Subgroups — C₃×#3520 #87404

Order 384.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#554	C₂	1	2	yes	maximal, complemented
3	C₃×#552	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×#547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#546	C₂	1	2	yes	maximal, complemented
10	C₃×#542	C₂	1	2	yes	maximal, complemented
11	C₃×#539	C₂	1	4	yes	maximal, complemented
12	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₃×#520	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	#3520	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×#41	C₂²	1	2	yes	—
20	C₂×C₃×#41	C₂²	1	2	yes	complemented
21	C₂²×C₃×Q₈	C₂²	1	2	yes	complemented
22	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₄	C₂²	1	2	yes	—
24	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×#126	C₂²	1	2	yes	complemented
28	C₃×#126	C₂²	1	4	yes	complemented
29	C₃×#126	C₂²	1	4	yes	complemented
30	C₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃×#125	C₂²	1	2	yes	complemented
32	C₃×#125	C₂²	1	4	yes	complemented
33	C₃×#124	C₂²	1	2	yes	—
34	C₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×#124	C₂²	1	4	yes	complemented
36	C₃×#123	C₂²	1	2	yes	—
37	C₃×#123	C₂²	1	4	yes	—
38	C₃×#123	C₂²	1	4	yes	complemented
39	C₃×#123	C₂²	1	4	yes	complemented
40	C₃×#123	C₂²	1	4	yes	complemented
41	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
44	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
48	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
49	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
50	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
51	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
52	C₃×#121	C₂²	1	1	yes	characteristic
53	C₃×#121	C₂²	1	4	yes	—
54	C₃×#121	C₂²	1	2	yes	—
55	C₃×#121	C₂²	1	2	yes	complemented
56	C₃×#120	C₂²	1	4	yes	—
57	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
58	C₃×C₄×Q₈	C₂²	1	2	yes	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	2	yes	—
63	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
64	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
65	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
66	C₃×C₄×D₄	C₂²	1	2	yes	—
67	C₃×C₄×D₄	C₂²	1	2	yes	—
68	C₃×C₄×D₄	C₂²	1	4	yes	—
69	C₃×C₄×D₄	C₂²	1	2	yes	—
70	C₃×C₄×D₄	C₂²	1	4	yes	complemented
71	C₃×C₄×D₄	C₂²	1	4	yes	complemented
72	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
73	C₃×#117	C₂²	1	2	yes	—
74	C₃×#117	C₂²	1	2	yes	complemented
75	C₃×#117	C₂²	1	4	yes	complemented
76	C₃×#117	C₂²	1	2	yes	complemented
77	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	complemented
79	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
84	#556	C₂×C₃	1	1	yes	characteristic, complemented
85	#554	C₂×C₃	1	2	yes	complemented
86	#552	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	#547	C₂×C₃	1	1	yes	characteristic, complemented
91	#547	C₂×C₃	1	1	yes	characteristic, complemented
92	#546	C₂×C₃	1	2	yes	complemented
93	#542	C₂×C₃	1	2	yes	complemented
94	#539	C₂×C₃	1	4	yes	complemented
95	#533	C₂×C₃	1	1	yes	characteristic, complemented
96	#529	C₂×C₃	1	1	yes	characteristic, complemented
97	#525	C₂×C₃	1	2	yes	complemented
98	C₂×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
99	#520	C₂×C₃	1	2	yes	complemented
100	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂⁴×C₃	C₂³	1	2	yes	—
102	C₃×#41	—	2	8	no	—
103	C₃×#41	—	4	4	no	—
104	C₂×C₃×Q₈	—	4	4	no	—
105	C₂×C₃×Q₈	C₂³	1	2	yes	—
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	4	no	—
110	C₂×C₃×D₄	C₂³	1	2	yes	—
111	C₂×C₃×D₄	C₂³	1	2	yes	—
112	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
113	C₂×C₃×D₄	C₂³	1	4	yes	—
114	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
115	C₂×C₃×D₄	C₂³	1	4	yes	—
116	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄	—	4	4	no	—
118	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂³	1	4	yes	—
122	C₂²×C₃×C₄	C₂³	1	2	yes	—
123	C₂²×C₃×C₄	C₂³	1	2	yes	—
124	C₂²×C₃×C₄	C₂³	1	2	yes	—
125	C₂²×C₃×C₄	C₂³	1	2	yes	—
