Subgroups — C₃×#3555 #87439

Order 384.

910 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	C₃×#563	C₂	1	4	yes	maximal, complemented
2	C₃×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#557	C₂	1	2	yes	maximal, complemented
5	C₃×#556	C₂	1	2	yes	maximal, complemented
6	C₃×#556	C₂	1	2	yes	maximal, complemented
7	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#552	C₂	1	2	yes	maximal, complemented
10	C₃×#544	C₂	1	2	yes	maximal, complemented
11	C₃×#542	C₂	1	2	yes	maximal
12	C₃×#541	C₂	1	2	yes	maximal, complemented
13	C₃×#541	C₂	1	2	yes	maximal, complemented
14	C₃×#541	C₂	1	4	yes	maximal, complemented
15	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#529	C₂	1	1	yes	maximal, characteristic
18	#3555	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×C₄⋊Q₈	C₂²	1	4	yes	—
20	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₄⋊Q₈	C₂²	1	4	yes	—
24	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₃×#126	C₂²	1	4	yes	—
29	C₃×#126	C₂²	1	4	yes	—
30	C₃×#126	C₂²	1	4	yes	—
31	C₃×#126	C₂²	1	4	yes	—
32	C₃×#126	C₂²	1	2	yes	—
33	C₃×#126	C₂²	1	4	yes	—
34	C₃×#126	C₂²	1	4	yes	—
35	C₃×#125	C₂²	1	4	yes	—
36	C₃×#125	C₂²	1	4	yes	—
37	C₃×#125	C₂²	1	1	yes	characteristic
38	C₃×#125	C₂²	1	2	yes	—
39	C₃×#125	C₂²	1	2	yes	—
40	C₃×#125	C₂²	1	4	yes	—
41	C₃×#125	C₂²	1	4	yes	—
42	C₃×#125	C₂²	1	4	yes	—
43	C₃×#125	C₂²	1	2	yes	—
44	C₃×#125	C₂²	1	2	yes	—
45	C₃×#124	C₂²	1	4	yes	—
46	C₃×#124	C₂²	1	1	yes	characteristic
47	C₃×#124	C₂²	1	2	yes	—
48	C₃×#123	C₂²	1	2	yes	—
49	C₃×#123	C₂²	1	4	yes	—
50	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
54	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
61	C₃×#121	C₂²	1	1	yes	characteristic
62	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
63	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
64	C₃×C₄×Q₈	C₂²	1	2	yes	—
65	C₃×C₄×Q₈	C₂²	1	2	yes	—
66	C₃×C₄×Q₈	C₂²	1	2	yes	—
67	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
68	C₃×C₄×Q₈	C₂²	1	2	yes	—
69	C₃×C₄×Q₈	C₂²	1	2	yes	—
70	C₃×C₄×Q₈	C₂²	1	4	yes	—
71	C₃×C₄×Q₈	C₂²	1	2	yes	—
72	C₃×C₄×Q₈	C₂²	1	2	yes	—
73	C₃×C₄×Q₈	C₂²	1	2	yes	—
74	C₃×C₄×D₄	C₂²	1	2	yes	—
75	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
76	C₃×C₄×D₄	C₂²	1	2	yes	—
77	C₃×#117	C₂²	1	2	yes	—
78	C₃×#117	C₂²	1	2	yes	—
79	C₃×#117	C₂²	1	2	yes	—
80	C₃×#117	C₂²	1	4	yes	—
81	C₃×#117	C₂²	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
83	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
84	#563	C₂×C₃	1	4	yes	complemented
85	Q₈²	C₂×C₃	1	1	yes	characteristic, complemented
86	#557	C₂×C₃	1	1	yes	characteristic, complemented
87	#557	C₂×C₃	1	2	yes	complemented
88	#556	C₂×C₃	1	2	yes	complemented
89	#556	C₂×C₃	1	2	yes	complemented
90	#556	C₂×C₃	1	1	yes	characteristic, complemented
91	#554	C₂×C₃	1	1	yes	characteristic, complemented
92	#552	C₂×C₃	1	2	yes	complemented
93	#544	C₂×C₃	1	2	yes	complemented
94	#542	C₂×C₃	1	2	yes	—
95	#541	C₂×C₃	1	2	yes	complemented
96	#541	C₂×C₃	1	2	yes	complemented
97	#541	C₂×C₃	1	4	yes	complemented
98	#533	C₂×C₃	1	1	yes	characteristic, complemented
99	#533	C₂×C₃	1	1	yes	characteristic, complemented
100	#529	C₂×C₃	1	1	yes	characteristic
