Subgroups — C₃×#3505 #87389

Order 384.

1152 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#553	C₂	1	2	yes	maximal, complemented
2	C₃×#553	C₂	1	4	yes	maximal, complemented
3	C₃×#552	C₂	1	2	yes	maximal, complemented
4	C₃×#551	C₂	1	4	yes	maximal, complemented
5	C₃×#548	C₂	1	2	yes	maximal, complemented
6	C₃×#546	C₂	1	2	yes	maximal, complemented
7	C₃×#539	C₂	1	2	yes	maximal, complemented
8	C₃×#538	C₂	1	2	yes	maximal, complemented
9	C₃×#534	C₂	1	2	yes	maximal, complemented
10	C₃×#529	C₂	1	2	yes	maximal, complemented
11	C₃×#525	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#518	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#3505	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×#41	C₂²	1	2	yes	complemented
18	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×D₄	C₂²	1	2	yes	—
21	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃×#126	C₂²	1	4	yes	complemented
25	C₃×#126	C₂²	1	4	yes	complemented
26	C₃×#126	C₂²	1	4	yes	complemented
27	C₃×#125	C₂²	1	2	yes	complemented
28	C₃×#125	C₂²	1	4	yes	complemented
29	C₃×#124	C₂²	1	2	yes	complemented
30	C₃×#124	C₂²	1	4	yes	complemented
31	C₃×#123	C₂²	1	4	yes	—
32	C₃×#123	C₂²	1	4	yes	complemented
33	C₃×#123	C₂²	1	4	yes	complemented
34	C₃×#123	C₂²	1	4	yes	complemented
35	C₃×#123	C₂²	1	4	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
42	C₃×#121	C₂²	1	2	yes	—
43	C₃×#121	C₂²	1	2	yes	—
44	C₃×#121	C₂²	1	2	yes	complemented
45	C₃×#121	C₂²	1	2	yes	complemented
46	C₃×#121	C₂²	1	2	yes	complemented
47	C₃×#121	C₂²	1	4	yes	complemented
48	C₃×#121	C₂²	1	4	yes	complemented
49	C₃×#121	C₂²	1	4	yes	complemented
50	C₃×#120	C₂²	1	4	yes	—
51	C₃×#120	C₂²	1	4	yes	complemented
52	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
53	C₃×C₄×D₄	C₂²	1	2	yes	—
54	C₃×C₄×D₄	C₂²	1	2	yes	—
55	C₃×C₄×D₄	C₂²	1	2	yes	complemented
56	C₃×C₄×D₄	C₂²	1	2	yes	complemented
57	C₃×C₄×D₄	C₂²	1	4	yes	complemented
58	C₃×C₄×D₄	C₂²	1	4	yes	complemented
59	C₃×C₄×D₄	C₂²	1	4	yes	complemented
60	C₃×C₄×D₄	C₂²	1	4	yes	complemented
61	C₃×C₄×D₄	C₂²	1	4	yes	complemented
62	C₃×C₄×D₄	C₂²	1	2	yes	complemented
63	C₃×#117	C₂²	1	4	yes	complemented
64	C₃×#117	C₂²	1	2	yes	complemented
65	C₃×#117	C₂²	1	4	yes	complemented
66	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
70	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
74	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
75	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
76	#553	C₂×C₃	1	2	yes	complemented
77	#553	C₂×C₃	1	4	yes	complemented
78	#552	C₂×C₃	1	2	yes	complemented
79	#551	C₂×C₃	1	4	yes	complemented
80	#548	C₂×C₃	1	2	yes	complemented
81	#546	C₂×C₃	1	2	yes	complemented
82	#539	C₂×C₃	1	2	yes	complemented
83	#538	C₂×C₃	1	2	yes	complemented
84	#534	C₂×C₃	1	2	yes	complemented
85	#529	C₂×C₃	1	2	yes	complemented
86	#525	C₂×C₃	1	2	yes	complemented
87	C₂×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂×#121	C₂×C₃	1	1	yes	characteristic, complemented
89	#518	C₂×C₃	1	2	yes	complemented
90	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂⁴×C₃	C₂³	1	2	yes	—
92	C₂⁴×C₃	C₂³	1	1	yes	characteristic
93	C₂⁴×C₃	C₂³	1	1	yes	characteristic
94	C₃×#41	—	4	4	no	—
95	C₂×C₃×Q₈	—	4	2	no	—
96	C₂×C₃×Q₈	C₂³	1	2	yes	—
