Subgroups — C₃×#3494 #87378

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#555	C₂	1	2	yes	maximal, complemented
2	C₃×#553	C₂	1	2	yes	maximal, complemented
3	C₃×#553	C₂	1	2	yes	maximal, complemented
4	C₃×#551	C₂	1	4	yes	maximal, complemented
5	C₃×#547	C₂	1	2	yes	maximal, complemented
6	C₃×#546	C₂	1	4	yes	maximal, complemented
7	C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#542	C₂	1	2	yes	maximal, complemented
9	C₃×#540	C₂	1	2	yes	maximal, complemented
10	C₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#532	C₂	1	2	yes	maximal, complemented
12	C₃×#529	C₂	1	2	yes	maximal, complemented
13	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	#3494	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	4	yes	complemented
21	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×D₄	C₂²	1	2	yes	—
23	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
24	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃×#127	C₂²	1	2	yes	complemented
27	C₃×#126	C₂²	1	4	yes	complemented
28	C₃×#126	C₂²	1	4	yes	complemented
29	C₃×#125	C₂²	1	2	yes	complemented
30	C₃×#125	C₂²	1	2	yes	complemented
31	C₃×#124	C₂²	1	2	yes	complemented
32	C₃×#124	C₂²	1	4	yes	complemented
33	C₃×#124	C₂²	1	4	yes	complemented
34	C₃×#123	C₂²	1	2	yes	—
35	C₃×#123	C₂²	1	4	yes	complemented
36	C₃×#123	C₂²	1	4	yes	complemented
37	C₃×#123	C₂²	1	4	yes	complemented
38	C₃×#123	C₂²	1	4	yes	complemented
39	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
40	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₃×#121	C₂²	1	2	yes	—
44	C₃×#121	C₂²	1	2	yes	—
45	C₃×#121	C₂²	1	2	yes	—
46	C₃×#121	C₂²	1	2	yes	—
47	C₃×#121	C₂²	1	1	yes	characteristic, complemented
48	C₃×#121	C₂²	1	1	yes	characteristic, complemented
49	C₃×#121	C₂²	1	4	yes	complemented
50	C₃×#121	C₂²	1	2	yes	complemented
51	C₃×#121	C₂²	1	2	yes	complemented
52	C₃×#121	C₂²	1	4	yes	complemented
53	C₃×#121	C₂²	1	4	yes	complemented
54	C₃×#120	C₂²	1	2	yes	—
55	C₃×#120	C₂²	1	4	yes	—
56	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
57	C₃×C₄×D₄	C₂²	1	4	yes	—
58	C₃×C₄×D₄	C₂²	1	2	yes	complemented
59	C₃×C₄×D₄	C₂²	1	2	yes	complemented
60	C₃×C₄×D₄	C₂²	1	2	yes	complemented
61	C₃×C₄×D₄	C₂²	1	2	yes	complemented
62	C₃×C₄×D₄	C₂²	1	2	yes	complemented
63	C₃×C₄×D₄	C₂²	1	2	yes	complemented
64	C₃×C₄×D₄	C₂²	1	2	yes	complemented
65	C₃×C₄×D₄	C₂²	1	4	yes	complemented
66	C₃×C₄×D₄	C₂²	1	4	yes	complemented
67	C₃×#117	C₂²	1	1	yes	characteristic
68	C₃×#117	C₂²	1	1	yes	characteristic
69	C₃×#117	C₂²	1	2	yes	—
70	C₃×#117	C₂²	1	1	yes	characteristic
71	C₃×#117	C₂²	1	2	yes	complemented
72	C₃×#117	C₂²	1	1	yes	characteristic, complemented
73	C₃×#117	C₂²	1	1	yes	characteristic, complemented
74	C₃×#117	C₂²	1	2	yes	complemented
75	C₃×#117	C₂²	1	4	yes	complemented
76	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₂×C₃×C₄²	C₂²	1	2	yes	complemented
