Subgroups — C₃×#3514 #87398

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#555	C₂	1	2	yes	maximal, complemented
4	C₃×#551	C₂	1	4	yes	maximal, complemented
5	C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#548	C₂	1	2	yes	maximal, complemented
7	C₃×#546	C₂	1	2	yes	maximal, complemented
8	C₃×#546	C₂	1	2	yes	maximal, complemented
9	C₃×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#542	C₂	1	2	yes	maximal, complemented
11	C₃×#538	C₂	1	4	yes	maximal, complemented
12	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#529	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×#124	C₂	1	2	yes	maximal, complemented
16	C₃×#518	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
18	#3514	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃×#41	C₂²	1	2	yes	complemented
21	C₂²×C₃×Q₈	C₂²	1	2	yes	complemented
22	C₂²×C₃×D₄	C₂²	1	2	yes	—
23	C₂²×C₃×D₄	C₂²	1	2	yes	—
24	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃×#127	C₂²	1	1	yes	characteristic
27	C₃×#126	C₂²	1	4	yes	complemented
28	C₃×#126	C₂²	1	2	yes	complemented
29	C₃×#126	C₂²	1	4	yes	complemented
30	C₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃×#124	C₂²	1	1	yes	characteristic
32	C₃×#124	C₂²	1	2	yes	—
33	C₃×#124	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	2	yes	complemented
35	C₃×#124	C₂²	1	2	yes	complemented
36	C₃×#124	C₂²	1	4	yes	complemented
37	C₃×#124	C₂²	1	4	yes	complemented
38	C₃×#124	C₂²	1	4	yes	complemented
39	C₃×#123	C₂²	1	4	yes	complemented
40	C₃×#123	C₂²	1	2	yes	complemented
41	C₃×#123	C₂²	1	4	yes	complemented
42	C₃×#123	C₂²	1	4	yes	complemented
43	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
48	C₃×#121	C₂²	1	2	yes	—
49	C₃×#121	C₂²	1	1	yes	characteristic
50	C₃×#121	C₂²	1	2	yes	—
51	C₃×#121	C₂²	1	2	yes	complemented
52	C₃×#121	C₂²	1	2	yes	complemented
53	C₃×#121	C₂²	1	4	yes	complemented
54	C₃×#121	C₂²	1	4	yes	complemented
55	C₃×#120	C₂²	1	4	yes	—
56	C₃×#120	C₂²	1	4	yes	complemented
57	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
61	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
62	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
63	C₃×C₄×D₄	C₂²	1	2	yes	—
64	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
65	C₃×C₄×D₄	C₂²	1	2	yes	complemented
66	C₃×C₄×D₄	C₂²	1	2	yes	complemented
67	C₃×C₄×D₄	C₂²	1	2	yes	complemented
68	C₃×C₄×D₄	C₂²	1	2	yes	complemented
69	C₃×C₄×D₄	C₂²	1	4	yes	complemented
70	C₃×C₄×D₄	C₂²	1	2	yes	complemented
71	C₃×C₄×D₄	C₂²	1	4	yes	complemented
72	C₃×C₄×D₄	C₂²	1	2	yes	complemented
73	C₃×C₄×D₄	C₂²	1	2	yes	complemented
74	C₃×#117	C₂²	1	2	yes	complemented
75	C₃×#117	C₂²	1	1	yes	characteristic, complemented
76	C₃×#117	C₂²	1	2	yes	complemented
77	C₃×#117	C₂²	1	2	yes	complemented
78	C₃×#117	C₂²	1	4	yes	complemented
79	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
80	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
81	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
82	C₂×C₃×C₄²	C₂²	1	2	yes	complemented
