Subgroups — C₃×#20512 #10639119

Order 768.

1014 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#443	C₂	1	1	yes	maximal, characteristic
3	C₃×#2943	C₂	1	1	yes	maximal, characteristic
4	C₃×#2875	C₂	1	2	yes	maximal, complemented
5	C₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1765	C₂	1	2	yes	maximal, complemented
9	C₃×#1764	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#104	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	#20512	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#135	C₂²	1	1	yes	characteristic
14	C₂×C₃×#131	C₂²	1	2	yes	—
15	C₂×C₃×#131	C₂²	1	2	yes	—
16	C₃×C₄×#41	C₂²	1	2	yes	—
17	C₃×#444	C₄	1	8	yes	complemented
18	C₃×#443	C₄	1	8	yes	complemented
19	C₃×#442	C₄	1	2	yes	complemented
20	C₃×#441	C₄	1	2	yes	complemented
21	C₃×#440	C₄	1	4	yes	complemented
22	C₂×C₃×#108	C₂²	1	1	yes	characteristic
23	C₂×C₃×#108	C₂²	1	1	yes	characteristic
24	C₃×#427	C₂²	1	1	yes	characteristic
25	C₂×C₃×#104	C₂²	1	2	yes	—
26	C₂×C₃×#104	C₂²	1	2	yes	—
27	C₃×#416	C₂²	1	2	yes	—
28	C₃×#405	—	2	2	no	—
29	C₃×#405	—	2	2	no	—
30	C₃×#405	C₂²	1	2	yes	—
31	C₃×#405	C₂²	1	2	yes	—
32	C₃×C₄×M₁₆	—	2	2	no	—
33	C₃×C₄×M₁₆	C₂²	1	2	yes	—
34	C₂×C₃×#97	—	2	2	no	—
35	C₂×C₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₃×#97	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
41	C₃×C₄³	C₂²	1	1	yes	characteristic
42	C₃×#341	C₂²	1	2	yes	—
43	C₃×#339	C₂²	1	2	yes	—
44	C₃×#339	C₂²	1	2	yes	—
45	C₂×#444	C₂×C₃	1	1	yes	characteristic
46	C₂×#443	C₂×C₃	1	1	yes	characteristic
47	#2943	C₂×C₃	1	1	yes	characteristic
48	#2875	C₂×C₃	1	2	yes	complemented
49	#1778	C₂×C₃	1	1	yes	characteristic, complemented
50	#1773	C₂×C₃	1	1	yes	characteristic, complemented
51	#1772	C₂×C₃	1	1	yes	characteristic, complemented
52	#1765	C₂×C₃	1	2	yes	complemented
53	#1764	C₂×C₃	1	2	yes	complemented
54	C₄×#104	C₂×C₃	1	2	yes	complemented
55	C₄×#97	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×#41	C₂³	1	2	yes	—
57	C₃×#135	C₂×C₄	1	4	yes	—
58	C₃×#135	C₂×C₄	1	4	yes	—
59	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×SD₁₆	C₂×C₄	1	2	yes	—
61	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
62	C₃×#131	—	2	4	no	—
63	C₃×#131	—	2	4	no	—
64	C₃×#131	C₂×C₄	1	8	yes	complemented
65	C₃×#131	C₂×C₄	1	8	yes	complemented
66	C₂×C₃×M₁₆	—	2	2	no	—
67	C₂×C₃×M₁₆	—	2	2	no	—
68	C₂×C₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₃×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₃×C₈	—	2	2	no	—
71	C₂²×C₃×C₈	—	2	2	no	—
72	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
76	C₃×C₄×Q₈	C₂×C₄	1	4	yes	—
77	C₃×C₄×D₄	—	2	4	no	—
78	C₃×C₄×D₄	C₂×C₄	1	4	yes	—
79	C₃×#117	—	2	2	no	—
80	C₃×#117	C₂³	1	2	yes	—
81	C₂×C₃×C₄²	—	2	2	no	—
82	C₂×C₃×C₄²	—	2	2	no	—
83	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
86	C₃×#108	C₂×C₄	1	4	yes	complemented
87	C₃×#108	C₂×C₄	1	4	yes	complemented
88	C₃×#107	C₂×C₄	1	2	yes	—
89	C₃×#106	C₂×C₄	1	2	yes	—
90	C₃×#104	C₂×C₄	1	8	yes	complemented
91	C₃×#104	C₂×C₄	1	8	yes	complemented
92	C₃×#103	C₂×C₄	1	4	yes	—
93	C₃×#102	C₂×C₄	1	4	yes	—
94	C₃×#97	—	2	2	no	—
95	C₃×#97	—	2	2	no	—
96	C₃×#97	—	2	2	no	—
97	C₃×#97	—	2	2	no	—
98	C₃×#97	C₂×C₄	1	2	yes	—
99	C₃×#97	C₂×C₄	1	2	yes	—
100	C₃×#97	C₂×C₄	1	4	yes	complemented
101	C₃×#97	D₄	1	2	yes	—
