Subgroups — C₃×#3554 #87438

Order 384.

1022 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#562	C₂	1	4	yes	maximal, complemented
2	C₃×#559	C₂	1	2	yes	maximal, complemented
3	C₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#554	C₂	1	2	yes	maximal, complemented
6	C₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#548	C₂	1	2	yes	maximal, complemented
9	C₃×#547	C₂	1	2	yes	maximal, complemented
10	C₃×#542	C₂	1	2	yes	maximal, complemented
11	C₃×#542	C₂	1	2	yes	maximal, complemented
12	C₃×#540	C₂	1	2	yes	maximal, complemented
13	C₃×#539	C₂	1	4	yes	maximal, complemented
14	C₃×#536	C₂	1	2	yes	maximal, complemented
15	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	#3554	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	—
21	C₂²×C₃×Q₈	C₂²	1	2	yes	—
22	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₃×#127	C₂²	1	1	yes	characteristic
28	C₃×#127	C₂²	1	2	yes	—
29	C₃×#126	C₂²	1	2	yes	—
30	C₃×#126	C₂²	1	4	yes	—
31	C₃×#125	C₂²	1	4	yes	—
32	C₃×#125	C₂²	1	1	yes	characteristic
33	C₃×#125	C₂²	1	2	yes	—
34	C₃×#125	C₂²	1	2	yes	—
35	C₃×#124	C₂²	1	1	yes	characteristic
36	C₃×#124	C₂²	1	2	yes	—
37	C₃×#124	C₂²	1	4	yes	—
38	C₃×#124	C₂²	1	2	yes	—
39	C₃×#124	C₂²	1	4	yes	—
40	C₃×#124	C₂²	1	2	yes	—
41	C₃×#123	C₂²	1	4	yes	—
42	C₃×#123	C₂²	1	4	yes	—
43	C₃×#123	C₂²	1	4	yes	—
44	C₃×#123	C₂²	1	2	yes	—
45	C₃×#123	C₂²	1	4	yes	—
46	C₃×#123	C₂²	1	4	yes	—
47	C₃×#123	C₂²	1	4	yes	—
48	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
50	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
51	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
52	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
54	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
56	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
57	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
58	C₃×#121	C₂²	1	2	yes	—
59	C₃×#121	C₂²	1	4	yes	—
60	C₃×#121	C₂²	1	4	yes	—
61	C₃×#121	C₂²	1	4	yes	—
62	C₃×#121	C₂²	1	1	yes	characteristic
63	C₃×#121	C₂²	1	2	yes	—
64	C₃×#121	C₂²	1	2	yes	—
65	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
66	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
67	C₃×C₄×Q₈	C₂²	1	2	yes	—
68	C₃×C₄×Q₈	C₂²	1	2	yes	—
69	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
70	C₃×C₄×Q₈	C₂²	1	2	yes	—
71	C₃×C₄×D₄	C₂²	1	2	yes	—
72	C₃×C₄×D₄	C₂²	1	4	yes	—
73	C₃×C₄×D₄	C₂²	1	2	yes	—
74	C₃×C₄×D₄	C₂²	1	2	yes	—
75	C₃×C₄×D₄	C₂²	1	2	yes	—
76	C₃×C₄×D₄	C₂²	1	2	yes	—
77	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
78	C₃×C₄×D₄	C₂²	1	2	yes	—
79	C₃×C₄×D₄	C₂²	1	2	yes	—
80	C₃×#117	C₂²	1	2	yes	—
81	C₃×#117	C₂²	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	—
83	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
84	#562	C₂×C₃	1	4	yes	complemented
85	#559	C₂×C₃	1	2	yes	complemented
86	#559	C₂×C₃	1	1	yes	characteristic, complemented
87	#557	C₂×C₃	1	1	yes	characteristic, complemented
88	#554	C₂×C₃	1	2	yes	complemented
89	#550	C₂×C₃	1	1	yes	characteristic, complemented
90	D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
91	#548	C₂×C₃	1	2	yes	complemented
92	#547	C₂×C₃	1	2	yes	complemented
93	#542	C₂×C₃	1	2	yes	complemented
94	#542	C₂×C₃	1	2	yes	complemented
95	#540	C₂×C₃	1	2	yes	complemented
96	#539	C₂×C₃	1	4	yes	complemented
97	#536	C₂×C₃	1	2	yes	complemented
