Subgroups — C₃×#79249 #11861198

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5745	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5139	C₂	1	2	yes	maximal, complemented
5	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4895	C₂	1	4	yes	maximal, complemented
7	C₃×#4894	C₂	1	4	yes	maximal, complemented
8	C₃×#2957	—	3	1	no	maximal
9	#79249	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	2	yes	—
11	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₃×#926	C₂²	1	1	yes	characteristic
14	C₂×C₃×#208	C₂²	1	1	yes	characteristic
15	C₃×#907	C₂²	1	8	yes	complemented
16	C₃×D₃×M₁₆	—	2	4	no	—
17	C₂×C₃×Dic₁₂	C₄	1	1	yes	characteristic, complemented
18	C₃×#904	C₄	1	2	yes	complemented
19	C₃×#904	C₄	1	2	yes	complemented
20	C₃×#904	C₂²	1	2	yes	—
21	C₃×#904	C₂²	1	2	yes	—
22	C₂×C₃×D₂₄	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×#204	C₄	1	2	yes	complemented
24	C₃×#901	—	2	4	no	—
25	C₃²×#108	C₂²	1	2	yes	complemented
26	C₃²×#108	C₂²	1	2	yes	complemented
27	C₃×#825	C₂²	1	8	yes	complemented
28	C₃×#815	C₂²	1	2	yes	complemented
29	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
30	C₂×C₃×#135	—	3	1	no	—
31	C₃×#568	—	3	2	no	—
32	#5745	C₂×C₃	1	2	yes	complemented
33	C₂×#904	C₂×C₃	1	1	yes	characteristic
34	C₃×#444	—	3	4	no	—
35	C₃×#443	—	3	4	no	—
36	C₂×C₃×#108	—	2	1	no	—
37	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
38	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×#421	—	3	2	no	—
40	C₃×#405	—	3	1	no	—
41	#5139	C₂×C₃	1	2	yes	complemented
42	#5101	C₂×C₃	1	1	yes	characteristic, complemented
43	#4895	C₂×C₃	1	4	yes	complemented
44	#4894	C₂×C₃	1	4	yes	complemented
45	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
46	C₂×C₃×#67	—	2	2	no	—
47	C₃×#235	—	2	2	no	—
48	C₃×#235	—	2	2	no	—
49	C₃×#235	C₂×C₄	1	4	yes	—
50	C₃×#235	C₂³	1	4	yes	—
51	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
52	C₂×C₃×C₄×D₃	—	2	2	no	—
53	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
54	C₃²×M₁₆	—	2	2	no	—
55	C₃²×M₁₆	C₂³	1	4	yes	—
56	C₂×C₃²×C₈	—	2	2	no	—
57	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
63	C₃×#217	—	2	1	no	—
64	C₃×C₄⋊Dic₃	—	2	1	no	—
65	C₃×C₄×Dic₃	C₂³	1	2	yes	—
66	C₃×#208	D₄	1	2	yes	—
67	C₃×#208	D₄	1	2	yes	—
68	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
69	C₃×Dic₁₂	C₂×C₄	1	2	yes	—
70	C₃×Dic₁₂	C₂×C₄	1	2	yes	—
71	C₃×D₂₄	C₂×C₄	1	2	yes	—
72	C₃×D₂₄	C₂×C₄	1	2	yes	—
73	C₃×#204	C₂×C₄	1	4	yes	—
74	C₃×#204	C₂×C₄	1	4	yes	—
75	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
76	C₃×D₃×C₈	—	2	8	no	—
77	#2957	—	3	1	no	Sylow
78	C₂×C₃×#41	—	3	2	no	—
79	C₂×#235	C₂²×C₃	1	2	yes	—
80	C₃×#135	—	3	2	no	—
81	C₃×#135	—	3	2	no	—
82	C₃×#135	—	3	2	no	—
83	C₃×#135	—	3	2	no	—
84	C₂×C₃×Q₁₆	—	3	1	no	—
85	C₂×C₃×SD₁₆	—	3	2	no	—
86	C₂×C₃×D₈	—	3	1	no	—
87	C₃×#131	—	3	8	no	—
88	C₃×#131	—	6	4	no	—
89	C₂×C₃×M₁₆	—	2	2	no	—
90	C₂×C₃×M₁₆	—	3	1	no	—
91	C₂×C₃×M₁₆	—	6	4	no	—
92	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
93	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×C₈	—	2	1	no	—