102	C₃×#97	D₄	1	2	yes	—
103	C₃×C₄×C₈	—	2	2	no	—
104	C₃×C₄×C₈	—	2	2	no	—
105	C₃×C₄×C₈	—	2	2	no	—
106	C₃×C₄×C₈	—	2	2	no	—
107	C₃×C₄×C₈	C₂×C₄	1	4	yes	complemented
108	C₂×#135	C₂²×C₃	1	1	yes	characteristic
109	C₂×#131	C₂²×C₃	1	2	yes	—
110	C₂×#131	C₂²×C₃	1	2	yes	—
111	C₄×#41	C₂²×C₃	1	2	yes	—
112	#444	C₃×C₄	1	8	yes	complemented
113	#443	C₃×C₄	1	8	yes	complemented
114	#442	C₃×C₄	1	2	yes	complemented
115	#441	C₃×C₄	1	2	yes	complemented
116	#440	C₃×C₄	1	4	yes	complemented
117	C₂×#108	C₂²×C₃	1	1	yes	characteristic
118	C₂×#108	C₂²×C₃	1	1	yes	characteristic
119	#427	C₂²×C₃	1	1	yes	characteristic
120	C₂×#104	C₂²×C₃	1	2	yes	—
121	C₂×#104	C₂²×C₃	1	2	yes	—
122	#416	C₂²×C₃	1	2	yes	—
123	#405	—	2	2	no	—
124	#405	—	2	2	no	—
125	#405	C₂²×C₃	1	2	yes	—
126	#405	C₂²×C₃	1	2	yes	—
127	C₄×M₁₆	—	2	2	no	—
128	C₄×M₁₆	C₂²×C₃	1	2	yes	—
129	C₂×#97	—	2	2	no	—
130	C₂×#97	C₂²×C₃	1	1	yes	characteristic
131	C₂×#97	C₂²×C₃	1	1	yes	characteristic
132	C₂×#97	C₂²×C₃	1	1	yes	characteristic
133	C₂×#97	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
136	C₄³	C₂²×C₃	1	1	yes	characteristic
137	#341	C₂²×C₃	1	2	yes	—
138	#339	C₂²×C₃	1	2	yes	—
139	#339	C₂²×C₃	1	2	yes	—
140	C₃×#41	—	2	2	no	—
141	C₃×#41	—	2	2	no	—
142	C₃×#41	C₂²×C₄	1	4	yes	—
143	C₃×#41	C₂²×C₄	1	4	yes	—
144	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	1	no	—
150	C₂²×C₃×C₄	—	2	4	no	—
151	C₂²×C₃×C₄	#41	1	2	yes	—
152	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
153	C₃×Q₁₆	C₄²	1	4	yes	complemented
154	C₃×SD₁₆	C₄²	1	8	yes	complemented
155	C₃×D₈	C₄²	1	4	yes	complemented
156	C₃×M₁₆	—	2	2	no	—
157	C₃×M₁₆	—	2	2	no	—
158	C₃×M₁₆	—	2	8	no	—
159	C₃×M₁₆	—	2	8	no	—
160	C₃×M₁₆	C₂²×C₄	1	4	yes	—
161	C₃×M₁₆	C₂²×C₄	1	4	yes	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	1	no	—
165	C₂×C₃×C₈	—	2	1	no	—
166	C₂×C₃×C₈	—	2	8	no	—
167	C₂×C₃×C₈	—	2	8	no	—
168	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
170	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
173	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
177	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
178	C₂×C₃×C₈	#41	1	2	yes	—
179	C₂×C₃×C₈	#41	1	2	yes	—
180	C₃×C₄⋊C₄	—	2	4	no	—
181	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
182	C₃×C₂²⋊C₄	—	2	2	no	—
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₄²	—	2	4	no	—
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	—	2	1	no	—
188	C₃×C₄²	—	4	4	no	—
189	C₃×C₄²	C₂²×C₄	1	2	yes	—
190	C₃×C₄²	C₂²×C₄	1	2	yes	—
191	C₃×C₄²	C₂²×C₄	1	2	yes	—
192	C₃×C₄²	C₂×D₄	1	2	yes	—
193	C₂×#41	C₂³×C₃	1	2	yes	—
194	#135	C₂×C₃×C₄	1	4	yes	—
195	#135	C₂×C₃×C₄	1	4	yes	—
196	C₂×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
197	C₂×SD₁₆	C₂×C₃×C₄	1	2	yes	—
198	C₂×D₈	C₂×C₃×C₄	1	1	yes	characteristic
199	#131	—	2	4	no	—
200	#131	—	2	4	no	—
201	#131	C₂×C₃×C₄	1	8	yes	complemented
202	#131	C₂×C₃×C₄	1	8	yes	complemented
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	2	no	—
205	C₂×M₁₆	C₂³×C₃	1	2	yes	—
206	C₂×M₁₆	C₂³×C₃	1	2	yes	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
213	C₄×Q₈	C₂×C₃×C₄	1	4	yes	—
214	C₄×D₄	—	2	4	no	—
215	C₄×D₄	C₂×C₃×C₄	1	4	yes	—
216	#117	—	2	2	no	—
217	#117	C₂³×C₃	1	2	yes	—
218	C₂×C₄²	—	2	2	no	—
219	C₂×C₄²	—	2	2	no	—
220	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
