Subgroups — C₃×#35284 #10653891

Order 768.

1722 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	2	yes	maximal
4	C₃×#2647	C₂	1	2	yes	maximal, complemented
5	C₃×#2629	C₂	1	2	yes	maximal
6	C₃×#2507	C₂	1	4	yes	maximal, complemented
7	C₃×#2497	C₂	1	4	yes	maximal
8	C₃×#2446	C₂	1	4	yes	maximal, complemented
9	C₃×#2429	C₂	1	4	yes	maximal
10	C₃×#2330	C₂	1	2	yes	maximal, complemented
11	C₃×#2314	C₂	1	2	yes	maximal
12	C₃×C₄×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic
14	#35284	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₃×#125	C₂²	1	2	yes	—
18	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	—
20	C₂×C₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
23	C₃×#400	C₂²	1	8	yes	—
24	C₃×#398	C₂²	1	8	yes	—
25	C₃×#398	C₂²	1	8	yes	—
26	C₃×#396	C₂²	1	8	yes	—
27	C₃×#391	C₂²	1	4	yes	—
28	C₃×#391	C₂²	1	4	yes	—
29	C₃×#389	C₂²	1	4	yes	—
30	C₃×#389	C₂²	1	4	yes	—
31	C₃×#389	C₂²	1	4	yes	—
32	C₃×#389	C₂²	1	8	yes	—
33	C₃×#389	C₂²	1	4	yes	—
34	C₃×#389	C₂²	1	4	yes	—
35	C₃×#389	C₂²	1	4	yes	—
36	C₃×#388	C₂²	1	8	yes	—
37	C₃×#387	C₂²	1	8	yes	—
38	C₃×#387	C₂²	1	8	yes	—
39	C₃×#384	C₂²	1	2	yes	—
40	C₃×#384	C₂²	1	2	yes	—
41	C₃×#384	C₂²	1	4	yes	—
42	C₃×#384	C₂²	1	2	yes	—
43	C₃×#382	C₂²	1	2	yes	—
44	C₃×#380	C₂²	1	4	yes	—
45	C₃×#380	C₂²	1	4	yes	—
46	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
47	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
48	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
49	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
50	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
52	C₃×#376	C₂²	1	1	yes	characteristic
53	C₃×#376	C₂²	1	1	yes	characteristic
54	C₃×C₄³	C₂²	1	1	yes	characteristic
55	C₃×C₄³	C₂²	1	1	yes	characteristic
56	#2868	C₂×C₃	1	1	yes	characteristic, complemented
57	#2859	C₂×C₃	1	1	yes	characteristic, complemented
58	#2857	C₂×C₃	1	2	yes	—
59	#2647	C₂×C₃	1	2	yes	complemented
60	#2629	C₂×C₃	1	2	yes	—
61	#2507	C₂×C₃	1	4	yes	complemented
62	#2497	C₂×C₃	1	4	yes	—
63	#2446	C₂×C₃	1	4	yes	complemented
64	#2429	C₂×C₃	1	4	yes	—
65	#2330	C₂×C₃	1	2	yes	complemented
66	#2314	C₂×C₃	1	2	yes	—
67	C₄×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
68	C₄×#117	C₂×C₃	1	1	yes	characteristic
69	C₂²×C₃×Q₈	C₂³	1	4	yes	—
70	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
71	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
72	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
73	C₃×C₄⋊Q₈	—	2	8	no	—
74	C₃×C₄⋊Q₈	—	4	8	no	—
75	C₃×#125	—	2	8	no	—
76	C₃×C₂²⋊Q₈	—	4	8	no	—
77	C₃×C₄×Q₈	—	4	8	no	—
78	C₃×#117	—	2	4	no	—
79	C₃×#117	Q₈	1	8	yes	complemented
80	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
89	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
90	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
91	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
95	C₂×C₃×C₄²	—	2	4	no	—
96	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄²	C₂³	1	2	yes	—
98	C₂×C₃×C₄²	C₂³	1	2	yes	—
99	C₂×C₃×C₄²	C₂³	1	2	yes	—
100	C₂×C₃×C₄²	C₂³	1	2	yes	—
101	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂³	1	8	yes	—
105	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
109	C₃×#95	C₂³	1	2	yes	—
110	C₃×#95	C₂³	1	2	yes	—
111	C₃×#95	C₂³	1	2	yes	—
112	C₃×#95	C₂³	1	2	yes	—
113	C₃×#95	C₂³	1	8	yes	—
114	C₃×#95	C₂³	1	8	yes	—
115	C₃×#95	C₂³	1	8	yes	—
116	C₃×#95	C₂³	1	8	yes	—
117	C₃×#95	C₂³	1	8	yes	—
118	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
119	C₂×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
120	C₂×#125	C₂²×C₃	1	2	yes	—
121	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
122	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	—
123	C₂×#117	C₂²×C₃	1	1	yes	characteristic
124	C₂×#117	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
126	#400	C₂²×C₃	1	8	yes	—
127	#398	C₂²×C₃	1	8	yes	—
128	#398	C₂²×C₃	1	8	yes	—
129	#396	C₂²×C₃	1	8	yes	—
130	#391	C₂²×C₃	1	4	yes	—
131	#391	C₂²×C₃	1	4	yes	—
132	#389	C₂²×C₃	1	4	yes	—
133	#389	C₂²×C₃	1	4	yes	—
134	#389	C₂²×C₃	1	4	yes	—
135	#389	C₂²×C₃	1	8	yes	—
136	#389	C₂²×C₃	1	4	yes	—
137	#389	C₂²×C₃	1	4	yes	—
138	#389	C₂²×C₃	1	4	yes	—
139	#388	C₂²×C₃	1	8	yes	—
140	#387	C₂²×C₃	1	8	yes	—
141	#387	C₂²×C₃	1	8	yes	—