95	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₃×#117	—	3	1	no	—
98	#926	C₂²×C₃	1	1	yes	characteristic
99	C₂×#208	C₂²×C₃	1	1	yes	characteristic
100	#907	C₂²×C₃	1	8	yes	complemented
101	D₃×M₁₆	—	2	4	no	—
102	C₂×Dic₁₂	C₃×C₄	1	1	yes	characteristic, complemented
103	#904	C₃×C₄	1	2	yes	complemented
104	#904	C₃×C₄	1	2	yes	complemented
105	#904	C₂²×C₃	1	2	yes	—
106	#904	C₂²×C₃	1	2	yes	—
107	C₂×D₂₄	C₃×C₄	1	1	yes	characteristic, complemented
108	C₂×#204	C₃×C₄	1	2	yes	complemented
109	#901	—	2	4	no	—
110	C₃×#108	—	2	2	no	—
111	C₃×#108	—	2	2	no	—
112	C₃×#108	C₂×D₃	1	2	yes	complemented
113	C₃×#108	C₂×D₃	1	2	yes	complemented
114	C₃×#108	C₂²×C₃	1	2	yes	complemented
115	C₃×#108	C₂²×C₃	1	2	yes	complemented
116	C₃×#104	—	3	8	no	—
117	C₃×#97	—	3	2	no	—
118	C₃×C₄×C₈	—	3	2	no	—
119	#825	C₂²×C₃	1	8	yes	complemented
120	#815	C₂²×C₃	1	2	yes	complemented
121	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
122	C₂³×C₃²	#41	1	1	yes	characteristic
123	C₂²×C₃×D₃	—	2	2	no	—
124	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	#41	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
130	C₃×#67	—	2	4	no	—
131	C₃×#67	—	2	4	no	—
132	C₂×C₃×Dic₃	—	2	2	no	—
133	C₂×C₃×Dic₃	—	2	2	no	—
134	C₃×D₁₂	—	2	2	no	—
135	C₃×D₁₂	C₂²×C₄	1	4	yes	—
136	C₃×C₄×D₃	—	2	4	no	—
137	C₃×C₄×D₃	—	2	4	no	—
138	C₃×Dic₆	—	2	2	no	—
139	C₃×Dic₆	C₂²×C₄	1	4	yes	—
140	C₃²×C₈	—	2	4	no	—
141	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
143	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
146	C₂×#135	—	3	1	no	—
147	#568	—	3	2	no	—
148	#444	—	3	4	no	—
149	#443	—	3	4	no	—
150	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
151	#421	—	3	2	no	—
152	#405	—	3	1	no	—
153	C₃×#41	—	3	4	no	—
154	C₃×#41	—	3	4	no	—
155	C₃×#41	—	6	2	no	—
156	C₃×#41	—	6	2	no	—
157	C₂×C₃×Q₈	—	3	2	no	—
158	C₂×C₃×D₄	—	3	2	no	—
159	C₂×C₃×D₄	—	6	2	no	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	6	2	no	—
162	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₂×#67	—	2	2	no	—
165	#235	—	2	2	no	—
166	#235	—	2	2	no	—
167	#235	C₂×C₃×C₄	1	4	yes	—
168	#235	C₂³×C₃	1	4	yes	—
169	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
170	C₂×C₄×D₃	—	2	2	no	—
171	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
172	C₃×Q₁₆	—	3	2	no	—
173	C₃×Q₁₆	—	3	2	no	—
174	C₃×SD₁₆	—	3	4	no	—
175	C₃×SD₁₆	—	3	4	no	—
176	C₃×D₈	—	3	2	no	—
177	C₃×D₈	—	3	2	no	—
178	C₃×M₁₆	—	2	2	no	—
179	C₃×M₁₆	—	2	2	no	—
180	C₃×M₁₆	—	2	4	no	—
181	C₃×M₁₆	—	3	2	no	—
182	C₃×M₁₆	—	3	2	no	—
183	C₃×M₁₆	—	4	2	no	—
184	C₃×M₁₆	—	6	8	no	—
185	C₃×M₁₆	C₂²×D₃	1	4	yes	—
186	C₃×M₁₆	C₂³×C₃	1	4	yes	—
187	C₂×C₃×C₈	—	2	2	no	—
188	C₂×C₃×C₈	—	2	2	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₂×C₃×C₈	—	2	1	no	—
195	C₂×C₃×C₈	—	3	2	no	—
196	C₂×C₃×C₈	—	4	2	no	—
197	C₂×C₃×C₈	—	6	8	no	—
198	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
199	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
200	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
201	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