223	#108	C₂×C₃×C₄	1	4	yes	complemented
224	#108	C₂×C₃×C₄	1	4	yes	complemented
225	#107	C₂×C₃×C₄	1	2	yes	—
226	#106	C₂×C₃×C₄	1	2	yes	—
227	#104	C₂×C₃×C₄	1	8	yes	complemented
228	#104	C₂×C₃×C₄	1	8	yes	complemented
229	#103	C₂×C₃×C₄	1	4	yes	—
230	#102	C₂×C₃×C₄	1	4	yes	—
231	#97	—	2	2	no	—
232	#97	—	2	2	no	—
233	#97	—	2	2	no	—
234	#97	—	2	2	no	—
235	#97	C₂×C₃×C₄	1	2	yes	—
236	#97	C₂×C₃×C₄	1	2	yes	—
237	#97	C₂×C₃×C₄	1	4	yes	complemented
238	#97	C₃×D₄	1	2	yes	—
239	#97	C₃×D₄	1	2	yes	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	—	2	2	no	—
242	C₄×C₈	—	2	2	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	C₂×C₃×C₄	1	4	yes	complemented
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	C₂×#41	1	1	yes	characteristic
247	C₃×Q₈	—	2	2	no	—
248	C₃×Q₈	C₂×C₄²	1	4	yes	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	4	no	—
251	C₃×D₄	—	2	2	no	—
252	C₃×D₄	C₂×C₄²	1	4	yes	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	—	8	4	no	—
263	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
264	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
270	C₃×C₈	—	2	4	no	—
271	C₃×C₈	—	2	4	no	—
272	C₃×C₈	—	2	2	no	—
273	C₃×C₈	C₂×C₄²	1	2	yes	—
274	C₃×C₈	C₂×C₄²	1	2	yes	—
275	C₃×C₈	C₄×D₄	1	2	yes	—
276	C₃×C₈	C₄×D₄	1	4	yes	—
277	C₃×C₈	C₄×D₄	1	2	yes	—
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	C₂²×C₃×C₄	1	4	yes	—
281	#41	C₂²×C₃×C₄	1	4	yes	—
282	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	C₃×#41	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
291	Q₁₆	C₃×C₄²	1	4	yes	complemented
292	SD₁₆	C₃×C₄²	1	8	yes	complemented
293	D₈	C₃×C₄²	1	4	yes	complemented
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	2	no	—
296	M₁₆	—	2	8	no	—
297	M₁₆	—	2	8	no	—
298	M₁₆	C₂²×C₃×C₄	1	4	yes	—
299	M₁₆	C₂²×C₃×C₄	1	4	yes	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	8	no	—
305	C₂×C₈	—	2	8	no	—
306	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
307	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
308	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
309	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
311	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
312	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
313	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
315	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
316	C₂×C₈	C₃×#41	1	2	yes	—
317	C₂×C₈	C₃×#41	1	2	yes	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	4	4	no	—
327	C₄²	C₂²×C₃×C₄	1	2	yes	—
328	C₄²	C₂²×C₃×C₄	1	2	yes	—
329	C₄²	C₂²×C₃×C₄	1	2	yes	—
330	C₄²	C₂×C₃×D₄	1	2	yes	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	4	no	—
333	C₂²×C₃	—	4	4	no	—
334	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
335	C₂²×C₃	C₄×#41	1	1	yes	characteristic
336	C₂²×C₃	C₄×#41	1	1	yes	characteristic
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	2	4	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	4	no	—
342	C₃×C₄	C₂²×C₄²	1	1	yes	characteristic
343	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
344	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
345	C₃×C₄	C₄×#41	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	C₂×C₃×#41	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	Q₈	C₂×C₃×C₄²	1	4	yes	—