84	#555	C₂×C₃	1	2	yes	complemented
85	#553	C₂×C₃	1	2	yes	complemented
86	#553	C₂×C₃	1	2	yes	complemented
87	#551	C₂×C₃	1	4	yes	complemented
88	#547	C₂×C₃	1	2	yes	complemented
89	#546	C₂×C₃	1	4	yes	complemented
90	#544	C₂×C₃	1	1	yes	characteristic, complemented
91	#542	C₂×C₃	1	2	yes	complemented
92	#540	C₂×C₃	1	2	yes	complemented
93	#535	C₂×C₃	1	1	yes	characteristic, complemented
94	#532	C₂×C₃	1	2	yes	complemented
95	#529	C₂×C₃	1	2	yes	complemented
96	#525	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#121	C₂×C₃	1	1	yes	characteristic, complemented
98	#520	C₂×C₃	1	1	yes	characteristic, complemented
99	#518	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂×#117	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂⁴×C₃	C₂³	1	1	yes	characteristic
102	C₂⁴×C₃	C₂³	1	2	yes	—
103	C₃×#41	—	2	4	no	—
104	C₃×#41	—	4	8	no	—
105	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×Q₈	C₂³	1	4	yes	—
107	C₂×C₃×D₄	—	2	4	no	—
108	C₂×C₃×D₄	—	4	4	no	—
109	C₂×C₃×D₄	C₂³	1	2	yes	—
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	2	yes	—
114	C₂×C₃×D₄	C₂³	1	4	yes	—
115	C₂×C₃×D₄	C₂³	1	2	yes	—
116	C₂×C₃×D₄	C₂³	1	4	yes	—
117	C₂×C₃×D₄	C₂³	1	4	yes	—
118	C₂×C₃×D₄	C₂³	1	4	yes	—
119	C₂²×C₃×C₄	—	2	4	no	—
120	C₂²×C₃×C₄	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	1	yes	characteristic
124	C₂²×C₃×C₄	C₂³	1	2	yes	—
125	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₂²×C₃×C₄	C₂³	1	2	yes	—
128	C₂²×C₃×C₄	C₂³	1	2	yes	—
129	C₂²×C₃×C₄	C₂³	1	4	yes	—
130	C₂²×C₃×C₄	C₂³	1	4	yes	—
131	C₂²×C₃×C₄	C₂³	1	4	yes	—
132	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
133	C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃×C₄⋊C₄	C₂³	1	4	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	2	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	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	4	yes	—
159	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₃×C₂²⋊C₄	C₂³	1	2	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×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
169	C₃×C₄²	C₂³	1	2	yes	—
170	C₃×C₄²	C₂³	1	4	yes	—
171	C₂×#41	C₂²×C₃	1	1	yes	characteristic
172	C₂×#41	C₂²×C₃	1	4	yes	complemented
173	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
174	C₂²×D₄	C₂²×C₃	1	2	yes	—
175	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
176	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
177	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
178	#127	C₂²×C₃	1	2	yes	complemented
179	#126	C₂²×C₃	1	4	yes	complemented
180	#126	C₂²×C₃	1	4	yes	complemented
181	#125	C₂²×C₃	1	2	yes	complemented
182	#125	C₂²×C₃	1	2	yes	complemented
183	#124	C₂²×C₃	1	2	yes	complemented
184	#124	C₂²×C₃	1	4	yes	complemented
185	#124	C₂²×C₃	1	4	yes	complemented
186	#123	C₂²×C₃	1	2	yes	—
187	#123	C₂²×C₃	1	4	yes	complemented
188	#123	C₂²×C₃	1	4	yes	complemented