83	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
84	#559	C₂×C₃	1	1	yes	characteristic, complemented
85	#556	C₂×C₃	1	1	yes	characteristic, complemented
86	#555	C₂×C₃	1	2	yes	complemented
87	#551	C₂×C₃	1	4	yes	complemented
88	D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
89	#548	C₂×C₃	1	2	yes	complemented
90	#546	C₂×C₃	1	2	yes	complemented
91	#546	C₂×C₃	1	2	yes	complemented
92	D₄²	C₂×C₃	1	1	yes	characteristic, complemented
93	#542	C₂×C₃	1	2	yes	complemented
94	#538	C₂×C₃	1	4	yes	complemented
95	#532	C₂×C₃	1	1	yes	characteristic, complemented
96	#529	C₂×C₃	1	1	yes	characteristic, complemented
97	#529	C₂×C₃	1	2	yes	complemented
98	C₂×#124	C₂×C₃	1	2	yes	complemented
99	#518	C₂×C₃	1	2	yes	complemented
100	C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂⁴×C₃	C₂³	1	4	yes	—
102	C₃×#41	—	2	4	no	—
103	C₃×#41	—	4	4	no	—
104	C₂×C₃×Q₈	—	4	4	no	—
105	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×Q₈	C₂³	1	2	yes	—
108	C₂×C₃×Q₈	C₂³	1	4	yes	—
109	C₂×C₃×D₄	—	2	8	no	—
110	C₂×C₃×D₄	—	4	4	no	—
111	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
112	C₂×C₃×D₄	C₂³	1	4	yes	—
113	C₂×C₃×D₄	C₂³	1	2	yes	—
114	C₂×C₃×D₄	C₂³	1	2	yes	—
115	C₂×C₃×D₄	C₂³	1	2	yes	—
116	C₂×C₃×D₄	C₂³	1	2	yes	—
117	C₂×C₃×D₄	C₂³	1	2	yes	—
118	C₂×C₃×D₄	C₂³	1	4	yes	—
119	C₂×C₃×D₄	C₂³	1	4	yes	—
120	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂³	1	2	yes	—
122	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
123	C₂²×C₃×C₄	C₂³	1	2	yes	—
124	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃×C₄	C₂³	1	2	yes	—
126	C₂²×C₃×C₄	C₂³	1	2	yes	—
127	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₂³	1	4	yes	—
129	C₂²×C₃×C₄	C₂³	1	4	yes	—
130	C₂²×C₃×C₄	C₂³	1	4	yes	—
131	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₃×C₄²	C₂³	1	2	yes	—
164	C₃×C₄²	C₂³	1	1	yes	characteristic
165	C₃×C₄²	C₂³	1	1	yes	characteristic
166	C₃×C₄²	C₂³	1	1	yes	characteristic
167	C₃×C₄²	C₂³	1	2	yes	—
168	C₃×C₄²	C₂³	1	2	yes	—
169	C₃×C₄²	C₂³	1	4	yes	—
170	C₃×C₄²	C₂³	1	2	yes	—
171	C₂×#41	C₂²×C₃	1	1	yes	characteristic
172	C₂×#41	C₂²×C₃	1	2	yes	complemented
173	C₂²×Q₈	C₂²×C₃	1	2	yes	complemented
174	C₂²×D₄	C₂²×C₃	1	2	yes	—
175	C₂²×D₄	C₂²×C₃	1	2	yes	—
176	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
178	#127	C₂²×C₃	1	1	yes	characteristic
179	#126	C₂²×C₃	1	4	yes	complemented
180	#126	C₂²×C₃	1	2	yes	complemented
181	#126	C₂²×C₃	1	4	yes	complemented
182	#125	C₂²×C₃	1	1	yes	characteristic, complemented
183	#124	C₂²×C₃	1	1	yes	characteristic
184	#124	C₂²×C₃	1	2	yes	—
185	#124	C₂²×C₃	1	2	yes	complemented
186	#124	C₂²×C₃	1	4	yes	complemented
187	#124	C₂²×C₃	1	2	yes	complemented
188	#124	C₂²×C₃	1	4	yes	complemented
189	#124	C₂²×C₃	1	4	yes	complemented
190	#124	C₂²×C₃	1	2	yes	complemented
191	#123	C₂²×C₃	1	2	yes	complemented
192	#123	C₂²×C₃	1	4	yes	complemented
193	#123	C₂²×C₃	1	4	yes	complemented
194	#123	C₂²×C₃	1	4	yes	complemented
195	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