350	D₄	—	2	4	no	—
351	D₄	—	2	4	no	—
352	D₄	—	2	2	no	—
353	D₄	C₂×C₃×C₄²	1	4	yes	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
365	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
366	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
367	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
370	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
371	C₈	—	2	4	no	—
372	C₈	—	2	4	no	—
373	C₈	—	2	2	no	—
374	C₈	C₂×C₃×C₄²	1	2	yes	—
375	C₈	C₂×C₃×C₄²	1	2	yes	—
376	C₈	C₃×C₄×D₄	1	2	yes	—
377	C₈	C₃×C₄×D₄	1	4	yes	—
378	C₈	C₃×C₄×D₄	1	2	yes	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	4	4	no	—
382	C₂×C₃	C₄²×D₄	1	1	yes	characteristic
383	C₂×C₃	#2956	1	2	yes	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	4	no	—
387	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
388	C₂²	C₃×C₄×#41	1	1	yes	characteristic
389	C₂²	C₃×C₄×#41	1	1	yes	characteristic
390	C₄	—	2	4	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	4	no	—
395	C₄	C₂²×C₃×C₄²	1	1	yes	characteristic
396	C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
397	C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
398	C₄	C₃×C₄×#41	1	1	yes	characteristic
399	C₃	#20512	1	1	yes	characteristic, direct product factor, Sylow
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	4	4	no	—
403	C₂	C₃×C₄²×D₄	1	1	yes	characteristic
404	C₂	C₃×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator	C₄	C₂²×C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₂×C₃×#135	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×#2875	C₂	semidirect
5. C₃×#1778	C₂	semidirect
6. C₃×#1773	C₂	semidirect
7. C₃×#1772	C₂	semidirect
8. C₃×#1765	C₂	semidirect
9. C₃×#1764	C₂	semidirect
10. C₃×C₄×#104	C₂	semidirect
11. C₃×C₄×#97	C₂	semidirect
12. #20512	C₃	direct (N × H)
17. C₃×#444	C₄	semidirect
18. C₃×#443	C₄	semidirect
19. C₃×#442	C₄	semidirect
20. C₃×#441	C₄	semidirect
21. C₃×#440	C₄	semidirect
48. #2875	C₂×C₃	semidirect
49. #1778	C₂×C₃	semidirect
50. #1773	C₂×C₃	semidirect
51. #1772	C₂×C₃	semidirect
52. #1765	C₂×C₃	semidirect
53. #1764	C₂×C₃	semidirect
54. C₄×#104	C₂×C₃	semidirect
55. C₄×#97	C₂×C₃	semidirect
64. C₃×#131	C₂×C₄	semidirect
65. C₃×#131	C₂×C₄	semidirect
86. C₃×#108	C₂×C₄	semidirect
87. C₃×#108	C₂×C₄	semidirect
90. C₃×#104	C₂×C₄	semidirect
91. C₃×#104	C₂×C₄	semidirect
100. C₃×#97	C₂×C₄	semidirect
107. C₃×C₄×C₈	C₂×C₄	semidirect
112. #444	C₃×C₄	semidirect
113. #443	C₃×C₄	semidirect
114. #442	C₃×C₄	semidirect
115. #441	C₃×C₄	semidirect
116. #440	C₃×C₄	semidirect
153. C₃×Q₁₆	C₄²	semidirect
154. C₃×SD₁₆	C₄²	semidirect
155. C₃×D₈	C₄²	semidirect
201. #131	C₂×C₃×C₄	semidirect
202. #131	C₂×C₃×C₄	semidirect
223. #108	C₂×C₃×C₄	semidirect
224. #108	C₂×C₃×C₄	semidirect
227. #104	C₂×C₃×C₄	semidirect
228. #104	C₂×C₃×C₄	semidirect
237. #97	C₂×C₃×C₄	semidirect
244. C₄×C₈	C₂×C₃×C₄	semidirect
291. Q₁₆	C₃×C₄²	semidirect
292. SD₁₆	C₃×C₄²	semidirect
293. D₈	C₃×C₄²	semidirect
399. C₃	#20512	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#444	2
C₂×C₃×#443	2
C₃×#2943	2
C₃×#2875	2
C₃×#1778	2
C₃×#1773	2
C₃×#1772	2
C₃×#1765	2
C₃×#1764	2
C₃×C₄×#104	2
C₃×C₄×#97	2
#20512	3

Subgroups — C3×#20512 #10639119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20512 #10639119