142	#384	C₂²×C₃	1	2	yes	—
143	#384	C₂²×C₃	1	2	yes	—
144	#384	C₂²×C₃	1	2	yes	—
145	#384	C₂²×C₃	1	4	yes	—
146	#382	C₂²×C₃	1	2	yes	—
147	#380	C₂²×C₃	1	4	yes	—
148	#380	C₂²×C₃	1	4	yes	—
149	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
150	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
151	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
152	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
153	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
154	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
155	#376	C₂²×C₃	1	1	yes	characteristic
156	#376	C₂²×C₃	1	1	yes	characteristic
157	C₄³	C₂²×C₃	1	1	yes	characteristic
158	C₄³	C₂²×C₃	1	1	yes	characteristic
159	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₃×Q₈	—	2	8	no	—
161	C₂×C₃×Q₈	—	2	8	no	—
162	C₂×C₃×Q₈	—	2	8	no	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	—	2	2	no	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	4	no	—
168	C₂²×C₃×C₄	—	2	4	no	—
169	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
170	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
172	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
173	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
175	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
177	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
178	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
179	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	16	no	—
184	C₃×C₄⋊C₄	—	2	8	no	—
185	C₃×C₄⋊C₄	—	2	8	no	—
186	C₃×C₄⋊C₄	—	2	8	no	—
187	C₃×C₄⋊C₄	—	2	8	no	—
188	C₃×C₄⋊C₄	—	2	8	no	—
189	C₃×C₄⋊C₄	—	4	8	no	—
190	C₃×C₄⋊C₄	—	4	8	no	—
191	C₃×C₄⋊C₄	—	4	8	no	—
192	C₃×C₄⋊C₄	—	4	8	no	—
193	C₃×C₄⋊C₄	C₂×Q₈	1	8	yes	—
194	C₃×C₂²⋊C₄	—	2	4	no	—
195	C₃×C₂²⋊C₄	—	4	8	no	—
196	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
197	C₃×C₄²	—	2	2	no	—
198	C₃×C₄²	—	2	2	no	—
199	C₃×C₄²	—	2	2	no	—
200	C₃×C₄²	—	2	2	no	—
201	C₃×C₄²	—	2	4	no	—
202	C₃×C₄²	—	2	4	no	—
203	C₃×C₄²	—	2	4	no	—
204	C₃×C₄²	—	2	4	no	—
205	C₃×C₄²	—	4	8	no	—
206	C₃×C₄²	C₂×Q₈	1	4	yes	—
207	C₃×C₄²	C₂×Q₈	1	4	yes	—
208	C₃×C₄²	#41	1	4	yes	—
209	C₃×C₄²	#41	1	4	yes	—
210	C₂²×Q₈	C₂³×C₃	1	4	yes	—
211	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
214	C₄⋊Q₈	—	2	8	no	—
215	C₄⋊Q₈	—	4	8	no	—
216	#125	—	2	8	no	—
217	C₂²⋊Q₈	—	4	8	no	—
218	C₄×Q₈	—	4	8	no	—
219	#117	—	2	4	no	—
220	#117	C₃×Q₈	1	8	yes	complemented
221	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
222	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
223	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
224	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
226	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
227	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
228	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
229	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
230	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
231	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
232	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
234	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
235	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₃	1	2	yes	—
239	C₂×C₄²	C₂³×C₃	1	2	yes	—
240	C₂×C₄²	C₂³×C₃	1	2	yes	—
241	C₂×C₄²	C₂³×C₃	1	2	yes	—
242	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₃	1	8	yes	—
246	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
250	#95	C₂³×C₃	1	2	yes	—
251	#95	C₂³×C₃	1	2	yes	—
252	#95	C₂³×C₃	1	2	yes	—
253	#95	C₂³×C₃	1	2	yes	—
254	#95	C₂³×C₃	1	8	yes	—
255	#95	C₂³×C₃	1	8	yes	—
256	#95	C₂³×C₃	1	8	yes	—
257	#95	C₂³×C₃	1	8	yes	—
258	#95	C₂³×C₃	1	8	yes	—
259	C₂³×C₃	—	2	1	no	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	2	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	C₂²×Q₈	1	2	yes	—
264	C₂³×C₃	C₂⁵	1	1	yes	characteristic
265	C₃×Q₈	—	4	16	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	8	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	8	no	—
279	C₂×C₃×C₄	—	2	8	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	8	no	—
282	C₂×C₃×C₄	—	2	8	no	—
283	C₂×C₃×C₄	—	2	8	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	8	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	4	4	no	—
289	C₂×C₃×C₄	—	4	4	no	—