126	C₂²×C₃×C₄	C₂³	1	4	yes	—
127	C₂²×C₃×C₄	C₂³	1	2	yes	—
128	C₂²×C₃×C₄	C₂³	1	4	yes	—
129	C₂²×C₃×C₄	C₂³	1	2	yes	—
130	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₃×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₃×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₃×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₃×C₄⋊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	2	yes	—
152	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃×C₂²⋊C₄	C₂³	1	2	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×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₃×C₂²⋊C₄	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	1	yes	characteristic
168	C₃×C₄²	C₂³	1	4	yes	—
169	C₃×C₄²	C₂³	1	4	yes	—
170	C₃×C₄²	C₂³	1	2	yes	—
171	C₂×#41	C₂²×C₃	1	2	yes	—
172	C₂×#41	C₂²×C₃	1	2	yes	complemented
173	C₂²×Q₈	C₂²×C₃	1	2	yes	complemented
174	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
175	C₂³×C₄	C₂²×C₃	1	2	yes	—
176	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
179	#126	C₂²×C₃	1	2	yes	complemented
180	#126	C₂²×C₃	1	4	yes	complemented
181	#126	C₂²×C₃	1	4	yes	complemented
182	#125	C₂²×C₃	1	1	yes	characteristic, complemented
183	#125	C₂²×C₃	1	2	yes	complemented
184	#125	C₂²×C₃	1	4	yes	complemented
185	#124	C₂²×C₃	1	2	yes	—
186	#124	C₂²×C₃	1	1	yes	characteristic, complemented
187	#124	C₂²×C₃	1	4	yes	complemented
188	#123	C₂²×C₃	1	2	yes	—
189	#123	C₂²×C₃	1	4	yes	—
190	#123	C₂²×C₃	1	4	yes	complemented
191	#123	C₂²×C₃	1	4	yes	complemented
192	#123	C₂²×C₃	1	4	yes	complemented
193	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
195	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
196	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
197	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
198	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
199	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
200	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
201	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
202	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
203	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
204	#121	C₂²×C₃	1	1	yes	characteristic
205	#121	C₂²×C₃	1	4	yes	—
206	#121	C₂²×C₃	1	2	yes	—
207	#121	C₂²×C₃	1	2	yes	complemented
208	#120	C₂²×C₃	1	4	yes	—
209	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
210	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
211	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
212	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
213	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
214	C₄×D₄	C₂²×C₃	1	2	yes	—
215	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
216	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
217	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
218	C₄×D₄	C₂²×C₃	1	2	yes	—
219	C₄×D₄	C₂²×C₃	1	2	yes	—
220	C₄×D₄	C₂²×C₃	1	4	yes	—
221	C₄×D₄	C₂²×C₃	1	2	yes	—
222	C₄×D₄	C₂²×C₃	1	4	yes	complemented
223	C₄×D₄	C₂²×C₃	1	4	yes	complemented
224	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
225	#117	C₂²×C₃	1	2	yes	—
226	#117	C₂²×C₃	1	2	yes	complemented
227	#117	C₂²×C₃	1	4	yes	complemented
228	#117	C₂²×C₃	1	2	yes	complemented
229	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
231	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
232	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
233	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
234	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
235	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
236	C₂³×C₃	—	2	4	no	—
237	C₂³×C₃	—	2	4	no	—
238	C₂³×C₃	—	4	2	no	—
239	C₂³×C₃	C₂⁴	1	2	yes	—
240	C₂³×C₃	C₂⁴	1	2	yes	—
241	C₂³×C₃	C₂⁴	1	2	yes	—
242	C₂³×C₃	C₂⁴	1	1	yes	characteristic
243	C₃×Q₈	—	2	4	no	—
244	C₃×Q₈	—	2	2	no	—
245	C₃×Q₈	—	2	4	no	—
246	C₃×Q₈	—	4	4	no	—
247	C₃×D₄	—	2	4	no	—
248	C₃×D₄	—	2	8	no	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	2	no	—
251	C₃×D₄	—	2	2	no	—
252	C₃×D₄	—	4	4	no	—
253	C₃×D₄	#41	1	4	yes	complemented