189	#123	C₂²×C₃	1	4	yes	complemented
190	#123	C₂²×C₃	1	4	yes	complemented
191	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
192	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
195	#121	C₂²×C₃	1	2	yes	—
196	#121	C₂²×C₃	1	2	yes	—
197	#121	C₂²×C₃	1	2	yes	—
198	#121	C₂²×C₃	1	2	yes	—
199	#121	C₂²×C₃	1	1	yes	characteristic, complemented
200	#121	C₂²×C₃	1	1	yes	characteristic, complemented
201	#121	C₂²×C₃	1	4	yes	complemented
202	#121	C₂²×C₃	1	2	yes	complemented
203	#121	C₂²×C₃	1	2	yes	complemented
204	#121	C₂²×C₃	1	4	yes	complemented
205	#121	C₂²×C₃	1	4	yes	complemented
206	#120	C₂²×C₃	1	2	yes	—
207	#120	C₂²×C₃	1	4	yes	—
208	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
209	C₄×D₄	C₂²×C₃	1	4	yes	—
210	C₄×D₄	C₂²×C₃	1	2	yes	complemented
211	C₄×D₄	C₂²×C₃	1	2	yes	complemented
212	C₄×D₄	C₂²×C₃	1	2	yes	complemented
213	C₄×D₄	C₂²×C₃	1	2	yes	complemented
214	C₄×D₄	C₂²×C₃	1	2	yes	complemented
215	C₄×D₄	C₂²×C₃	1	2	yes	complemented
216	C₄×D₄	C₂²×C₃	1	2	yes	complemented
217	C₄×D₄	C₂²×C₃	1	4	yes	complemented
218	C₄×D₄	C₂²×C₃	1	4	yes	complemented
219	#117	C₂²×C₃	1	1	yes	characteristic
220	#117	C₂²×C₃	1	1	yes	characteristic
221	#117	C₂²×C₃	1	2	yes	—
222	#117	C₂²×C₃	1	1	yes	characteristic
223	#117	C₂²×C₃	1	2	yes	complemented
224	#117	C₂²×C₃	1	1	yes	characteristic, complemented
225	#117	C₂²×C₃	1	1	yes	characteristic, complemented
226	#117	C₂²×C₃	1	2	yes	complemented
227	#117	C₂²×C₃	1	4	yes	complemented
228	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
230	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
231	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
232	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
233	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
235	C₂×C₄²	C₂²×C₃	1	2	yes	complemented
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	4	1	no	—
240	C₂³×C₃	—	4	2	no	—
241	C₂³×C₃	—	4	2	no	—
242	C₂³×C₃	C₂⁴	1	1	yes	characteristic
243	C₂³×C₃	C₂⁴	1	4	yes	—
244	C₂³×C₃	C₂⁴	1	2	yes	—
245	C₂³×C₃	C₂⁴	1	1	yes	characteristic
246	C₂³×C₃	C₂⁴	1	1	yes	characteristic
247	C₃×Q₈	—	2	2	no	—
248	C₃×Q₈	—	4	4	no	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	8	no	—
251	C₃×D₄	—	2	4	no	—
252	C₃×D₄	—	2	4	no	—
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	2	no	—
255	C₃×D₄	—	4	4	no	—
256	C₃×D₄	—	4	2	no	—
257	C₃×D₄	—	4	4	no	—
258	C₃×D₄	—	4	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	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	4	4	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	—	4	4	no	—
270	C₂×C₃×C₄	—	4	4	no	—
271	C₂×C₃×C₄	#41	1	4	yes	complemented
272	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	2	yes	—
278	C₂×C₃×C₄	C₂⁴	1	2	yes	—
279	C₂×C₃×C₄	C₂⁴	1	2	yes	—
280	C₂×C₃×C₄	C₂⁴	1	4	yes	—
281	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
284	C₂⁴	C₂³×C₃	1	1	yes	characteristic
