C₈	—	6	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	4	no	—
196	C₃×C₄⋊C₄	—	6	4	no	—
197	C₃×C₂²⋊C₄	—	6	4	no	—
198	C₃×C₂²⋊C₄	—	6	2	no	—
199	C₃×C₄²	—	3	1	no	—
200	C₃×C₄²	—	3	1	no	—
201	C₃×C₄²	—	3	2	no	—
202	C₃×C₄²	—	6	4	no	—
203	C₃×C₄²	—	6	2	no	—
204	#217	—	2	2	no	—
205	#217	—	2	4	no	—
206	C₄⋊Dic₃	—	2	4	no	—
207	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
208	C₄×Dic₃	—	2	2	no	—
209	C₄×Dic₃	—	2	4	no	—
210	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
211	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
212	C₄×Dic₃	C₂³×C₃	1	2	yes	—
213	C₂×C₃⋊C₈	—	2	2	no	—
214	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
215	C₂²×C₃²	—	2	2	no	—
216	C₂²×C₃²	—	2	4	no	—
217	C₂²×C₃²	—	4	4	no	—
218	C₂²×C₃²	C₄×D₄	1	2	yes	—
219	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
220	C₃²×C₄	—	2	4	no	—
221	C₃²×C₄	C₄×D₄	1	2	yes	—
222	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
223	C₃²×C₄	C₂×#41	1	1	yes	characteristic
224	C₃×Dic₃	—	2	2	no	—
225	C₃×Dic₃	—	4	4	no	—
226	C₃×Dic₃	#135	1	4	yes	direct product factor
227	C₂×#41	C₂×C₃×D₃	1	2	yes	—
228	#135	C₃×Dic₃	1	8	yes	direct product factor
229	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
230	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	—
231	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂²×C₈	—	3	1	no	—
233	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
234	C₄×Q₈	—	3	4	no	—
235	C₄×D₄	—	3	4	no	—
236	C₄×D₄	—	6	4	no	—
237	#117	—	3	2	no	—
238	#117	—	6	2	no	—
239	C₂×C₄²	—	3	1	no	—
240	C₂×C₄²	—	6	2	no	—
241	#107	—	3	2	no	—
242	#106	—	3	2	no	—
243	#103	—	3	4	no	—
244	#102	—	3	4	no	—
245	C₄×C₈	—	3	2	no	—
246	C₄×C₈	—	3	2	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	2	no	—
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	—	4	2	no	—
251	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
252	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
253	C₃×Q₈	—	2	2	no	—
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×Q₈	—	4	2	no	—
257	C₃×Q₈	C₂²×Dic₃	1	4	yes	—
258	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
259	C₃×D₄	—	2	8	no	—
260	C₃×D₄	—	2	8	no	—
261	C₃×D₄	—	2	2	no	—
262	C₃×D₄	—	2	2	no	—
263	C₃×D₄	—	2	4	no	—
264	C₃×D₄	—	4	2	no	—
265	C₃×D₄	—	4	8	no	—
266	C₃×D₄	C₂²×Dic₃	1	4	yes	—
267	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	8	no	—
271	C₂×C₃×C₄	—	2	8	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	3	2	no	—
277	C₂×C₃×C₄	—	3	2	no	—
278	C₂×C₃×C₄	—	4	8	no	—
279	C₂×C₃×C₄	—	4	2	no	—
280	C₂×C₃×C₄	—	6	4	no	—
281	C₂×C₃×C₄	—	6	4	no	—
282	C₂×C₃×C₄	—	12	8	no	—
283	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	#237	1	2	yes	—
285	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
286	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₃×#41	1	2	yes	—
289	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
291	C₂×Dic₃	—	2	4	no	—
292	C₂×Dic₃	—	2	4	no	—
293	C₂×Dic₃	—	4	8	no	—
294	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
295	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	2	2	no	—
298	C₃×C₈	—	6	2	no	—
299	C₃×C₈	C₂²×Dic₃	1	2	yes	—
300	C₃×C₈	C₂²×Dic₃	1	2	yes	—
301	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
302	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
303	C₃⋊C₈	—	2	2	no	—
304	C₂×C₃²	—	2	2	no	—
305	C₂×C₃²	—	4	4	no	—
306	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
307	C₂×C₃²	C₂×#135	1	2	yes	—
308	#41	—	2	4	no	—
309	#41	C₂×C₃×Dic₃	1	8	yes	complemented
310	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	3	2	no	—
315	C₂²×C₄	—	6	4	no	—
316	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
317	Q₁₆	C₂×C₃×Dic₃	1	4	yes	complemented
318	SD₁₆	C₂×C₃×Dic₃	1	8	yes	complemented
319	D₈	C₂×C₃×Dic₃	1	4	yes	complemented
320	C₂×C₈	—	3	2	no	—
321	C₂×C₈	—	6	2	no	—
322	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	complemented
323	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
324	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
325	C₄⋊C₄	—	3	4	no	—
326	C₄⋊C₄	—	6	4	no	—
327	C₂²⋊C₄	—	6	4	no	—
328	C₂²⋊C₄	—	6	2	no	—
329	C₄²	—	3	2	no	—
330	C₄²	—	3	1	no	—