254	C₂×C₃×C₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	—	4	2	no	—
264	C₂×C₃×C₄	—	4	4	no	—
265	C₂×C₃×C₄	—	4	4	no	—
266	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂⁴	1	2	yes	—
268	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂⁴	1	4	yes	—
270	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂⁴	1	2	yes	—
273	C₂×C₃×C₄	C₂⁴	1	2	yes	—
274	C₂×C₃×C₄	C₂⁴	1	4	yes	—
275	C₂×C₃×C₄	C₂⁴	1	2	yes	—
276	C₂×C₃×C₄	C₂⁴	1	2	yes	—
277	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
279	C₂⁴	C₂³×C₃	1	2	yes	—
280	#41	—	2	8	no	—
281	#41	—	4	4	no	—
282	C₂×Q₈	—	4	4	no	—
283	C₂×Q₈	C₂³×C₃	1	2	yes	—
284	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
285	C₂×Q₈	C₂³×C₃	1	2	yes	—
286	C₂×Q₈	C₂³×C₃	1	4	yes	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	C₂³×C₃	1	2	yes	—
289	C₂×D₄	C₂³×C₃	1	2	yes	—
290	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
291	C₂×D₄	C₂³×C₃	1	4	yes	—
292	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
293	C₂×D₄	C₂³×C₃	1	4	yes	—
294	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₄	—	4	4	no	—
296	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₃	1	4	yes	—
300	C₂²×C₄	C₂³×C₃	1	2	yes	—
301	C₂²×C₄	C₂³×C₃	1	2	yes	—
302	C₂²×C₄	C₂³×C₃	1	2	yes	—
303	C₂²×C₄	C₂³×C₃	1	2	yes	—
304	C₂²×C₄	C₂³×C₃	1	4	yes	—
305	C₂²×C₄	C₂³×C₃	1	2	yes	—
306	C₂²×C₄	C₂³×C₃	1	4	yes	—
307	C₂²×C₄	C₂³×C₃	1	2	yes	—
308	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
309	C₄⋊C₄	C₂³×C₃	1	2	yes	—
310	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
311	C₄⋊C₄	C₂³×C₃	1	2	yes	—
312	C₄⋊C₄	C₂³×C₃	1	4	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	4	yes	—
317	C₄⋊C₄	C₂³×C₃	1	4	yes	—
318	C₄⋊C₄	C₂³×C₃	1	4	yes	—
319	C₄⋊C₄	C₂³×C₃	1	2	yes	—
320	C₄⋊C₄	C₂³×C₃	1	2	yes	—
321	C₄⋊C₄	C₂³×C₃	1	2	yes	—
322	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
323	C₄⋊C₄	C₂³×C₃	1	4	yes	—
324	C₄⋊C₄	C₂³×C₃	1	2	yes	—
325	C₄⋊C₄	C₂³×C₃	1	4	yes	—
326	C₄⋊C₄	C₂³×C₃	1	2	yes	—
327	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
328	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
329	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
330	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
331	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
332	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
333	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
334	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
335	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
336	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
337	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
338	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
339	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
340	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
341	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
342	C₄²	C₂³×C₃	1	1	yes	characteristic
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	4	yes	—
347	C₄²	C₂³×C₃	1	4	yes	—
348	C₄²	C₂³×C₃	1	2	yes	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	2	2	no	—
359	C₂²×C₃	—	4	8	no	—
360	C₂²×C₃	C₂×#41	1	4	yes	—
361	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
362	C₂²×C₃	C₂⁵	1	1	yes	characteristic
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	2	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	1	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	C₂×#41	1	2	yes	—
375	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₂⁴×C₃	1	2	yes	—
380	C₂³	C₂⁴×C₃	1	2	yes	—
381	C₂³	C₂⁴×C₃	1	2	yes	—
382	C₂³	C₂⁴×C₃	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	2	8	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	4	no	—
393	D₄	C₃×#41	1	4	yes	complemented
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
407	C₂×C₄	C₂⁴×C₃	1	2	yes	—
408	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
409	C₂×C₄	C₂⁴×C₃	1	4	yes	—
410	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
411	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