285	C₂⁴	C₂³×C₃	1	2	yes	—
286	#41	—	2	4	no	—
287	#41	—	4	8	no	—
288	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×Q₈	C₂³×C₃	1	4	yes	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	4	4	no	—
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	1	yes	characteristic
296	C₂×D₄	C₂³×C₃	1	2	yes	—
297	C₂×D₄	C₂³×C₃	1	4	yes	—
298	C₂×D₄	C₂³×C₃	1	2	yes	—
299	C₂×D₄	C₂³×C₃	1	4	yes	—
300	C₂×D₄	C₂³×C₃	1	4	yes	—
301	C₂×D₄	C₂³×C₃	1	4	yes	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
304	C₂²×C₄	C₂³×C₃	1	2	yes	—
305	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
306	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₃	1	2	yes	—
308	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
309	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
310	C₂²×C₄	C₂³×C₃	1	2	yes	—
311	C₂²×C₄	C₂³×C₃	1	2	yes	—
312	C₂²×C₄	C₂³×C₃	1	4	yes	—
313	C₂²×C₄	C₂³×C₃	1	4	yes	—
314	C₂²×C₄	C₂³×C₃	1	4	yes	—
315	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
316	C₄⋊C₄	C₂³×C₃	1	2	yes	—
317	C₄⋊C₄	C₂³×C₃	1	2	yes	—
318	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
319	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
320	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
321	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
322	C₄⋊C₄	C₂³×C₃	1	2	yes	—
323	C₄⋊C₄	C₂³×C₃	1	2	yes	—
324	C₄⋊C₄	C₂³×C₃	1	4	yes	—
325	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
326	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
327	C₄⋊C₄	C₂³×C₃	1	2	yes	—
328	C₄⋊C₄	C₂³×C₃	1	4	yes	—
329	C₄⋊C₄	C₂³×C₃	1	4	yes	—
330	C₄⋊C₄	C₂³×C₃	1	4	yes	—
331	C₄⋊C₄	C₂³×C₃	1	2	yes	—
332	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
333	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
334	C₂²⋊C₄	C₂³×C₃	1	2	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	4	yes	—
339	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
340	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
341	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
342	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
343	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
344	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
346	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
347	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
348	C₄²	C₂³×C₃	1	2	yes	—
349	C₄²	C₂³×C₃	1	2	yes	—
350	C₄²	C₂³×C₃	1	2	yes	—
351	C₄²	C₂³×C₃	1	2	yes	—
352	C₄²	C₂³×C₃	1	2	yes	—
353	C₄²	C₂³×C₃	1	4	yes	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	2	4	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	2	4	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	4	no	—
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	2	1	no	—
367	C₂²×C₃	—	4	4	no	—
368	C₂²×C₃	—	8	4	no	—
369	C₂²×C₃	C₂×#41	1	2	yes	—
370	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
371	C₂²×C₃	C₂⁵	1	1	yes	characteristic