202	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
207	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
210	C₃×C₄⋊C₄	—	6	1	no	—
211	C₃×C₂²⋊C₄	—	6	1	no	—
212	C₃×C₄²	—	3	2	no	—
213	#217	—	2	1	no	—
214	C₄⋊Dic₃	—	2	1	no	—
215	C₄×Dic₃	C₂³×C₃	1	2	yes	—
216	#208	C₃×D₄	1	2	yes	—
217	#208	C₃×D₄	1	2	yes	—
218	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
219	Dic₁₂	C₂×C₃×C₄	1	2	yes	—
220	Dic₁₂	C₂×C₃×C₄	1	2	yes	—
221	D₂₄	C₂×C₃×C₄	1	2	yes	—
222	D₂₄	C₂×C₃×C₄	1	2	yes	—
223	#204	C₂×C₃×C₄	1	4	yes	—
224	#204	C₂×C₃×C₄	1	4	yes	—
225	ΓL(1,𝔽₂₅)	—	2	8	no	—
226	D₃×C₈	—	2	8	no	—
227	C₂²×C₃²	—	4	1	no	—
228	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
229	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
230	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
231	C₂×C₃×D₃	—	2	4	no	—
232	C₂×C₃×D₃	—	8	2	no	—
233	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
234	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
235	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
236	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
237	C₃×Dic₃	—	2	4	no	—
238	C₃×Dic₃	—	4	2	no	—
239	C₂×#41	—	3	2	no	—
240	#135	—	3	2	no	—
241	#135	—	3	2	no	—
242	#135	—	3	2	no	—
243	#135	—	3	2	no	—
244	C₂×Q₁₆	—	3	1	no	—
245	C₂×SD₁₆	—	3	2	no	—
246	C₂×D₈	—	3	1	no	—
247	#131	—	3	8	no	—
248	#131	—	6	4	no	—
249	C₂×M₁₆	—	3	1	no	—
250	C₂×M₁₆	—	6	4	no	—
251	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
252	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
253	#117	—	3	1	no	—
254	#108	C₂×C₃×D₃	1	2	yes	complemented
255	#108	C₂×C₃×D₃	1	2	yes	complemented
256	#104	—	3	8	no	—
257	#97	—	3	2	no	—
258	C₄×C₈	—	3	2	no	—
259	C₂³×C₃	—	2	1	no	—
260	C₂³×C₃	—	6	2	no	—
261	C₂³×C₃	#239	1	1	yes	characteristic
262	C₂³×C₃	C₃×#41	1	1	yes	characteristic
263	C₂²×D₃	—	2	2	no	—
264	C₃×Q₈	—	3	4	no	—
265	C₃×Q₈	—	6	2	no	—
266	C₃×D₄	—	3	4	no	—
267	C₃×D₄	—	6	4	no	—
268	C₃×D₄	—	6	4	no	—
269	C₃×D₄	—	6	2	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	6	2	no	—
277	C₂×C₃×C₄	—	6	4	no	—
278	C₂×C₃×C₄	—	6	4	no	—
279	C₂×C₃×C₄	—	6	2	no	—
280	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
282	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	#239	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
292	#67	—	2	4	no	—
293	#67	—	2	4	no	—
294	C₂×Dic₃	—	2	2	no	—
295	C₂×Dic₃	—	2	2	no	—
296	D₁₂	—	2	2	no	—
297	D₁₂	C₂²×C₃×C₄	1	4	yes	—
298	C₄×D₃	—	2	4	no	—
299	C₄×D₃	—	2	4	no	—
300	Dic₆	—	2	2	no	—
301	Dic₆	C₂²×C₃×C₄	1	4	yes	—
302	C₃×C₈	—	2	4	no	—
303	C₃×C₈	—	2	4	no	—
304	C₃×C₈	—	2	1	no	—
305	C₃×C₈	—	2	1	no	—
306	C₃×C₈	—	2	1	no	—
307	C₃×C₈	—	2	1	no	—
308	C₃×C₈	—	3	4	no	—
309	C₃×C₈	—	4	4	no	—
310	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
311	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
312	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
313	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
314	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
316	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