97	C₂×C₃×Q₈	C₂³	1	2	yes	—
98	C₂×C₃×D₄	—	2	4	no	—
99	C₂×C₃×D₄	—	2	8	no	—
100	C₂×C₃×D₄	—	4	2	no	—
101	C₂×C₃×D₄	C₂³	1	2	yes	—
102	C₂×C₃×D₄	C₂³	1	4	yes	—
103	C₂×C₃×D₄	C₂³	1	2	yes	—
104	C₂×C₃×D₄	C₂³	1	4	yes	—
105	C₂×C₃×D₄	C₂³	1	2	yes	—
106	C₂×C₃×D₄	C₂³	1	4	yes	—
107	C₂×C₃×D₄	C₂³	1	4	yes	—
108	C₂×C₃×D₄	C₂³	1	2	yes	—
109	C₂²×C₃×C₄	—	4	2	no	—
110	C₂²×C₃×C₄	—	4	2	no	—
111	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
112	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
113	C₂²×C₃×C₄	C₂³	1	2	yes	—
114	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
115	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃×C₄	C₂³	1	2	yes	—
117	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃×C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
123	C₂²×C₃×C₄	C₂³	1	4	yes	—
124	C₂²×C₃×C₄	C₂³	1	4	yes	—
125	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
126	C₂²×C₃×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	2	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	4	yes	—
134	C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₃×C₂²⋊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	4	yes	—
147	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₃×C₄²	C₂³	1	2	yes	—
154	C₃×C₄²	C₂³	1	2	yes	—
155	C₃×C₄²	C₂³	1	4	yes	—
156	C₃×C₄²	C₂³	1	4	yes	—
157	C₂×#41	C₂²×C₃	1	2	yes	complemented
158	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
160	C₂²×D₄	C₂²×C₃	1	2	yes	—
161	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
163	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
164	#126	C₂²×C₃	1	4	yes	complemented
165	#126	C₂²×C₃	1	4	yes	complemented
166	#126	C₂²×C₃	1	4	yes	complemented
167	#125	C₂²×C₃	1	2	yes	complemented
168	#125	C₂²×C₃	1	4	yes	complemented
169	#124	C₂²×C₃	1	2	yes	complemented
170	#124	C₂²×C₃	1	4	yes	complemented
171	#123	C₂²×C₃	1	4	yes	—
172	#123	C₂²×C₃	1	4	yes	complemented
173	#123	C₂²×C₃	1	4	yes	complemented
174	#123	C₂²×C₃	1	4	yes	complemented
175	#123	C₂²×C₃	1	4	yes	complemented
176	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
177	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
178	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
179	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
180	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
181	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
182	#121	C₂²×C₃	1	2	yes	—
183	#121	C₂²×C₃	1	2	yes	—
184	#121	C₂²×C₃	1	2	yes	complemented
185	#121	C₂²×C₃	1	2	yes	complemented
186	#121	C₂²×C₃	1	2	yes	complemented
187	#121	C₂²×C₃	1	4	yes	complemented
188	#121	C₂²×C₃	1	4	yes	complemented
189	#121	C₂²×C₃	1	4	yes	complemented
190	#120	C₂²×C₃	1	4	yes	—
191	#120	C₂²×C₃	1	4	yes	complemented
192	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
193	C₄×D₄	C₂²×C₃	1	2	yes	—
194	C₄×D₄	C₂²×C₃	1	2	yes	—
195	C₄×D₄	C₂²×C₃	1	2	yes	complemented
196	C₄×D₄	C₂²×C₃	1	2	yes	complemented
197	C₄×D₄	C₂²×C₃	1	4	yes	complemented
198	C₄×D₄	C₂²×C₃	1	4	yes	complemented
199	C₄×D₄	C₂²×C₃	1	4	yes	complemented
200	C₄×D₄	C₂²×C₃	1	4	yes	complemented
201	C₄×D₄	C₂²×C₃	1	4	yes	complemented
202	C₄×D₄	C₂²×C₃	1	2	yes	complemented
203	#117	C₂²×C₃	1	4	yes	complemented
204	#117	C₂²×C₃	1	2	yes	complemented
205	#117	C₂²×C₃	1	4	yes	complemented