196	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
198	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
199	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
200	#121	C₂²×C₃	1	2	yes	—
201	#121	C₂²×C₃	1	1	yes	characteristic
202	#121	C₂²×C₃	1	2	yes	—
203	#121	C₂²×C₃	1	2	yes	complemented
204	#121	C₂²×C₃	1	2	yes	complemented
205	#121	C₂²×C₃	1	4	yes	complemented
206	#121	C₂²×C₃	1	4	yes	complemented
207	#120	C₂²×C₃	1	4	yes	—
208	#120	C₂²×C₃	1	4	yes	complemented
209	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
211	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
212	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
213	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
214	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
215	C₄×D₄	C₂²×C₃	1	2	yes	—
216	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
217	C₄×D₄	C₂²×C₃	1	2	yes	complemented
218	C₄×D₄	C₂²×C₃	1	2	yes	complemented
219	C₄×D₄	C₂²×C₃	1	4	yes	complemented
220	C₄×D₄	C₂²×C₃	1	2	yes	complemented
221	C₄×D₄	C₂²×C₃	1	4	yes	complemented
222	C₄×D₄	C₂²×C₃	1	2	yes	complemented
223	C₄×D₄	C₂²×C₃	1	2	yes	complemented
224	C₄×D₄	C₂²×C₃	1	2	yes	complemented
225	C₄×D₄	C₂²×C₃	1	2	yes	complemented
226	#117	C₂²×C₃	1	2	yes	complemented
227	#117	C₂²×C₃	1	1	yes	characteristic, complemented
228	#117	C₂²×C₃	1	2	yes	complemented
229	#117	C₂²×C₃	1	2	yes	complemented
230	#117	C₂²×C₃	1	4	yes	complemented
231	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
232	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
233	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
234	C₂×C₄²	C₂²×C₃	1	2	yes	complemented
235	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
236	C₂³×C₃	—	2	8	no	—
237	C₂³×C₃	—	4	4	no	—
238	C₂³×C₃	—	4	4	no	—
239	C₂³×C₃	C₂⁴	1	2	yes	—
240	C₂³×C₃	C₂⁴	1	4	yes	—
241	C₂³×C₃	C₂⁴	1	1	yes	characteristic
242	C₂³×C₃	C₂⁴	1	2	yes	—
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	2	2	no	—
245	C₃×Q₈	—	2	4	no	—
246	C₃×Q₈	—	4	4	no	—
247	C₃×D₄	—	2	8	no	—
248	C₃×D₄	—	2	4	no	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	2	no	—
251	C₃×D₄	—	2	4	no	—
252	C₃×D₄	—	4	4	no	—
253	C₃×D₄	—	4	2	no	—
254	C₃×D₄	—	4	2	no	—
255	C₃×D₄	—	4	4	no	—
256	C₃×D₄	#41	1	4	yes	complemented
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	—	2	4	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	—	4	4	no	—
264	C₂×C₃×C₄	—	4	1	no	—
265	C₂×C₃×C₄	—	4	4	no	—
266	C₂×C₃×C₄	—	4	4	no	—
267	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂⁴	1	2	yes	—
270	C₂×C₃×C₄	C₂⁴	1	2	yes	—
271	C₂×C₃×C₄	C₂⁴	1	2	yes	—
272	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂⁴	1	2	yes	—
275	C₂×C₃×C₄	C₂⁴	1	2	yes	—
276	C₂×C₃×C₄	C₂⁴	1	2	yes	—
277	C₂×C₃×C₄	C₂⁴	1	4	yes	—
278	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
280	C₂⁴	C₂³×C₃	1	4	yes	—
281	#41	—	2	4	no	—
282	#41	—	4	4	no	—
283	C₂×Q₈	—	4	4	no	—
284	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
285	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