317	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
318	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
319	C₂×C₃²	—	2	1	no	—
320	C₂×C₃²	—	2	1	no	—
321	C₂×C₃²	—	2	1	no	—
322	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
323	C₃×D₃	—	4	4	no	—
324	#41	—	3	4	no	—
325	#41	—	3	4	no	—
326	#41	—	6	2	no	—
327	#41	—	6	2	no	—
328	C₂×Q₈	—	3	2	no	—
329	C₂×D₄	—	3	2	no	—
330	C₂×D₄	—	6	2	no	—
331	C₂²×C₄	—	6	2	no	—
332	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
333	Q₁₆	—	3	2	no	—
334	Q₁₆	—	3	2	no	—
335	SD₁₆	—	3	4	no	—
336	SD₁₆	—	3	4	no	—
337	D₈	—	3	2	no	—
338	D₈	—	3	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	3	2	no	—
341	M₁₆	—	3	2	no	—
342	M₁₆	—	6	8	no	—
343	M₁₆	C₂²×C₃×D₃	1	4	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	3	2	no	—
346	C₂×C₈	—	6	8	no	—
347	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
348	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
349	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
350	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
351	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
352	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
353	C₄⋊C₄	—	6	1	no	—
354	C₂²⋊C₄	—	6	1	no	—
355	C₄²	—	3	2	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	4	1	no	—
360	C₂²×C₃	—	4	1	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	—	6	4	no	—
363	C₂²×C₃	—	24	2	no	—
364	C₂²×C₃	#893	1	1	yes	characteristic
365	C₂²×C₃	#893	1	1	yes	characteristic
366	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
367	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
368	C₂²×C₃	C₂×#239	1	1	yes	characteristic
369	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
370	C₂×D₃	—	2	4	no	—
371	C₂×D₃	—	8	2	no	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	6	4	no	—
377	C₃×C₄	—	12	2	no	—
378	C₃×C₄	#893	1	1	yes	characteristic
379	C₃×C₄	#893	1	1	yes	characteristic
380	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
381	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
382	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
383	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
384	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
385	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
386	Dic₃	—	2	4	no	—
387	Dic₃	—	4	2	no	—
388	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
389	C₂³	—	6	2	no	—
390	C₂³	C₃×#239	1	1	yes	characteristic
391	Q₈	—	3	4	no	—
392	Q₈	—	6	2	no	—
393	D₄	—	3	4	no	—
394	D₄	—	6	4	no	—
395	D₄	—	6	4	no	—
396	D₄	—	6	2	no	—
397	C₂×C₄	—	6	2	no	—
398	C₂×C₄	—	6	4	no	—
399	C₂×C₄	—	6	4	no	—
400	C₂×C₄	—	6	2	no	—
401	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
402	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
403	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
404	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
405	C₂×C₄	C₃×#239	1	1	yes	characteristic
406	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
407	C₈	—	2	4	no	—
408	C₈	—	3	4	no	—