412	C₂×C₄	C₂⁴×C₃	1	2	yes	—
413	C₂×C₄	C₂⁴×C₃	1	2	yes	—
414	C₂×C₄	C₂⁴×C₃	1	4	yes	—
415	C₂×C₄	C₂⁴×C₃	1	2	yes	—
416	C₂×C₄	C₂⁴×C₃	1	2	yes	—
417	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
418	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	2	4	no	—
421	C₂×C₃	—	4	2	no	—
422	C₂×C₃	—	4	2	no	—
423	C₂×C₃	C₂²×#41	1	1	yes	characteristic
424	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	8	no	—
437	C₂²	C₂×C₃×#41	1	4	yes	—
438	C₂²	C₃×2₋¹⁺⁴	1	2	yes	—
439	C₂²	C₂⁵×C₃	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	C₂×C₃×#41	1	2	yes	—
452	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
453	C₃	#3520	1	1	yes	characteristic, direct product factor, Sylow
454	C₂	—	2	2	no	—
455	C₂	—	2	4	no	—
456	C₂	—	4	2	no	—
457	C₂	—	4	2	no	—
458	C₂	C₂²×C₃×#41	1	1	yes	characteristic
459	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂	C₂×C₃×2₋¹⁺⁴	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×#556	C₂	semidirect
2. C₃×#554	C₂	semidirect
3. C₃×#552	C₂	semidirect
4. C₃×#551	C₂	semidirect
5. C₃×D₄×Q₈	C₂	semidirect
6. C₃×#548	C₂	semidirect
7. C₃×#547	C₂	semidirect
8. C₃×#547	C₂	semidirect
9. C₃×#546	C₂	semidirect
10. C₃×#542	C₂	semidirect
11. C₃×#539	C₂	semidirect
12. C₃×#533	C₂	semidirect
13. C₃×#529	C₂	semidirect
14. C₃×#525	C₂	semidirect
15. C₂×C₃×C₂²⋊Q₈	C₂	semidirect
16. C₃×#520	C₂	semidirect
17. C₂×C₃×C₄×D₄	C₂	semidirect
18. #3520	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
26. 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
31. C₃×#125	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
38. C₃×#123	C₂²	semidirect
39. C₃×#123	C₂²	semidirect
40. C₃×#123	C₂²	semidirect
45. C₃×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₂²⋊Q₈	C₂²	semidirect
47. C₃×C₂²⋊Q₈	C₂²	semidirect
48. C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₃×C₂²⋊Q₈	C₂²	semidirect
50. C₃×C₂²⋊Q₈	C₂²	semidirect
51. C₃×C₂²⋊Q₈	C₂²	semidirect
55. C₃×#121	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
70. C₃×C₄×D₄	C₂²	semidirect
71. C₃×C₄×D₄	C₂²	semidirect
72. C₃×C₄×D₄	C₂²	semidirect
74. C₃×#117	C₂²	semidirect
75. C₃×#117	C₂²	semidirect
76. C₃×#117	C₂²	semidirect
78. C₂×C₃×C₄⋊C₄	C₂²	semidirect
79. C₂×C₃×C₄⋊C₄	C₂²	semidirect
80. C₂×C₃×C₄⋊C₄	C₂²	semidirect
84. #556	C₂×C₃	semidirect
85. #554	C₂×C₃	semidirect
86. #552	C₂×C₃	semidirect
87. #551	C₂×C₃	semidirect
88. D₄×Q₈	C₂×C₃	semidirect
89. #548	C₂×C₃	semidirect
90. #547	C₂×C₃	semidirect
91. #547	C₂×C₃	semidirect
92. #546	C₂×C₃	semidirect
93. #542	C₂×C₃	semidirect
94. #539	C₂×C₃	semidirect
95. #533	C₂×C₃	semidirect
96. #529	C₂×C₃	semidirect
97. #525	C₂×C₃	semidirect
98. C₂×C₂²⋊Q₈	C₂×C₃	semidirect
99. #520	C₂×C₃	semidirect
100. C₂×C₄×D₄	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
178. 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
183. #125	C₂²×C₃	semidirect
184. #125	C₂²×C₃	semidirect
186. #124	C₂²×C₃	semidirect
187. #124	C₂²×C₃	semidirect
190. #123	C₂²×C₃	semidirect
191. #123	C₂²×C₃	semidirect
192. #123	C₂²×C₃	semidirect
197. C₂²⋊Q₈	C₂²×C₃	semidirect
198. C₂²⋊Q₈	C₂²×C₃	semidirect
199. C₂²⋊Q₈	C₂²×C₃	semidirect
200. C₂²⋊Q₈	C₂²×C₃	semidirect
201. C₂²⋊Q₈	C₂²×C₃	semidirect
202. C₂²⋊Q₈	C₂²×C₃	semidirect
203. C₂²⋊Q₈	C₂²×C₃	semidirect
207. #121	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
222. C₄×D₄	C₂²×C₃	semidirect
223. C₄×D₄	C₂²×C₃	semidirect
224. C₄×D₄	C₂²×C₃	semidirect
226. #117	C₂²×C₃	semidirect
227. #117	C₂²×C₃	semidirect
228. #117	C₂²×C₃	semidirect
230. C₂×C₄⋊C₄	C₂²×C₃	semidirect
231. C₂×C₄⋊C₄	C₂²×C₃	semidirect
232. C₂×C₄⋊C₄	C₂²×C₃	semidirect
253. C₃×D₄	#41	semidirect
393. D₄	C₃×#41	semidirect
453. C₃	#3520	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×#556	2
C₃×#554	2
C₃×#552	2
C₃×#551	2
C₃×D₄×Q₈	2
C₃×#548	2
C₃×#547	2
C₃×#546	2
C₃×#542	2
C₃×#539	2
C₃×#533	2
C₃×#529	2
C₃×#525	2
C₂×C₃×C₂²⋊Q₈	2
C₃×#520	2
C₂×C₃×C₄×D₄	2
#3520	3

Subgroups — C3×#3520 #87404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3520 #87404