101	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×Q₈	C₂³	1	2	yes	—
105	C₂×C₃×Q₈	C₂³	1	2	yes	—
106	C₂×C₃×Q₈	C₂³	1	2	yes	—
107	C₂×C₃×Q₈	C₂³	1	4	yes	—
108	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
109	C₂×C₃×D₄	C₂³	1	2	yes	—
110	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
111	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
112	C₂²×C₃×C₄	C₂³	1	2	yes	—
113	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂³	1	4	yes	—
115	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃×C₂²⋊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	2	yes	—
148	C₃×C₂²⋊C₄	C₂³	1	4	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	2	yes	—
153	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃×C₄²	C₂³	1	1	yes	characteristic
156	C₃×C₄²	C₂³	1	1	yes	characteristic
157	C₃×C₄²	C₂³	1	1	yes	characteristic
158	C₃×C₄²	C₂³	1	1	yes	characteristic
159	C₃×C₄²	C₂³	1	4	yes	—
160	C₃×C₄²	C₂³	1	2	yes	—
161	C₃×C₄²	C₂³	1	2	yes	—
162	C₃×C₄²	C₂³	1	2	yes	—
163	C₃×C₄²	C₂³	1	4	yes	—
164	C₃×C₄²	C₂³	1	4	yes	—
165	C₃×C₄²	C₂³	1	4	yes	—
166	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
167	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
168	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
169	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
170	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
171	C₄⋊Q₈	C₂²×C₃	1	4	yes	—
172	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
173	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
174	C₄⋊Q₈	C₂²×C₃	1	4	yes	—
175	#126	C₂²×C₃	1	2	yes	—
176	#126	C₂²×C₃	1	4	yes	—
177	#126	C₂²×C₃	1	4	yes	—
178	#126	C₂²×C₃	1	4	yes	—
179	#126	C₂²×C₃	1	4	yes	—
180	#126	C₂²×C₃	1	4	yes	—
181	#126	C₂²×C₃	1	4	yes	—
182	#125	C₂²×C₃	1	1	yes	characteristic
183	#125	C₂²×C₃	1	2	yes	—
184	#125	C₂²×C₃	1	2	yes	—
185	#125	C₂²×C₃	1	4	yes	—
186	#125	C₂²×C₃	1	4	yes	—
187	#125	C₂²×C₃	1	4	yes	—
188	#125	C₂²×C₃	1	2	yes	—
189	#125	C₂²×C₃	1	4	yes	—
190	#125	C₂²×C₃	1	4	yes	—
191	#125	C₂²×C₃	1	2	yes	—
192	#124	C₂²×C₃	1	1	yes	characteristic
193	#124	C₂²×C₃	1	2	yes	—
194	#124	C₂²×C₃	1	4	yes	—
195	#123	C₂²×C₃	1	2	yes	—
196	#123	C₂²×C₃	1	4	yes	—
197	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
198	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
199	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
200	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
201	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
202	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
203	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
204	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
205	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
206	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
207	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
208	#121	C₂²×C₃	1	1	yes	characteristic
209	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
210	C₄×Q₈	C₂²×C₃	1	2	yes	—
211	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
212	C₄×Q₈	C₂²×C₃	1	2	yes	—
213	C₄×Q₈	C₂²×C₃	1	2	yes	—
214	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
215	C₄×Q₈	C₂²×C₃	1	2	yes	—
216	C₄×Q₈	C₂²×C₃	1	4	yes	—
217	C₄×Q₈	C₂²×C₃	1	2	yes	—
218	C₄×Q₈	C₂²×C₃	1	2	yes	—