286	C₂×Q₈	C₂³×C₃	1	2	yes	—
287	C₂×Q₈	C₂³×C₃	1	4	yes	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
291	C₂×D₄	C₂³×C₃	1	4	yes	—
292	C₂×D₄	C₂³×C₃	1	2	yes	—
293	C₂×D₄	C₂³×C₃	1	2	yes	—
294	C₂×D₄	C₂³×C₃	1	2	yes	—
295	C₂×D₄	C₂³×C₃	1	2	yes	—
296	C₂×D₄	C₂³×C₃	1	2	yes	—
297	C₂×D₄	C₂³×C₃	1	4	yes	—
298	C₂×D₄	C₂³×C₃	1	4	yes	—
299	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₃	1	2	yes	—
301	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₃	1	2	yes	—
303	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
304	C₂²×C₄	C₂³×C₃	1	2	yes	—
305	C₂²×C₄	C₂³×C₃	1	2	yes	—
306	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₃	1	4	yes	—
308	C₂²×C₄	C₂³×C₃	1	4	yes	—
309	C₂²×C₄	C₂³×C₃	1	4	yes	—
310	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
311	C₄⋊C₄	C₂³×C₃	1	2	yes	—
312	C₄⋊C₄	C₂³×C₃	1	2	yes	—
313	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
314	C₄⋊C₄	C₂³×C₃	1	2	yes	—
315	C₄⋊C₄	C₂³×C₃	1	2	yes	—
316	C₄⋊C₄	C₂³×C₃	1	2	yes	—
317	C₄⋊C₄	C₂³×C₃	1	2	yes	—
318	C₄⋊C₄	C₂³×C₃	1	4	yes	—
319	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
320	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
321	C₄⋊C₄	C₂³×C₃	1	2	yes	—
322	C₄⋊C₄	C₂³×C₃	1	4	yes	—
323	C₄⋊C₄	C₂³×C₃	1	2	yes	—
324	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
325	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
326	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
327	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
328	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
329	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
330	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
331	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
332	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
333	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
334	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
335	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
336	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
337	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
338	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
339	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
340	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
341	C₄²	C₂³×C₃	1	1	yes	characteristic
342	C₄²	C₂³×C₃	1	2	yes	—
343	C₄²	C₂³×C₃	1	1	yes	characteristic
344	C₄²	C₂³×C₃	1	1	yes	characteristic
345	C₄²	C₂³×C₃	1	1	yes	characteristic
346	C₄²	C₂³×C₃	1	2	yes	—
347	C₄²	C₂³×C₃	1	2	yes	—
348	C₄²	C₂³×C₃	1	4	yes	—
349	C₄²	C₂³×C₃	1	2	yes	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	4	no	—
360	C₂²×C₃	—	2	2	no	—
361	C₂²×C₃	—	8	8	no	—
362	C₂²×C₃	C₂×#41	1	4	yes	—
363	C₂²×C₃	C₂⁵	1	1	yes	characteristic
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	4	no	—
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	—	2	2	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	C₂×#41	1	2	yes	—
376	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