206	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
207	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
209	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
210	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
213	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
214	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
215	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₂³×C₃	—	2	2	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	4	1	no	—
219	C₂³×C₃	—	4	1	no	—
220	C₂³×C₃	—	4	1	no	—
221	C₂³×C₃	—	4	1	no	—
222	C₂³×C₃	—	4	2	no	—
223	C₂³×C₃	—	4	2	no	—
224	C₂³×C₃	#41	1	4	yes	complemented
225	C₂³×C₃	C₂⁴	1	2	yes	—
226	C₂³×C₃	C₂⁴	1	4	yes	—
227	C₂³×C₃	C₂⁴	1	1	yes	characteristic
228	C₂³×C₃	C₂⁴	1	1	yes	characteristic
229	C₂³×C₃	C₂⁴	1	1	yes	characteristic
230	C₃×Q₈	—	2	4	no	—
231	C₃×Q₈	—	4	2	no	—
232	C₃×D₄	—	2	4	no	—
233	C₃×D₄	—	2	8	no	—
234	C₃×D₄	—	2	4	no	—
235	C₃×D₄	—	2	8	no	—
236	C₃×D₄	—	2	4	no	—
237	C₃×D₄	—	4	2	no	—
238	C₃×D₄	—	4	4	no	—
239	C₃×D₄	—	4	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	—	4	1	no	—
251	C₂×C₃×C₄	—	4	1	no	—
252	C₂×C₃×C₄	—	4	4	no	—
253	C₂×C₃×C₄	—	4	2	no	—
254	C₂×C₃×C₄	—	4	2	no	—
255	C₂×C₃×C₄	—	4	4	no	—
256	C₂×C₃×C₄	C₂⁴	1	2	yes	—
257	C₂×C₃×C₄	C₂⁴	1	2	yes	—
258	C₂×C₃×C₄	C₂⁴	1	4	yes	—
259	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂⁴	1	2	yes	—
261	C₂×C₃×C₄	C₂⁴	1	4	yes	—
262	C₂×C₃×C₄	C₂⁴	1	4	yes	—
263	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
266	C₂⁴	C₂³×C₃	1	2	yes	—
267	C₂⁴	C₂³×C₃	1	1	yes	characteristic
268	C₂⁴	C₂³×C₃	1	1	yes	characteristic
269	#41	—	4	4	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	C₂³×C₃	1	2	yes	—
272	C₂×Q₈	C₂³×C₃	1	2	yes	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	8	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	C₂³×C₃	1	2	yes	—
277	C₂×D₄	C₂³×C₃	1	4	yes	—
278	C₂×D₄	C₂³×C₃	1	2	yes	—
279	C₂×D₄	C₂³×C₃	1	4	yes	—
280	C₂×D₄	C₂³×C₃	1	2	yes	—
281	C₂×D₄	C₂³×C₃	1	4	yes	—
282	C₂×D₄	C₂³×C₃	1	4	yes	—
283	C₂×D₄	C₂³×C₃	1	2	yes	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₃	1	2	yes	—
289	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₃	1	2	yes	—
292	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₃	1	2	yes	—
294	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₃	1	2	yes	—
296	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₃	1	4	yes	—
299	C₂²×C₄	C₂³×C₃	1	4	yes	—
300	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₃	1	2	yes	—
302	C₄⋊C₄	C₂³×C₃	1	2	yes	—
303	C₄⋊C₄	C₂³×C₃	1	4	yes	—
304	C₄⋊C₄	C₂³×C₃	1	2	yes	—
305	C₄⋊C₄	C₂³×C₃	1	2	yes	—
306	C₄⋊C₄	C₂³×C₃	1	2	yes	—
307	C₄⋊C₄	C₂³×C₃	1	2	yes	—
308	C₄⋊C₄	C₂³×C₃	1	4	yes	—
309	C₄⋊C₄	C₂³×C₃	1	2	yes	—
310	C₄⋊C₄	C₂³×C₃	1	4	yes	—
311	C₄⋊C₄	C₂³×C₃	1	4	yes	—
312	C₄⋊C₄	C₂³×C₃	1	4	yes	—
313	C₄⋊C₄	C₂³×C₃	1	4	yes	—
314	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
315	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
316	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
317	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
318	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
319	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
320	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