219	C₄×Q₈	C₂²×C₃	1	2	yes	—
220	C₄×Q₈	C₂²×C₃	1	2	yes	—
221	C₄×D₄	C₂²×C₃	1	2	yes	—
222	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
223	C₄×D₄	C₂²×C₃	1	2	yes	—
224	#117	C₂²×C₃	1	2	yes	—
225	#117	C₂²×C₃	1	2	yes	—
226	#117	C₂²×C₃	1	2	yes	—
227	#117	C₂²×C₃	1	4	yes	—
228	#117	C₂²×C₃	1	2	yes	—
229	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
230	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
231	C₂³×C₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₃	C₂⁴	1	2	yes	—
233	C₃×Q₈	—	2	2	no	—
234	C₃×Q₈	—	2	2	no	—
235	C₃×Q₈	—	2	2	no	—
236	C₃×Q₈	—	2	4	no	—
237	C₃×Q₈	—	4	2	no	—
238	C₃×Q₈	—	4	2	no	—
239	C₃×Q₈	—	4	4	no	—
240	C₃×D₄	—	2	2	no	—
241	C₃×D₄	—	4	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	4	4	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂⁴	1	4	yes	—
249	C₂×C₃×C₄	C₂⁴	1	2	yes	—
250	C₂×C₃×C₄	C₂⁴	1	2	yes	—
251	C₂×C₃×C₄	C₂⁴	1	2	yes	—
252	C₂×C₃×C₄	C₂⁴	1	2	yes	—
253	C₂×C₃×C₄	C₂⁴	1	2	yes	—
254	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂⁴	1	2	yes	—
256	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂⁴	1	4	yes	—
259	C₂×C₃×C₄	C₂⁴	1	2	yes	—
260	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
262	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
263	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
265	C₂×Q₈	C₂³×C₃	1	2	yes	—
266	C₂×Q₈	C₂³×C₃	1	2	yes	—
267	C₂×Q₈	C₂³×C₃	1	2	yes	—
268	C₂×Q₈	C₂³×C₃	1	4	yes	—
269	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
270	C₂×D₄	C₂³×C₃	1	2	yes	—
271	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₃	1	2	yes	—
274	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
275	C₂²×C₄	C₂³×C₃	1	4	yes	—
276	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
277	C₄⋊C₄	C₂³×C₃	1	2	yes	—
278	C₄⋊C₄	C₂³×C₃	1	4	yes	—
279	C₄⋊C₄	C₂³×C₃	1	2	yes	—
280	C₄⋊C₄	C₂³×C₃	1	2	yes	—
281	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
282	C₄⋊C₄	C₂³×C₃	1	2	yes	—
283	C₄⋊C₄	C₂³×C₃	1	2	yes	—
284	C₄⋊C₄	C₂³×C₃	1	4	yes	—
285	C₄⋊C₄	C₂³×C₃	1	2	yes	—
286	C₄⋊C₄	C₂³×C₃	1	2	yes	—
287	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
288	C₄⋊C₄	C₂³×C₃	1	2	yes	—
289	C₄⋊C₄	C₂³×C₃	1	2	yes	—
290	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
291	C₄⋊C₄	C₂³×C₃	1	2	yes	—
292	C₄⋊C₄	C₂³×C₃	1	2	yes	—
293	C₄⋊C₄	C₂³×C₃	1	4	yes	—
294	C₄⋊C₄	C₂³×C₃	1	4	yes	—
295	C₄⋊C₄	C₂³×C₃	1	4	yes	—
296	C₄⋊C₄	C₂³×C₃	1	4	yes	—
297	C₄⋊C₄	C₂³×C₃	1	4	yes	—
298	C₄⋊C₄	C₂³×C₃	1	2	yes	—
299	C₄⋊C₄	C₂³×C₃	1	2	yes	—
300	C₄⋊C₄	C₂³×C₃	1	2	yes	—
301	C₄⋊C₄	C₂³×C₃	1	4	yes	—
302	C₄⋊C₄	C₂³×C₃	1	2	yes	—
303	C₄⋊C₄	C₂³×C₃	1	4	yes	—
304	C₄⋊C₄	C₂³×C₃	1	4	yes	—
305	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
306	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
307	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
308	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
309	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
310	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
311	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
312	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
313	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
314	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
