Subgroups — C₃×#83899 #11860932

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 414 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×#5184	C₂	1	2	yes	maximal, complemented
5	C₃×Dic₃×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₃×#5152	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#817	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2952	—	3	1	no	maximal
10	#83899	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×#817	C₂²	1	2	yes	—
28	C₃×#817	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×#442	—	3	2	no	—
37	C₃×#441	—	3	2	no	—
38	C₃×C₄×SD₁₆	—	3	4	no	—
39	C₂×C₃×#106	—	3	1	no	—
40	C₃×#417	—	3	2	no	—
41	C₃×#405	—	3	1	no	—
42	#5232	C₂×C₃	1	2	yes	complemented
43	#5184	C₂×C₃	1	2	yes	complemented
44	Dic₃×SD₁₆	C₂×C₃	1	4	yes	complemented
45	#5152	C₂×C₃	1	2	yes	complemented
46	C₂×#817	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	2	yes	—
68	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
69	C₃×C₄×Dic₃	—	2	4	no	—
70	C₃×C₄×Dic₃	C₂³	1	2	yes	—
71	C₃×#208	—	2	2	no	—
72	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
73	#2952	—	3	1	no	Sylow
74	C₂×C₃×#41	—	2	2	no	—
75	C₂×C₃×#41	C₂×D₃	1	2	yes	—
76	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
77	C₃×#135	—	2	8	no	—
78	C₃×#135	Dic₃	1	8	yes	complemented
79	C₃×#135	C₃×C₄	1	8	yes	complemented
80	C₂×C₃×Q₁₆	—	2	1	no	—
81	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
82	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×SD₁₆	—	2	2	no	—
84	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	—
85	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
86	C₂×C₃×D₈	—	2	1	no	—
87	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
88	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×M₁₆	—	3	1	no	—
90	C₂²×C₃×C₈	—	2	1	no	—
91	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
92	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
93	C₃×C₄×Q₈	—	3	4	no	—
94	C₃×C₄×D₄	—	3	4	no	—
95	C₃×C₄×D₄	—	6	4	no	—
96	C₃×#117	—	3	1	no	—
97	C₃×#117	—	6	2	no	—
98	C₂×C₃×C₄⋊C₄	—	3	2	no	—
99	C₂×C₃×C₄⋊C₄	—	6	2	no	—
100	Q₈×Dic₃	C₂²×C₃	1	4	yes	—
101	D₄×Dic₃	—	2	4	no	—
102	D₄×Dic₃	C₂²×C₃	1	4	yes	—
103	#926	—	2	2	no	—
104	#926	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄⋊Dic₃	—	2	2	no	—
106	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
107	C₂×#208	C₂²×C₃	1	1	yes	characteristic
108	C₃×#106	—	3	2	no	—
109	C₃×#106	—	3	2	no	—
110	C₃×#103	—	3	4	no	—
111	C₃×#102	—	3	4	no	—
112	C₃×#97	—	3	2	no	—
113	C₃×C₄×C₈	—	3	2	no	—
114	#835	C₂²×C₃	1	4	yes	—
115	#832	C₂²×C₃	1	4	yes	—
116	#817	C₂²×C₃	1	2	yes	—
117	#817	C₂²×C₃	1	2	yes	—
118	#815	C₂²×C₃	1	2	yes	—
119	C₈×Dic₃	C₂²×C₃	1	2	yes	—
120	C₂³×C₃²	—	2	2	no	—
121	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
122	C₃²×Q₈	—	2	2	no	—
123	C₃²×Q₈	C₂²×C₄	1	4	yes	—
124	C₃²×D₄	—	2	8	no	—
125	C₃²×D₄	—	2	2	no	—
126	C₃²×D₄	C₂²×C₄	1	4	yes	—
127	C₂×C₃²×C₄	—	2	2	no	—
128	C₂×C₃²×C₄	—	2	8	no	—
129	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	#41	1	2	yes	—
132	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
133	C₂×C₃×Dic₃	—	2	4	no	—
134	C₂×C₃×Dic₃	—	8	4	no	—
135	C₂×C₃×Dic₃	—	8	2	no	—