331	C₄²	—	3	1	no	—
332	C₄²	—	6	4	no	—
333	C₄²	—	6	2	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	4	no	—
337	C₂²×C₃	—	2	4	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	1	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	—	4	4	no	—
342	C₂²×C₃	—	4	4	no	—
343	C₂²×C₃	—	4	4	no	—
344	C₂²×C₃	—	8	4	no	—
345	C₂²×C₃	D₄×Dic₃	1	2	yes	—
346	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
347	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
348	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
349	C₃×C₄	—	2	4	no	—
350	C₃×C₄	—	2	4	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	3	4	no	—
355	C₃×C₄	—	4	4	no	—
356	C₃×C₄	—	6	2	no	—
357	C₃×C₄	—	12	4	no	—
358	C₃×C₄	D₄×Dic₃	1	2	yes	—
359	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
360	C₃×C₄	C₂×#237	1	1	yes	characteristic
361	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
362	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
363	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
364	Dic₃	—	2	2	no	—
365	Dic₃	—	4	4	no	—
366	Dic₃	C₃×#135	1	4	yes	direct product factor
367	C₃²	C₄×#135	1	1	yes	characteristic, complemented, Sylow
368	C₂³	—	2	2	no	—
369	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	C₂²×C₃×Dic₃	1	4	yes	—
372	D₄	—	2	8	no	—
373	D₄	—	2	2	no	—
374	D₄	C₂²×C₃×Dic₃	1	4	yes	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	3	2	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	6	4	no	—
380	C₂×C₄	—	6	4	no	—
381	C₂×C₄	—	12	8	no	—
382	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
383	C₂×C₄	C₃×#237	1	2	yes	—
384	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
385	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
386	C₈	—	6	2	no	—
387	C₈	C₂²×C₃×Dic₃	1	2	yes	—
388	C₈	C₂²×C₃×Dic₃	1	2	yes	—
389	C₂×C₃	—	2	2	no	—
390	C₂×C₃	—	2	2	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	4	2	no	—
394	C₂×C₃	—	4	4	no	—
395	C₂×C₃	—	4	4	no	—
396	C₂×C₃	—	8	4	no	—
397	C₂×C₃	D₃×#135	1	2	yes	—
398	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
399	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
400	C₂×C₃	C₂×C₃×#135	1	2	yes	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	C₃×D₄×Dic₃	1	2	yes	—
405	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
406	C₄	—	2	4	no	—
407	C₄	—	3	4	no	—
408	C₄	—	6	2	no	—
409	C₄	—	12	4	no	—
410	C₄	C₃×D₄×Dic₃	1	2	yes	—
411	C₄	C₂×C₃×#237	1	1	yes	characteristic
412	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
413	C₃	—	2	1	no	—
414	C₃	Dic₃×#135	1	1	yes	characteristic, direct product factor
415	C₃	C₃×C₄×#135	1	1	yes	characteristic, complemented
416	C₂	—	2	2	no	—
417	C₂	—	4	4	no	—
418	C₂	C₃×D₃×#135	1	2	yes	—
419	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	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×C₄×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×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×Dic₃×#41	C₂	semidirect
3. C₃×#5233	C₂	semidirect
4. C₃×Dic₃×Q₁₆	C₂	semidirect
5. C₃×Dic₃×SD₁₆	C₂	semidirect
6. C₃×Dic₃×D₈	C₂	semidirect
7. C₃×#5106	C₂	semidirect
8. C₂×C₃×C₈×Dic₃	C₂	semidirect
10. Dic₃×#135	C₃	direct (N × H)
12. C₃²×#135	C₄	semidirect
35. Dic₃×#41	C₂×C₃	semidirect
42. #5233	C₂×C₃	semidirect
43. Dic₃×Q₁₆	C₂×C₃	semidirect
44. Dic₃×SD₁₆	C₂×C₃	semidirect
45. Dic₃×D₈	C₂×C₃	semidirect
46. #5106	C₂×C₃	semidirect
47. C₂×C₈×Dic₃	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	direct (N × H)
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
226. C₃×Dic₃	#135	direct (N × H)
228. #135	C₃×Dic₃	direct (N × H)
309. #41	C₂×C₃×Dic₃	semidirect
317. Q₁₆	C₂×C₃×Dic₃	semidirect
318. SD₁₆	C₂×C₃×Dic₃	semidirect
319. D₈	C₂×C₃×Dic₃	semidirect
322. C₂×C₈	C₂×C₃×Dic₃	semidirect
366. Dic₃	C₃×#135	direct (N × H)
367. C₃²	C₄×#135	semidirect
414. C₃	Dic₃×#135	direct (N × H)
415. C₃	C₃×C₄×#135	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×Dic₃×#41	2
C₃×#5233	2
C₃×Dic₃×Q₁₆	2
C₃×Dic₃×SD₁₆	2
C₃×Dic₃×D₈	2
C₃×#5106	2
C₂×C₃×C₈×Dic₃	2
C₃×C₄×#135	3
Dic₃×#135	3

Subgroups — C3×Dic3×#135 #11859980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃×#135 #11859980