98	#533	C₂×C₃	1	1	yes	characteristic, complemented
99	#532	C₂×C₃	1	1	yes	characteristic, complemented
100	#529	C₂×C₃	1	1	yes	characteristic, complemented
101	C₃×#41	—	4	4	no	—
102	C₃×#41	—	4	4	no	—
103	C₂×C₃×Q₈	—	4	4	no	—
104	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×Q₈	C₂³	1	2	yes	—
107	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×Q₈	C₂³	1	2	yes	—
109	C₂×C₃×Q₈	C₂³	1	4	yes	—
110	C₂×C₃×D₄	C₂³	1	2	yes	—
111	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
112	C₂×C₃×D₄	C₂³	1	2	yes	—
113	C₂×C₃×D₄	C₂³	1	2	yes	—
114	C₂×C₃×D₄	C₂³	1	2	yes	—
115	C₂×C₃×D₄	C₂³	1	4	yes	—
116	C₂×C₃×D₄	C₂³	1	4	yes	—
117	C₂×C₃×D₄	C₂³	1	4	yes	—
118	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂³	1	2	yes	—
121	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
122	C₂²×C₃×C₄	C₂³	1	4	yes	—
123	C₂²×C₃×C₄	C₂³	1	4	yes	—
124	C₂²×C₃×C₄	C₂³	1	4	yes	—
125	C₂²×C₃×C₄	C₂³	1	4	yes	—
126	C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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	1	yes	characteristic
139	C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
157	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₃×C₄²	C₂³	1	1	yes	characteristic
162	C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₃×C₄²	C₂³	1	1	yes	characteristic
164	C₃×C₄²	C₂³	1	1	yes	characteristic
165	C₃×C₄²	C₂³	1	2	yes	—
166	C₃×C₄²	C₂³	1	2	yes	—
167	C₃×C₄²	C₂³	1	2	yes	—
168	C₃×C₄²	C₂³	1	4	yes	—
169	C₂×#41	C₂²×C₃	1	2	yes	—
170	C₂×#41	C₂²×C₃	1	2	yes	—
171	C₂²×Q₈	C₂²×C₃	1	2	yes	—
172	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
173	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
174	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
175	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
176	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
177	#127	C₂²×C₃	1	1	yes	characteristic
178	#127	C₂²×C₃	1	2	yes	—
179	#126	C₂²×C₃	1	2	yes	—
180	#126	C₂²×C₃	1	4	yes	—
181	#125	C₂²×C₃	1	1	yes	characteristic
182	#125	C₂²×C₃	1	2	yes	—
183	#125	C₂²×C₃	1	4	yes	—
184	#125	C₂²×C₃	1	2	yes	—
185	#124	C₂²×C₃	1	1	yes	characteristic
186	#124	C₂²×C₃	1	2	yes	—
187	#124	C₂²×C₃	1	2	yes	—
188	#124	C₂²×C₃	1	4	yes	—
189	#124	C₂²×C₃	1	2	yes	—
190	#124	C₂²×C₃	1	4	yes	—
191	#123	C₂²×C₃	1	2	yes	—
192	#123	C₂²×C₃	1	4	yes	—
193	#123	C₂²×C₃	1	4	yes	—
194	#123	C₂²×C₃	1	4	yes	—
195	#123	C₂²×C₃	1	4	yes	—
196	#123	C₂²×C₃	1	4	yes	—
197	#123	C₂²×C₃	1	4	yes	—
198	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
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	4	yes	—
203	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
204	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
205	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
206	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
207	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
208	#121	C₂²×C₃	1	1	yes	characteristic
209	#121	C₂²×C₃	1	2	yes	—
210	#121	C₂²×C₃	1	2	yes	—
211	#121	C₂²×C₃	1	4	yes	—
212	#121	C₂²×C₃	1	4	yes	—
213	#121	C₂²×C₃	1	4	yes	—
214	#121	C₂²×C₃	1	2	yes	—
215	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
216	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
217	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
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	C₄×D₄	C₂²×C₃	1	2	yes	—
225	C₄×D₄	C₂²×C₃	1	4	yes	—
226	C₄×D₄	C₂²×C₃	1	2	yes	—