321	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
322	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
323	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
324	C₂²⋊C₄	C₂³×C₃	1	4	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	C₄²	C₂³×C₃	1	2	yes	—
329	C₄²	C₂³×C₃	1	2	yes	—
330	C₄²	C₂³×C₃	1	4	yes	—
331	C₄²	C₂³×C₃	1	4	yes	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	2	1	no	—
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	4	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	4	4	no	—
345	C₂²×C₃	—	4	4	no	—
346	C₂²×C₃	—	8	4	no	—
347	C₂²×C₃	C₂×#41	1	2	yes	—
348	C₂²×C₃	C₂×#41	1	2	yes	—
349	C₂²×C₃	C₂×#41	1	2	yes	—
350	C₂²×C₃	C₂⁵	1	1	yes	characteristic
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	4	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₃×#41	1	4	yes	complemented
370	C₂³	C₂⁴×C₃	1	2	yes	—
371	C₂³	C₂⁴×C₃	1	4	yes	—
372	C₂³	C₂⁴×C₃	1	1	yes	characteristic
373	C₂³	C₂⁴×C₃	1	1	yes	characteristic
374	C₂³	C₂⁴×C₃	1	1	yes	characteristic
375	Q₈	—	2	4	no	—
376	Q₈	—	4	2	no	—
377	D₄	—	2	4	no	—
378	D₄	—	2	8	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	8	no	—
381	D₄	—	2	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	C₂⁴×C₃	1	2	yes	—
402	C₂×C₄	C₂⁴×C₃	1	2	yes	—
403	C₂×C₄	C₂⁴×C₃	1	4	yes	—
404	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
405	C₂×C₄	C₂⁴×C₃	1	2	yes	—
406	C₂×C₄	C₂⁴×C₃	1	4	yes	—
407	C₂×C₄	C₂⁴×C₃	1	4	yes	—
408	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
409	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
410	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
411	C₂×C₃	—	2	2	no	—
412	C₂×C₃	—	2	2	no	—
413	C₂×C₃	—	2	2	no	—
414	C₂×C₃	—	4	2	no	—
415	C₂×C₃	—	4	4	no	—
416	C₂×C₃	C₂²×#41	1	1	yes	characteristic
417	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×C₃	#585	1	1	yes	characteristic
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	4	no	—
434	C₂²	C₂×C₃×#41	1	2	yes	—
435	C₂²	C₂×C₃×#41	1	2	yes	—
436	C₂²	C₂×C₃×#41	1	2	yes	—
437	C₂²	C₂⁵×C₃	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
448	C₃	#3505	1	1	yes	characteristic, direct product factor, Sylow
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	2	no	—
452	C₂	—	4	2	no	—
453	C₂	—	4	4	no	—
454	C₂	C₂²×C₃×#41	1	1	yes	characteristic
455	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
456	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×#553	C₂	semidirect
2. C₃×#553	C₂	semidirect
3. C₃×#552	C₂	semidirect
4. C₃×#551	C₂	semidirect
5. C₃×#548	C₂	semidirect
6. C₃×#546	C₂	semidirect
7. C₃×#539	C₂	semidirect
8. C₃×#538	C₂	semidirect
9. C₃×#534	C₂	semidirect
10. C₃×#529	C₂	semidirect
11. C₃×#525	C₂	semidirect
12. C₂×C₃×C₂²⋊Q₈	C₂	semidirect
13. C₂×C₃×#121	C₂	semidirect
14. C₃×#518	C₂	semidirect
15. C₂×C₃×C₄×D₄	C₂	semidirect
16. #3505	C₃	direct (N × H)
17. C₂×C₃×#41	C₂²	semidirect
18. C₂²×C₃×Q₈	C₂²	semidirect
21. C₂²×C₃×D₄	C₂²	semidirect
23. C₂³×C₃×C₄	C₂²	semidirect
24. C₃×#126	C₂²	semidirect
25. C₃×#126	C₂²	semidirect
26. C₃×#126	C₂²	semidirect
27. C₃×#125	C₂²	semidirect
28. C₃×#125	C₂²	semidirect
29. C₃×#124	C₂²	semidirect
30. C₃×#124	C₂²	semidirect
32. C₃×#123	C₂²	semidirect
33. C₃×#123	C₂²	semidirect