136	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
137	C₃²×C₈	C₂²×C₄	1	2	yes	—
138	C₃²×C₈	C₂²×C₄	1	2	yes	—
139	C₃×C₃⋊C₈	—	2	2	no	—
140	C₂×#135	C₃×D₃	1	1	yes	characteristic
141	#520	—	3	2	no	—
142	#442	—	3	2	no	—
143	#441	—	3	2	no	—
144	C₄×SD₁₆	—	3	4	no	—
145	C₂×#106	—	3	1	no	—
146	#417	—	3	2	no	—
147	#405	—	3	1	no	—
148	C₃×#41	—	2	4	no	—
149	C₃×#41	—	2	4	no	—
150	C₃×#41	—	2	8	no	—
151	C₃×#41	—	4	4	no	—
152	C₃×#41	C₂×Dic₃	1	8	yes	complemented
153	C₃×#41	C₂×C₃×C₄	1	8	yes	complemented
154	C₂×C₃×Q₈	—	2	2	no	—
155	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
156	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	4	2	no	—
161	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
162	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	—	2	2	no	—
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	—	4	2	no	—
167	C₂²×C₃×C₄	—	6	4	no	—
168	C₂²×C₃×C₄	—	6	2	no	—
169	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂²×Dic₃	—	2	2	no	—
172	C₂²×Dic₃	—	2	4	no	—
173	C₃×Q₁₆	—	2	4	no	—
174	C₃×Q₁₆	C₂×Dic₃	1	4	yes	complemented
175	C₃×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
176	C₃×SD₁₆	—	2	8	no	—
177	C₃×SD₁₆	C₂×Dic₃	1	8	yes	complemented
178	C₃×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
179	C₃×D₈	—	2	4	no	—
180	C₃×D₈	C₂×Dic₃	1	4	yes	complemented
181	C₃×D₈	C₂×C₃×C₄	1	4	yes	complemented
182	C₃×M₁₆	—	6	2	no	—
183	C₂×C₃×C₈	—	2	4	no	—
184	C₂×C₃×C₈	—	2	1	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	3	2	no	—
187	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	complemented
188	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
189	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
193	C₃×C₄⋊C₄	—	3	2	no	—
194	C₃×C₄⋊C₄	—	3	4	no	—
195	C₃×C₄⋊C₄	—	6	4	no	—
196	C₃×C₄⋊C₄	—	6	2	no	—
197	C₃×C₂²⋊C₄	—	3	2	no	—
198	C₃×C₂²⋊C₄	—	6	4	no	—
199	C₃×C₄²	—	3	2	no	—
200	C₃×C₄²	—	6	4	no	—
201	#217	—	2	4	no	—
202	#217	C₃×D₄	1	2	yes	—
203	C₄⋊Dic₃	—	2	2	no	—
204	C₄⋊Dic₃	—	2	4	no	—
205	C₄⋊Dic₃	C₃×D₄	1	2	yes	—
206	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
207	C₄×Dic₃	—	2	4	no	—
208	C₄×Dic₃	C₂³×C₃	1	2	yes	—
209	#208	—	2	2	no	—
210	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
211	C₂²×C₃²	—	2	2	no	—
212	C₂²×C₃²	—	2	4	no	—
213	C₂²×C₃²	—	4	2	no	—
214	C₂²×C₃²	—	4	2	no	—
215	C₂²×C₃²	C₄×D₄	1	2	yes	—
216	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
217	C₃²×C₄	—	2	4	no	—
218	C₃²×C₄	C₄×D₄	1	2	yes	—
219	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
220	C₃²×C₄	C₂×#41	1	1	yes	characteristic
221	C₃×Dic₃	—	2	4	no	—
222	C₃×Dic₃	—	4	4	no	—
223	C₂×#41	C₂×C₃×D₃	1	2	yes	—
224	#135	C₃×Dic₃	1	8	yes	complemented
225	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
226	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	—
227	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
228	C₂×M₁₆	—	3	1	no	—
229	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
230	C₄×Q₈	—	3	4	no	—
231	C₄×D₄	—	3	4	no	—
232	C₄×D₄	—	6	4	no	—
233	#117	—	3	1	no	—
234	#117	—	6	2	no	—
235	C₂×C₄⋊C₄	—	3	2	no	—
236	C₂×C₄⋊C₄	—	6	2	no	—
237	#106	—	3	2	no	—
238	#106	—	3	2	no	—
239	#103	—	3	4	no	—
240	#102	—	3	4	no	—