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	C₂×#41	1	2	yes	—
383	C₃×C₄	C₂×#41	1	2	yes	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	C₂⁴×C₃	1	1	yes	characteristic
391	C₂³	C₂⁴×C₃	1	4	yes	—
392	C₂³	C₂⁴×C₃	1	2	yes	—
393	C₂³	C₂⁴×C₃	1	1	yes	characteristic
394	C₂³	C₂⁴×C₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	4	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	2	no	—
403	D₄	—	4	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	C₃×#41	1	4	yes	complemented
420	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
421	C₂×C₄	C₂⁴×C₃	1	2	yes	—
422	C₂×C₄	C₂⁴×C₃	1	2	yes	—
423	C₂×C₄	C₂⁴×C₃	1	2	yes	—
424	C₂×C₄	C₂⁴×C₃	1	2	yes	—
425	C₂×C₄	C₂⁴×C₃	1	2	yes	—
426	C₂×C₄	C₂⁴×C₃	1	2	yes	—
427	C₂×C₄	C₂⁴×C₃	1	2	yes	—
428	C₂×C₄	C₂⁴×C₃	1	4	yes	—
429	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
430	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
431	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
432	C₂×C₃	—	2	2	no	—
433	C₂×C₃	—	2	2	no	—
434	C₂×C₃	—	4	2	no	—
435	C₂×C₃	—	4	1	no	—
436	C₂×C₃	—	4	4	no	—
437	C₂×C₃	C₂²×#41	1	1	yes	characteristic
438	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₃	#585	1	1	yes	characteristic
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	8	4	no	—
455	C₂²	C₂×C₃×#41	1	2	yes	—
456	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
457	C₂²	C₂⁵×C₃	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	4	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	C₂×C₃×#41	1	2	yes	—
469	C₄	C₂×C₃×#41	1	2	yes	—
470	C₃	#3494	1	1	yes	characteristic, direct product factor, Sylow
471	C₂	—	2	2	no	—
472	C₂	—	2	2	no	—
473	C₂	—	4	1	no	—
474	C₂	—	4	4	no	—
475	C₂	—	4	2	no	—
476	C₂	C₂²×C₃×#41	1	1	yes	characteristic
477	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
478	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×#555	C₂	semidirect
2. C₃×#553	C₂	semidirect
3. C₃×#553	C₂	semidirect
4. C₃×#551	C₂	semidirect
5. C₃×#547	C₂	semidirect
6. C₃×#546	C₂	semidirect
7. C₃×#544	C₂	semidirect
8. C₃×#542	C₂	semidirect
9. C₃×#540	C₂	semidirect
10. C₃×#535	C₂	semidirect
11. C₃×#532	C₂	semidirect
12. C₃×#529	C₂	semidirect
13. C₃×#525	C₂	semidirect
14. C₂×C₃×#121	C₂	semidirect
15. C₃×#520	C₂	semidirect
16. C₃×#518	C₂	semidirect
17. C₂×C₃×#117	C₂	semidirect
18. #3494	C₃	direct (N × H)
20. C₂×C₃×#41	C₂²	semidirect
24. C₃×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₄⋊Q₈	C₂²	semidirect
26. C₃×#127	C₂²	semidirect
27. C₃×#126	C₂²	semidirect
28. C₃×#126	C₂²	semidirect
29. C₃×#125	C₂²	semidirect
30. C₃×#125	C₂²	semidirect
31. C₃×#124	C₂²	semidirect
32. C₃×#124	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
37. C₃×#123	C₂²	semidirect
38. C₃×#123	C₂²	semidirect
40. C₃×C₂²⋊Q₈	C₂²	semidirect
41. C₃×C₂²⋊Q₈	C₂²	semidirect
42. C₃×C₂²⋊Q₈	C₂²	semidirect
47. C₃×#121	C₂²	semidirect