34. C₃×#123	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₂²⋊Q₈	C₂²	semidirect
40. C₃×C₂²⋊Q₈	C₂²	semidirect
41. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×#121	C₂²	semidirect
45. C₃×#121	C₂²	semidirect
46. C₃×#121	C₂²	semidirect
47. C₃×#121	C₂²	semidirect
48. C₃×#121	C₂²	semidirect
49. C₃×#121	C₂²	semidirect
51. C₃×#120	C₂²	semidirect
52. C₃×C₄×Q₈	C₂²	semidirect
55. C₃×C₄×D₄	C₂²	semidirect
56. C₃×C₄×D₄	C₂²	semidirect
57. C₃×C₄×D₄	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×#117	C₂²	semidirect
64. C₃×#117	C₂²	semidirect
65. C₃×#117	C₂²	semidirect
66. C₂×C₃×C₄⋊C₄	C₂²	semidirect
67. C₂×C₃×C₄⋊C₄	C₂²	semidirect
68. C₂×C₃×C₄⋊C₄	C₂²	semidirect
69. C₂×C₃×C₄⋊C₄	C₂²	semidirect
72. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
73. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
74. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
75. C₂×C₃×C₄²	C₂²	semidirect
76. #553	C₂×C₃	semidirect
77. #553	C₂×C₃	semidirect
78. #552	C₂×C₃	semidirect
79. #551	C₂×C₃	semidirect
80. #548	C₂×C₃	semidirect
81. #546	C₂×C₃	semidirect
82. #539	C₂×C₃	semidirect
83. #538	C₂×C₃	semidirect
84. #534	C₂×C₃	semidirect
85. #529	C₂×C₃	semidirect
86. #525	C₂×C₃	semidirect
87. C₂×C₂²⋊Q₈	C₂×C₃	semidirect
88. C₂×#121	C₂×C₃	semidirect
89. #518	C₂×C₃	semidirect
90. C₂×C₄×D₄	C₂×C₃	semidirect
157. C₂×#41	C₂²×C₃	semidirect
158. C₂²×Q₈	C₂²×C₃	semidirect
161. C₂²×D₄	C₂²×C₃	semidirect
163. C₂³×C₄	C₂²×C₃	semidirect
164. #126	C₂²×C₃	semidirect
165. #126	C₂²×C₃	semidirect
166. #126	C₂²×C₃	semidirect
167. #125	C₂²×C₃	semidirect
168. #125	C₂²×C₃	semidirect
169. #124	C₂²×C₃	semidirect
170. #124	C₂²×C₃	semidirect
172. #123	C₂²×C₃	semidirect
173. #123	C₂²×C₃	semidirect
174. #123	C₂²×C₃	semidirect
175. #123	C₂²×C₃	semidirect
176. C₂²⋊Q₈	C₂²×C₃	semidirect
177. C₂²⋊Q₈	C₂²×C₃	semidirect
178. C₂²⋊Q₈	C₂²×C₃	semidirect
179. C₂²⋊Q₈	C₂²×C₃	semidirect
180. C₂²⋊Q₈	C₂²×C₃	semidirect
181. C₂²⋊Q₈	C₂²×C₃	semidirect
184. #121	C₂²×C₃	semidirect
185. #121	C₂²×C₃	semidirect
186. #121	C₂²×C₃	semidirect
187. #121	C₂²×C₃	semidirect
188. #121	C₂²×C₃	semidirect
189. #121	C₂²×C₃	semidirect
191. #120	C₂²×C₃	semidirect
192. C₄×Q₈	C₂²×C₃	semidirect
195. C₄×D₄	C₂²×C₃	semidirect
196. C₄×D₄	C₂²×C₃	semidirect
197. C₄×D₄	C₂²×C₃	semidirect
198. C₄×D₄	C₂²×C₃	semidirect
199. C₄×D₄	C₂²×C₃	semidirect
200. C₄×D₄	C₂²×C₃	semidirect
201. C₄×D₄	C₂²×C₃	semidirect
202. C₄×D₄	C₂²×C₃	semidirect
203. #117	C₂²×C₃	semidirect
204. #117	C₂²×C₃	semidirect
205. #117	C₂²×C₃	semidirect
206. C₂×C₄⋊C₄	C₂²×C₃	semidirect
207. C₂×C₄⋊C₄	C₂²×C₃	semidirect
208. C₂×C₄⋊C₄	C₂²×C₃	semidirect
209. C₂×C₄⋊C₄	C₂²×C₃	semidirect
212. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
213. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
214. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
215. C₂×C₄²	C₂²×C₃	semidirect
224. C₂³×C₃	#41	semidirect
369. C₂³	C₃×#41	semidirect
448. C₃	#3505	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×#553	2
C₃×#552	2
C₃×#551	2
C₃×#548	2
C₃×#546	2
C₃×#539	2
C₃×#538	2
C₃×#534	2
C₃×#529	2
C₃×#525	2
C₂×C₃×C₂²⋊Q₈	2
C₂×C₃×#121	2
C₃×#518	2
C₂×C₃×C₄×D₄	2
#3505	3

Subgroups — C3×#3505 #87389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3505 #87389