241	#97	—	3	2	no	—
242	C₄×C₈	—	3	2	no	—
243	C₂³×C₃	—	2	2	no	—
244	C₂³×C₃	—	2	2	no	—
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	—	4	2	no	—
247	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
248	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
249	C₃×Q₈	—	2	2	no	—
250	C₃×Q₈	—	2	2	no	—
251	C₃×Q₈	—	2	4	no	—
252	C₃×Q₈	—	4	2	no	—
253	C₃×Q₈	C₂²×Dic₃	1	4	yes	—
254	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
255	C₃×D₄	—	2	8	no	—
256	C₃×D₄	—	2	8	no	—
257	C₃×D₄	—	2	2	no	—
258	C₃×D₄	—	2	2	no	—
259	C₃×D₄	—	2	4	no	—
260	C₃×D₄	—	4	2	no	—
261	C₃×D₄	—	4	8	no	—
262	C₃×D₄	C₂²×Dic₃	1	4	yes	—
263	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	—	2	8	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	3	4	no	—
273	C₂×C₃×C₄	—	4	8	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	6	4	no	—
276	C₂×C₃×C₄	—	24	4	no	—
277	C₂×C₃×C₄	—	24	2	no	—
278	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
279	C₂×C₃×C₄	#237	1	2	yes	—
280	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
281	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₃×#41	1	2	yes	—
284	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
286	C₂×Dic₃	—	2	4	no	—
287	C₂×Dic₃	—	8	4	no	—
288	C₂×Dic₃	—	8	2	no	—
289	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₃×C₈	—	6	2	no	—
293	C₃×C₈	C₂²×Dic₃	1	2	yes	—
294	C₃×C₈	C₂²×Dic₃	1	2	yes	—
295	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
296	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
297	C₃⋊C₈	—	2	2	no	—
298	C₂×C₃²	—	2	2	no	—
299	C₂×C₃²	—	4	4	no	—
300	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
301	C₂×C₃²	#577	1	2	yes	—
302	#41	—	2	4	no	—
303	#41	C₂×C₃×Dic₃	1	8	yes	complemented
304	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	6	4	no	—
309	C₂²×C₄	—	6	2	no	—
310	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
311	Q₁₆	C₂×C₃×Dic₃	1	4	yes	complemented
312	SD₁₆	C₂×C₃×Dic₃	1	8	yes	complemented
313	D₈	C₂×C₃×Dic₃	1	4	yes	complemented
314	M₁₆	—	6	2	no	—
315	C₂×C₈	—	3	2	no	—
316	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	complemented
317	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
318	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
319	C₄⋊C₄	—	3	2	no	—
320	C₄⋊C₄	—	3	4	no	—
321	C₄⋊C₄	—	6	4	no	—
322	C₄⋊C₄	—	6	2	no	—
323	C₂²⋊C₄	—	3	2	no	—
324	C₂²⋊C₄	—	6	4	no	—
325	C₄²	—	3	2	no	—
326	C₄²	—	6	4	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	4	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	4	2	no	—
334	C₂²×C₃	—	4	4	no	—
335	C₂²×C₃	—	4	2	no	—
336	C₂²×C₃	—	4	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	—	8	2	no	—
340	C₂²×C₃	—	8	2	no	—
341	C₂²×C₃	D₄×Dic₃	1	2	yes	—
342	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
343	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
344	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
345	C₃×C₄	—	2	4	no	—
346	C₃×C₄	—	2	4	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	4	4	no	—
351	C₃×C₄	—	6	4	no	—
352	C₃×C₄	—	12	4	no	—
353	C₃×C₄	D₄×Dic₃	1	2	yes	—
354	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
355	C₃×C₄	C₂×#237	1	1	yes	characteristic