48. C₃×#121	C₂²	semidirect
49. C₃×#121	C₂²	semidirect
50. C₃×#121	C₂²	semidirect
51. C₃×#121	C₂²	semidirect
52. C₃×#121	C₂²	semidirect
53. C₃×#121	C₂²	semidirect
56. C₃×C₄×Q₈	C₂²	semidirect
58. C₃×C₄×D₄	C₂²	semidirect
59. C₃×C₄×D₄	C₂²	semidirect
60. C₃×C₄×D₄	C₂²	semidirect
61. C₃×C₄×D₄	C₂²	semidirect
62. C₃×C₄×D₄	C₂²	semidirect
63. C₃×C₄×D₄	C₂²	semidirect
64. C₃×C₄×D₄	C₂²	semidirect
65. C₃×C₄×D₄	C₂²	semidirect
66. C₃×C₄×D₄	C₂²	semidirect
71. C₃×#117	C₂²	semidirect
72. C₃×#117	C₂²	semidirect
73. C₃×#117	C₂²	semidirect
74. C₃×#117	C₂²	semidirect
75. C₃×#117	C₂²	semidirect
77. C₂×C₃×C₄⋊C₄	C₂²	semidirect
78. C₂×C₃×C₄⋊C₄	C₂²	semidirect
79. C₂×C₃×C₄⋊C₄	C₂²	semidirect
83. C₂×C₃×C₄²	C₂²	semidirect
84. #555	C₂×C₃	semidirect
85. #553	C₂×C₃	semidirect
86. #553	C₂×C₃	semidirect
87. #551	C₂×C₃	semidirect
88. #547	C₂×C₃	semidirect
89. #546	C₂×C₃	semidirect
90. #544	C₂×C₃	semidirect
91. #542	C₂×C₃	semidirect
92. #540	C₂×C₃	semidirect
93. #535	C₂×C₃	semidirect
94. #532	C₂×C₃	semidirect
95. #529	C₂×C₃	semidirect
96. #525	C₂×C₃	semidirect
97. C₂×#121	C₂×C₃	semidirect
98. #520	C₂×C₃	semidirect
99. #518	C₂×C₃	semidirect
100. C₂×#117	C₂×C₃	semidirect
172. C₂×#41	C₂²×C₃	semidirect
176. C₄⋊Q₈	C₂²×C₃	semidirect
177. C₄⋊Q₈	C₂²×C₃	semidirect
178. #127	C₂²×C₃	semidirect
179. #126	C₂²×C₃	semidirect
180. #126	C₂²×C₃	semidirect
181. #125	C₂²×C₃	semidirect
182. #125	C₂²×C₃	semidirect
183. #124	C₂²×C₃	semidirect
184. #124	C₂²×C₃	semidirect
185. #124	C₂²×C₃	semidirect
187. #123	C₂²×C₃	semidirect
188. #123	C₂²×C₃	semidirect
189. #123	C₂²×C₃	semidirect
190. #123	C₂²×C₃	semidirect
192. C₂²⋊Q₈	C₂²×C₃	semidirect
193. C₂²⋊Q₈	C₂²×C₃	semidirect
194. C₂²⋊Q₈	C₂²×C₃	semidirect
199. #121	C₂²×C₃	semidirect
200. #121	C₂²×C₃	semidirect
201. #121	C₂²×C₃	semidirect
202. #121	C₂²×C₃	semidirect
203. #121	C₂²×C₃	semidirect
204. #121	C₂²×C₃	semidirect
205. #121	C₂²×C₃	semidirect
208. C₄×Q₈	C₂²×C₃	semidirect
210. C₄×D₄	C₂²×C₃	semidirect
211. C₄×D₄	C₂²×C₃	semidirect
212. C₄×D₄	C₂²×C₃	semidirect
213. C₄×D₄	C₂²×C₃	semidirect
214. C₄×D₄	C₂²×C₃	semidirect
215. C₄×D₄	C₂²×C₃	semidirect
216. C₄×D₄	C₂²×C₃	semidirect
217. C₄×D₄	C₂²×C₃	semidirect
218. C₄×D₄	C₂²×C₃	semidirect
223. #117	C₂²×C₃	semidirect
224. #117	C₂²×C₃	semidirect
225. #117	C₂²×C₃	semidirect
226. #117	C₂²×C₃	semidirect
227. #117	C₂²×C₃	semidirect
229. C₂×C₄⋊C₄	C₂²×C₃	semidirect
230. C₂×C₄⋊C₄	C₂²×C₃	semidirect
231. C₂×C₄⋊C₄	C₂²×C₃	semidirect
235. C₂×C₄²	C₂²×C₃	semidirect
271. C₂×C₃×C₄	#41	semidirect
419. C₂×C₄	C₃×#41	semidirect
470. C₃	#3494	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×#555	2
C₃×#553	2
C₃×#551	2
C₃×#547	2
C₃×#546	2
C₃×#544	2
C₃×#542	2
C₃×#540	2
C₃×#535	2
C₃×#532	2
C₃×#529	2
C₃×#525	2
C₂×C₃×#121	2
C₃×#520	2
C₃×#518	2
C₂×C₃×#117	2
#3494	3

Subgroups — C3×#3494 #87378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3494 #87378