377	C₂³	—	2	8	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	4	no	—
380	C₂³	C₂⁴×C₃	1	2	yes	—
381	C₂³	C₂⁴×C₃	1	4	yes	—
382	C₂³	C₂⁴×C₃	1	1	yes	characteristic
383	C₂³	C₂⁴×C₃	1	2	yes	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	2	4	no	—
387	Q₈	—	4	4	no	—
388	D₄	—	2	8	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	C₃×#41	1	4	yes	complemented
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
409	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
410	C₂×C₄	C₂⁴×C₃	1	2	yes	—
411	C₂×C₄	C₂⁴×C₃	1	2	yes	—
412	C₂×C₄	C₂⁴×C₃	1	2	yes	—
413	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
414	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
415	C₂×C₄	C₂⁴×C₃	1	2	yes	—
416	C₂×C₄	C₂⁴×C₃	1	2	yes	—
417	C₂×C₄	C₂⁴×C₃	1	2	yes	—
418	C₂×C₄	C₂⁴×C₃	1	4	yes	—
419	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
420	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
421	C₂×C₃	—	2	4	no	—
422	C₂×C₃	—	4	1	no	—
423	C₂×C₃	—	4	4	no	—
424	C₂×C₃	—	4	2	no	—
425	C₂×C₃	C₂²×#41	1	1	yes	characteristic
426	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₃	#585	1	1	yes	characteristic
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	8	8	no	—
440	C₂²	C₂×C₃×#41	1	4	yes	—
441	C₂²	C₂⁵×C₃	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	C₂×C₃×#41	1	2	yes	—
454	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
455	C₃	#3514	1	1	yes	characteristic, direct product factor, Sylow
456	C₂	—	2	4	no	—
457	C₂	—	4	2	no	—
458	C₂	—	4	4	no	—
459	C₂	—	4	1	no	—
460	C₂	C₂²×C₃×#41	1	1	yes	characteristic
461	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#559	C₂	semidirect
2. C₃×#556	C₂	semidirect
3. C₃×#555	C₂	semidirect
4. C₃×#551	C₂	semidirect
5. C₃×D₄×Q₈	C₂	semidirect
6. C₃×#548	C₂	semidirect
7. C₃×#546	C₂	semidirect
8. C₃×#546	C₂	semidirect
9. C₃×D₄²	C₂	semidirect
10. C₃×#542	C₂	semidirect
11. C₃×#538	C₂	semidirect
12. C₃×#532	C₂	semidirect
13. C₃×#529	C₂	semidirect
14. C₃×#529	C₂	semidirect
15. C₂×C₃×#124	C₂	semidirect
16. C₃×#518	C₂	semidirect
17. C₃×C₄×#41	C₂	semidirect
18. #3514	C₃	direct (N × H)
20. C₂×C₃×#41	C₂²	semidirect
21. C₂²×C₃×Q₈	C₂²	semidirect
24. C₃×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₄⋊Q₈	C₂²	semidirect
27. C₃×#126	C₂²	semidirect
28. C₃×#126	C₂²	semidirect
29. C₃×#126	C₂²	semidirect
30. C₃×#125	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
36. C₃×#124	C₂²	semidirect
37. C₃×#124	C₂²	semidirect
38. C₃×#124	C₂²	semidirect
39. C₃×#123	C₂²	semidirect
40. C₃×#123	C₂²	semidirect
41. C₃×#123	C₂²	semidirect
42. C₃×#123	C₂²	semidirect
43. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₂²⋊Q₈	C₂²	semidirect
47. C₃×C₂²⋊Q₈	C₂²	semidirect
51. C₃×#121	C₂²	semidirect
52. C₃×#121	C₂²	semidirect
53. C₃×#121	C₂²	semidirect
54. C₃×#121	C₂²	semidirect
56. C₃×#120	C₂²	semidirect
57. C₃×C₄×Q₈	C₂²	semidirect
58. C₃×C₄×Q₈	C₂²	semidirect
59. C₃×C₄×Q₈	C₂²	semidirect
60. C₃×C₄×Q₈	C₂²	semidirect
65. C₃×C₄×D₄	C₂²	semidirect
66. C₃×C₄×D₄	C₂²	semidirect
67. C₃×C₄×D₄	C₂²	semidirect