409	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
410	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
411	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
412	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
413	C₂×C₃	—	2	2	no	—
414	C₂×C₃	—	2	1	no	—
415	C₂×C₃	—	2	1	no	—
416	C₂×C₃	—	2	1	no	—
417	C₂×C₃	—	2	1	no	—
418	C₂×C₃	—	2	1	no	—
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	4	1	no	—
422	C₂×C₃	—	4	1	no	—
423	C₂×C₃	—	12	4	no	—
424	C₂×C₃	C₂×#893	1	1	yes	characteristic
425	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
426	D₃	—	4	4	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	6	4	no	—
429	C₂²	—	24	2	no	—
430	C₂²	C₃×#893	1	1	yes	characteristic
431	C₂²	C₃×#893	1	1	yes	characteristic
432	C₂²	C₂×C₃×#239	1	1	yes	characteristic
433	C₄	—	6	4	no	—
434	C₄	—	12	2	no	—
435	C₄	C₃×#893	1	1	yes	characteristic
436	C₄	C₃×#893	1	1	yes	characteristic
437	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
438	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
439	C₃	—	2	1	no	—
440	C₃	#79249	1	1	yes	characteristic, direct product factor
441	C₃	C₃×#2957	1	1	yes	characteristic, complemented
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	12	4	no	—
446	C₂	C₂×C₃×#893	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	C₂×C₃²×#108	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₃×#2957
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#108

Complements

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

N	H ≅ G/N	type
1. C₃×#5745	C₂	semidirect
3. C₂×C₃²×#108	C₂	semidirect
4. C₃×#5139	C₂	semidirect
5. C₃×#5101	C₂	semidirect
6. C₃×#4895	C₂	semidirect
7. C₃×#4894	C₂	semidirect
9. #79249	C₃	direct (N × H)
15. C₃×#907	C₂²	semidirect
17. C₂×C₃×Dic₁₂	C₄	semidirect
18. C₃×#904	C₄	semidirect
19. C₃×#904	C₄	semidirect
22. C₂×C₃×D₂₄	C₄	semidirect
23. C₂×C₃×#204	C₄	semidirect
25. C₃²×#108	C₂²	semidirect
26. C₃²×#108	C₂²	semidirect
27. C₃×#825	C₂²	semidirect
28. C₃×#815	C₂²	semidirect
29. C₃×C₈×Dic₃	C₂²	semidirect
32. #5745	C₂×C₃	semidirect
37. C₂×C₃×#108	D₃	semidirect
38. C₂×C₃×#108	C₂×C₃	semidirect
41. #5139	C₂×C₃	semidirect
42. #5101	C₂×C₃	semidirect
43. #4895	C₂×C₃	semidirect
44. #4894	C₂×C₃	semidirect
100. #907	C₂²×C₃	semidirect
102. C₂×Dic₁₂	C₃×C₄	semidirect
103. #904	C₃×C₄	semidirect
104. #904	C₃×C₄	semidirect
107. C₂×D₂₄	C₃×C₄	semidirect
108. C₂×#204	C₃×C₄	semidirect
112. C₃×#108	C₂×D₃	semidirect
113. C₃×#108	C₂×D₃	semidirect
114. C₃×#108	C₂²×C₃	semidirect
115. C₃×#108	C₂²×C₃	semidirect
119. #825	C₂²×C₃	semidirect
120. #815	C₂²×C₃	semidirect
121. C₈×Dic₃	C₂²×C₃	semidirect
150. C₂×#108	C₃×D₃	semidirect
254. #108	C₂×C₃×D₃	semidirect
255. #108	C₂×C₃×D₃	semidirect
388. C₃²	#2957	semidirect
440. C₃	#79249	direct (N × H)
441. 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
C₃×#5745	2
C₂×C₃×#904	2
C₂×C₃²×#108	2
C₃×#5139	2
C₃×#5101	2
C₃×#4895	2
C₃×#4894	2
C₃×#2957	3
#79249	3

Subgroups — C3×#79249 #11861198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79249 #11861198