356	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
357	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
358	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
359	Dic₃	—	2	4	no	—
360	Dic₃	—	4	4	no	—
361	C₃²	#2952	1	1	yes	characteristic, complemented, Sylow
362	C₂³	—	2	2	no	—
363	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	C₂²×C₃×Dic₃	1	4	yes	—
366	D₄	—	2	8	no	—
367	D₄	—	2	2	no	—
368	D₄	C₂²×C₃×Dic₃	1	4	yes	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	3	4	no	—
372	C₂×C₄	—	6	4	no	—
373	C₂×C₄	—	24	4	no	—
374	C₂×C₄	—	24	2	no	—
375	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
376	C₂×C₄	C₃×#237	1	2	yes	—
377	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
378	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
379	C₈	—	6	2	no	—
380	C₈	C₂²×C₃×Dic₃	1	2	yes	—
381	C₈	C₂²×C₃×Dic₃	1	2	yes	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	—	2	2	no	—
384	C₂×C₃	—	2	2	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	4	2	no	—
387	C₂×C₃	—	4	4	no	—
388	C₂×C₃	—	4	4	no	—
389	C₂×C₃	—	8	4	no	—
390	C₂×C₃	#5770	1	2	yes	—
391	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
392	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
393	C₂×C₃	C₃×#577	1	2	yes	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	C₃×D₄×Dic₃	1	2	yes	—
399	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	6	4	no	—
402	C₄	—	12	4	no	—
403	C₄	C₃×D₄×Dic₃	1	2	yes	—
404	C₄	C₂×C₃×#237	1	1	yes	characteristic
405	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
406	C₃	—	2	1	no	—
407	C₃	#83899	1	1	yes	characteristic, direct product factor
408	C₃	C₃×#2952	1	1	yes	characteristic, complemented
409	C₂	—	2	2	no	—
410	C₂	—	4	4	no	—
411	C₂	C₃×#5770	1	2	yes	—
412	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×#2952
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×#5184	C₂	semidirect
5. C₃×Dic₃×SD₁₆	C₂	semidirect
6. C₃×#5152	C₂	semidirect
7. C₂×C₃×#817	C₂	semidirect
8. C₃×#5101	C₂	semidirect
10. #83899	C₃	direct (N × H)
12. C₃²×#135	C₄	semidirect
35. #5827	C₂×C₃	semidirect
42. #5232	C₂×C₃	semidirect
43. #5184	C₂×C₃	semidirect
44. Dic₃×SD₁₆	C₂×C₃	semidirect
45. #5152	C₂×C₃	semidirect
46. C₂×#817	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
78. C₃×#135	Dic₃	semidirect
79. C₃×#135	C₃×C₄	semidirect
152. C₃×#41	C₂×Dic₃	semidirect
153. C₃×#41	C₂×C₃×C₄	semidirect
174. C₃×Q₁₆	C₂×Dic₃	semidirect
175. C₃×Q₁₆	C₂×C₃×C₄	semidirect
177. C₃×SD₁₆	C₂×Dic₃	semidirect
178. C₃×SD₁₆	C₂×C₃×C₄	semidirect
180. C₃×D₈	C₂×Dic₃	semidirect
181. C₃×D₈	C₂×C₃×C₄	semidirect
187. C₂×C₃×C₈	C₂×Dic₃	semidirect
188. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
224. #135	C₃×Dic₃	semidirect
303. #41	C₂×C₃×Dic₃	semidirect
311. Q₁₆	C₂×C₃×Dic₃	semidirect
312. SD₁₆	C₂×C₃×Dic₃	semidirect
313. D₈	C₂×C₃×Dic₃	semidirect
316. C₂×C₈	C₂×C₃×Dic₃	semidirect
361. C₃²	#2952	semidirect
407. C₃	#83899	direct (N × H)
408. C₃	C₃×#2952	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×#5184	2
C₃×Dic₃×SD₁₆	2
C₃×#5152	2
C₂×C₃×#817	2
C₃×#5101	2
C₃×#2952	3
#83899	3

Subgroups — C3×#83899 #11860932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83899 #11860932