68. C₃×C₄×D₄	C₂²	semidirect
69. C₃×C₄×D₄	C₂²	semidirect
70. C₃×C₄×D₄	C₂²	semidirect
71. C₃×C₄×D₄	C₂²	semidirect
72. C₃×C₄×D₄	C₂²	semidirect
73. C₃×C₄×D₄	C₂²	semidirect
74. C₃×#117	C₂²	semidirect
75. C₃×#117	C₂²	semidirect
76. C₃×#117	C₂²	semidirect
77. C₃×#117	C₂²	semidirect
78. C₃×#117	C₂²	semidirect
79. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
80. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
81. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
82. C₂×C₃×C₄²	C₂²	semidirect
83. C₂×C₃×C₄²	C₂²	semidirect
84. #559	C₂×C₃	semidirect
85. #556	C₂×C₃	semidirect
86. #555	C₂×C₃	semidirect
87. #551	C₂×C₃	semidirect
88. D₄×Q₈	C₂×C₃	semidirect
89. #548	C₂×C₃	semidirect
90. #546	C₂×C₃	semidirect
91. #546	C₂×C₃	semidirect
92. D₄²	C₂×C₃	semidirect
93. #542	C₂×C₃	semidirect
94. #538	C₂×C₃	semidirect
95. #532	C₂×C₃	semidirect
96. #529	C₂×C₃	semidirect
97. #529	C₂×C₃	semidirect
98. C₂×#124	C₂×C₃	semidirect
99. #518	C₂×C₃	semidirect
100. C₄×#41	C₂×C₃	semidirect
172. C₂×#41	C₂²×C₃	semidirect
173. C₂²×Q₈	C₂²×C₃	semidirect
176. C₄⋊Q₈	C₂²×C₃	semidirect
177. C₄⋊Q₈	C₂²×C₃	semidirect
179. #126	C₂²×C₃	semidirect
180. #126	C₂²×C₃	semidirect
181. #126	C₂²×C₃	semidirect
182. #125	C₂²×C₃	semidirect
185. #124	C₂²×C₃	semidirect
186. #124	C₂²×C₃	semidirect
187. #124	C₂²×C₃	semidirect
188. #124	C₂²×C₃	semidirect
189. #124	C₂²×C₃	semidirect
190. #124	C₂²×C₃	semidirect
191. #123	C₂²×C₃	semidirect
192. #123	C₂²×C₃	semidirect
193. #123	C₂²×C₃	semidirect
194. #123	C₂²×C₃	semidirect
195. C₂²⋊Q₈	C₂²×C₃	semidirect
196. C₂²⋊Q₈	C₂²×C₃	semidirect
197. C₂²⋊Q₈	C₂²×C₃	semidirect
198. C₂²⋊Q₈	C₂²×C₃	semidirect
199. C₂²⋊Q₈	C₂²×C₃	semidirect
203. #121	C₂²×C₃	semidirect
204. #121	C₂²×C₃	semidirect
205. #121	C₂²×C₃	semidirect
206. #121	C₂²×C₃	semidirect
208. #120	C₂²×C₃	semidirect
209. C₄×Q₈	C₂²×C₃	semidirect
210. C₄×Q₈	C₂²×C₃	semidirect
211. C₄×Q₈	C₂²×C₃	semidirect
212. C₄×Q₈	C₂²×C₃	semidirect
217. C₄×D₄	C₂²×C₃	semidirect
218. C₄×D₄	C₂²×C₃	semidirect
219. C₄×D₄	C₂²×C₃	semidirect
220. C₄×D₄	C₂²×C₃	semidirect
221. C₄×D₄	C₂²×C₃	semidirect
222. C₄×D₄	C₂²×C₃	semidirect
223. C₄×D₄	C₂²×C₃	semidirect
224. C₄×D₄	C₂²×C₃	semidirect
225. C₄×D₄	C₂²×C₃	semidirect
226. #117	C₂²×C₃	semidirect
227. #117	C₂²×C₃	semidirect
228. #117	C₂²×C₃	semidirect
229. #117	C₂²×C₃	semidirect
230. #117	C₂²×C₃	semidirect
231. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
232. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
233. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
234. C₂×C₄²	C₂²×C₃	semidirect
235. C₂×C₄²	C₂²×C₃	semidirect
256. C₃×D₄	#41	semidirect
397. D₄	C₃×#41	semidirect
455. C₃	#3514	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#559	2
C₃×#556	2
C₃×#555	2
C₃×#551	2
C₃×D₄×Q₈	2
C₃×#548	2
C₃×#546	2
C₃×D₄²	2
C₃×#542	2
C₃×#538	2
C₃×#532	2
C₃×#529	2
C₂×C₃×#124	2
C₃×#518	2
C₃×C₄×#41	2
#3514	3

Subgroups — C3×#3514 #87398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3514 #87398