227	C₄×D₄	C₂²×C₃	1	2	yes	—
228	C₄×D₄	C₂²×C₃	1	2	yes	—
229	C₄×D₄	C₂²×C₃	1	2	yes	—
230	#117	C₂²×C₃	1	2	yes	—
231	#117	C₂²×C₃	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	—
233	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
234	C₂³×C₃	C₂⁴	1	2	yes	—
235	C₂³×C₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₃	C₂⁴	1	4	yes	—
237	C₃×Q₈	—	2	2	no	—
238	C₃×Q₈	—	2	4	no	—
239	C₃×Q₈	—	2	2	no	—
240	C₃×Q₈	—	2	2	no	—
241	C₃×Q₈	—	4	4	no	—
242	C₃×Q₈	—	4	2	no	—
243	C₃×D₄	—	2	4	no	—
244	C₃×D₄	—	2	4	no	—
245	C₃×D₄	—	2	2	no	—
246	C₃×D₄	—	4	2	no	—
247	C₃×D₄	—	4	2	no	—
248	C₃×D₄	—	4	4	no	—
249	C₃×D₄	—	4	4	no	—
250	C₃×D₄	—	4	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	4	4	no	—
255	C₂×C₃×C₄	—	4	1	no	—
256	C₂×C₃×C₄	—	4	4	no	—
257	C₂×C₃×C₄	—	4	4	no	—
258	C₂×C₃×C₄	—	4	4	no	—
259	C₂×C₃×C₄	C₂⁴	1	2	yes	—
260	C₂×C₃×C₄	C₂⁴	1	2	yes	—
261	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂⁴	1	2	yes	—
266	C₂×C₃×C₄	C₂⁴	1	2	yes	—
267	C₂×C₃×C₄	C₂⁴	1	2	yes	—
268	C₂×C₃×C₄	C₂⁴	1	4	yes	—
269	C₂×C₃×C₄	C₂⁴	1	2	yes	—
270	C₂×C₃×C₄	C₂⁴	1	2	yes	—
271	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
273	#41	—	4	4	no	—
274	#41	—	4	4	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
277	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
278	C₂×Q₈	C₂³×C₃	1	2	yes	—
279	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
280	C₂×Q₈	C₂³×C₃	1	2	yes	—
281	C₂×Q₈	C₂³×C₃	1	4	yes	—
282	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
283	C₂×D₄	C₂³×C₃	1	2	yes	—
284	C₂×D₄	C₂³×C₃	1	2	yes	—
285	C₂×D₄	C₂³×C₃	1	2	yes	—
286	C₂×D₄	C₂³×C₃	1	2	yes	—
287	C₂×D₄	C₂³×C₃	1	4	yes	—
288	C₂×D₄	C₂³×C₃	1	4	yes	—
289	C₂×D₄	C₂³×C₃	1	4	yes	—
290	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₃	1	2	yes	—
293	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₃	1	4	yes	—
295	C₂²×C₄	C₂³×C₃	1	4	yes	—
296	C₂²×C₄	C₂³×C₃	1	4	yes	—
297	C₂²×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	4	yes	—
301	C₄⋊C₄	C₂³×C₃	1	4	yes	—
302	C₄⋊C₄	C₂³×C₃	1	2	yes	—
303	C₄⋊C₄	C₂³×C₃	1	2	yes	—
304	C₄⋊C₄	C₂³×C₃	1	2	yes	—
305	C₄⋊C₄	C₂³×C₃	1	2	yes	—
306	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
307	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
308	C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
313	C₄⋊C₄	C₂³×C₃	1	2	yes	—
314	C₄⋊C₄	C₂³×C₃	1	4	yes	—
315	C₄⋊C₄	C₂³×C₃	1	2	yes	—
316	C₄⋊C₄	C₂³×C₃	1	2	yes	—
317	C₄⋊C₄	C₂³×C₃	1	4	yes	—
318	C₄⋊C₄	C₂³×C₃	1	2	yes	—
319	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
320	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
321	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
322	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
323	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
324	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
325	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
326	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
327	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
328	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
329	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
330	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
331	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
332	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
333	C₄²	C₂³×C₃	1	1	yes	characteristic