290	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
291	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
292	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
293	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
294	C₂×C₃×C₄	C₂×#41	1	4	yes	—
295	C₂×C₃×C₄	C₂×#41	1	2	yes	—
296	C₂×C₃×C₄	C₂×#41	1	2	yes	—
297	C₂×C₃×C₄	C₂×#41	1	2	yes	—
298	C₂×C₃×C₄	C₂×#41	1	2	yes	—
299	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
300	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
301	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	2	8	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
313	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
315	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
317	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	16	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	4	8	no	—
332	C₄⋊C₄	—	4	8	no	—
333	C₄⋊C₄	—	4	8	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	C₂×C₃×Q₈	1	8	yes	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	4	8	no	—
338	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	4	8	no	—
348	C₄²	C₂×C₃×Q₈	1	4	yes	—
349	C₄²	C₂×C₃×Q₈	1	4	yes	—
350	C₄²	C₃×#41	1	4	yes	—
351	C₄²	C₃×#41	1	4	yes	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	4	no	—
354	C₂²×C₃	—	4	1	no	—
355	C₂²×C₃	—	4	1	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
358	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
361	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	4	no	—
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	4	1	no	—
367	C₃×C₄	—	4	8	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	8	no	—
371	C₃×C₄	#533	1	4	yes	—
372	C₃×C₄	#540	1	4	yes	—
373	C₃×C₄	#541	1	4	yes	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₂²×C₃×Q₈	1	2	yes	—
379	C₂³	C₂⁵×C₃	1	1	yes	characteristic
380	Q₈	—	4	16	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
406	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
407	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
408	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
409	C₂×C₄	C₂×C₃×#41	1	4	yes	—
410	C₂×C₄	C₂×C₃×#41	1	2	yes	—
411	C₂×C₄	C₂×C₃×#41	1	2	yes	—
412	C₂×C₄	C₂×C₃×#41	1	2	yes	—
413	C₂×C₄	C₂×C₃×#41	1	2	yes	—
414	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
415	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
416	C₂×C₃	—	4	2	no	—
417	C₂×C₃	C₂×#533	1	1	yes	characteristic
418	C₂×C₃	C₂×#540	1	1	yes	characteristic
419	C₂×C₃	C₂×#541	1	1	yes	characteristic
420	C₂×C₃	#3503	1	2	yes	—
421	C₂×C₃	#3511	1	2	yes	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
428	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
429	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
430	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
431	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	8	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	8	no	—
441	C₄	C₃×#533	1	4	yes	—
442	C₄	C₃×#540	1	4	yes	—
443	C₄	C₃×#541	1	4	yes	—
444	C₃	#35284	1	1	yes	characteristic, direct product factor, Sylow
445	C₂	—	4	2	no	—
446	C₂	C₂×C₃×#533	1	1	yes	characteristic
447	C₂	C₂×C₃×#540	1	1	yes	characteristic
448	C₂	C₂×C₃×#541	1	1	yes	characteristic
449	C₂	C₃×#3503	1	2	yes	—
450	C₂	C₃×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁴×C₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2868	C₂	semidirect
2. C₃×#2859	C₂	semidirect
4. C₃×#2647	C₂	semidirect
6. C₃×#2507	C₂	semidirect
8. C₃×#2446	C₂	semidirect
10. C₃×#2330	C₂	semidirect
12. C₃×C₄×C₄⋊Q₈	C₂	semidirect
14. #35284	C₃	direct (N × H)
56. #2868	C₂×C₃	semidirect
57. #2859	C₂×C₃	semidirect
59. #2647	C₂×C₃	semidirect
61. #2507	C₂×C₃	semidirect
63. #2446	C₂×C₃	semidirect
65. #2330	C₂×C₃	semidirect
67. C₄×C₄⋊Q₈	C₂×C₃	semidirect
79. C₃×#117	Q₈	semidirect
220. #117	C₃×Q₈	semidirect
444. C₃	#35284	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×#2868	2
C₃×#2859	2
C₃×#2857	2
C₃×#2647	2
C₃×#2629	2
C₃×#2507	2
C₃×#2497	2
C₃×#2446	2
C₃×#2429	2
C₃×#2330	2
C₃×#2314	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#117	2
#35284	3

Subgroups — C3×#35284 #10653891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35284 #10653891