315	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
316	C₄²	C₂³×C₃	1	1	yes	characteristic
317	C₄²	C₂³×C₃	1	1	yes	characteristic
318	C₄²	C₂³×C₃	1	1	yes	characteristic
319	C₄²	C₂³×C₃	1	1	yes	characteristic
320	C₄²	C₂³×C₃	1	4	yes	—
321	C₄²	C₂³×C₃	1	2	yes	—
322	C₄²	C₂³×C₃	1	2	yes	—
323	C₄²	C₂³×C₃	1	2	yes	—
324	C₄²	C₂³×C₃	1	4	yes	—
325	C₄²	C₂³×C₃	1	4	yes	—
326	C₄²	C₂³×C₃	1	4	yes	—
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	C₂⁵	1	1	yes	characteristic
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	—	2	4	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	2	4	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
348	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
349	C₂³	C₂⁴×C₃	1	1	yes	characteristic
350	C₂³	C₂⁴×C₃	1	2	yes	—
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	2	2	no	—
354	Q₈	—	2	4	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	4	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
366	C₂×C₄	C₂⁴×C₃	1	4	yes	—
367	C₂×C₄	C₂⁴×C₃	1	2	yes	—
368	C₂×C₄	C₂⁴×C₃	1	2	yes	—
369	C₂×C₄	C₂⁴×C₃	1	2	yes	—
370	C₂×C₄	C₂⁴×C₃	1	2	yes	—
371	C₂×C₄	C₂⁴×C₃	1	2	yes	—
372	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
373	C₂×C₄	C₂⁴×C₃	1	2	yes	—
374	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
375	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
376	C₂×C₄	C₂⁴×C₃	1	4	yes	—
377	C₂×C₄	C₂⁴×C₃	1	2	yes	—
378	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
379	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
380	C₂×C₃	—	4	1	no	—
381	C₂×C₃	—	4	2	no	—
382	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
384	C₂×C₃	#585	1	1	yes	characteristic
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	C₂⁵×C₃	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
406	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
407	C₃	#3555	1	1	yes	characteristic, direct product factor, Sylow
408	C₂	—	4	1	no	—
409	C₂	—	4	2	no	—
410	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
prime radical	C₃×#121	C₂²
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×#563	C₂	semidirect
2. C₃×Q₈²	C₂	semidirect
3. C₃×#557	C₂	semidirect
4. C₃×#557	C₂	semidirect
5. C₃×#556	C₂	semidirect
6. C₃×#556	C₂	semidirect
7. C₃×#556	C₂	semidirect
8. C₃×#554	C₂	semidirect
9. C₃×#552	C₂	semidirect
10. C₃×#544	C₂	semidirect
12. C₃×#541	C₂	semidirect
13. C₃×#541	C₂	semidirect
14. C₃×#541	C₂	semidirect
15. C₃×#533	C₂	semidirect
16. C₃×#533	C₂	semidirect
18. #3555	C₃	direct (N × H)
84. #563	C₂×C₃	semidirect
85. Q₈²	C₂×C₃	semidirect
86. #557	C₂×C₃	semidirect
87. #557	C₂×C₃	semidirect
88. #556	C₂×C₃	semidirect
89. #556	C₂×C₃	semidirect
90. #556	C₂×C₃	semidirect
91. #554	C₂×C₃	semidirect
92. #552	C₂×C₃	semidirect
93. #544	C₂×C₃	semidirect
95. #541	C₂×C₃	semidirect
96. #541	C₂×C₃	semidirect
97. #541	C₂×C₃	semidirect
98. #533	C₂×C₃	semidirect
99. #533	C₂×C₃	semidirect
407. C₃	#3555	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×#563	2
C₃×Q₈²	2
C₃×#557	2
C₃×#556	2
C₃×#554	2
C₃×#552	2
C₃×#544	2
C₃×#542	2
C₃×#541	2
C₃×#533	2
C₃×#529	2
#3555	3

Subgroups — C3×#3555 #87439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3555 #87439