334	C₄²	C₂³×C₃	1	1	yes	characteristic
335	C₄²	C₂³×C₃	1	1	yes	characteristic
336	C₄²	C₂³×C₃	1	1	yes	characteristic
337	C₄²	C₂³×C₃	1	2	yes	—
338	C₄²	C₂³×C₃	1	2	yes	—
339	C₄²	C₂³×C₃	1	2	yes	—
340	C₄²	C₂³×C₃	1	4	yes	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	2	4	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	4	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	4	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	C₂⁵	1	1	yes	characteristic
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	2	4	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
364	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
365	C₂³	C₂⁴×C₃	1	2	yes	—
366	C₂³	C₂⁴×C₃	1	1	yes	characteristic
367	C₂³	C₂⁴×C₃	1	4	yes	—
368	Q₈	—	2	2	no	—
369	Q₈	—	2	4	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	4	4	no	—
373	Q₈	—	4	2	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	C₂⁴×C₃	1	2	yes	—
391	C₂×C₄	C₂⁴×C₃	1	2	yes	—
392	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
393	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
394	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
395	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
396	C₂×C₄	C₂⁴×C₃	1	2	yes	—
397	C₂×C₄	C₂⁴×C₃	1	2	yes	—
398	C₂×C₄	C₂⁴×C₃	1	2	yes	—
399	C₂×C₄	C₂⁴×C₃	1	4	yes	—
400	C₂×C₄	C₂⁴×C₃	1	2	yes	—
401	C₂×C₄	C₂⁴×C₃	1	2	yes	—
402	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
403	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
404	C₂×C₃	—	4	2	no	—
405	C₂×C₃	—	4	1	no	—
406	C₂×C₃	—	4	4	no	—
407	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂×C₃	#585	1	1	yes	characteristic
410	C₂²	—	2	2	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	2	no	—
419	C₂²	C₂⁵×C₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
433	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
434	C₃	#3554	1	1	yes	characteristic, direct product factor, Sylow
435	C₂	—	4	2	no	—
436	C₂	—	4	1	no	—
437	C₂	—	4	4	no	—
438	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
440	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×#562	C₂	semidirect
2. C₃×#559	C₂	semidirect
3. C₃×#559	C₂	semidirect
4. C₃×#557	C₂	semidirect
5. C₃×#554	C₂	semidirect
6. C₃×#550	C₂	semidirect
7. C₃×D₄×Q₈	C₂	semidirect
8. C₃×#548	C₂	semidirect
9. C₃×#547	C₂	semidirect
10. C₃×#542	C₂	semidirect
11. C₃×#542	C₂	semidirect
12. C₃×#540	C₂	semidirect
13. C₃×#539	C₂	semidirect
14. C₃×#536	C₂	semidirect
15. C₃×#533	C₂	semidirect
16. C₃×#532	C₂	semidirect
17. C₃×#529	C₂	semidirect
18. #3554	C₃	direct (N × H)
84. #562	C₂×C₃	semidirect
85. #559	C₂×C₃	semidirect
86. #559	C₂×C₃	semidirect
87. #557	C₂×C₃	semidirect
88. #554	C₂×C₃	semidirect
89. #550	C₂×C₃	semidirect
90. D₄×Q₈	C₂×C₃	semidirect
91. #548	C₂×C₃	semidirect
92. #547	C₂×C₃	semidirect
93. #542	C₂×C₃	semidirect
94. #542	C₂×C₃	semidirect
95. #540	C₂×C₃	semidirect
96. #539	C₂×C₃	semidirect
97. #536	C₂×C₃	semidirect
98. #533	C₂×C₃	semidirect
99. #532	C₂×C₃	semidirect
100. #529	C₂×C₃	semidirect
434. C₃	#3554	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×#562	2
C₃×#559	2
C₃×#557	2
C₃×#554	2
C₃×#550	2
C₃×D₄×Q₈	2
C₃×#548	2
C₃×#547	2
C₃×#542	2
C₃×#540	2
C₃×#539	2
C₃×#536	2
C₃×#533	2
C₃×#532	2
C₃×#529	2
#3554	3

Subgroups — C3×#3554 #87438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3554 #87438