Subgroups — C₃×#83796 #11859566

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5828	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5234	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5128	C₂	1	2	yes	maximal, complemented
6	C₃×#5127	C₂	1	2	yes	maximal, complemented
7	C₃×#5122	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5111	C₂	1	2	yes	maximal, complemented
9	C₃×C₈×#67	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2933	—	3	1	no	maximal
13	#83796	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
16	C₃²×#131	—	2	4	no	—
17	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃²×M₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
21	C₃×#946	C₄	1	1	yes	characteristic
22	C₃×#946	C₄	1	1	yes	characteristic
23	C₃×#938	C₄	1	1	yes	characteristic
24	C₃×#938	C₄	1	1	yes	characteristic
25	C₃×#937	C₄	1	2	yes	—
26	C₃×#935	C₄	1	2	yes	—
27	C₃×C₄×#67	C₂²	1	2	yes	—
28	C₃×C₄×#67	C₂²	1	2	yes	—
29	C₃×#926	C₂²	1	1	yes	characteristic
30	C₂×C₃×#208	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₃×D₃×M₁₆	—	2	4	no	—
33	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
34	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
35	C₃×#830	C₂²	1	2	yes	complemented
36	C₃×#830	C₂²	1	2	yes	complemented
37	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×#815	C₂²	1	2	yes	complemented
42	C₃×Dic₃⋊C₈	C₂²	1	2	yes	complemented
43	C₃×Dic₃⋊C₈	C₂²	1	2	yes	complemented
44	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
45	C₂×C₃×#131	—	2	1	no	—
46	C₂×C₃×#131	D₃	1	1	yes	characteristic, complemented
47	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×C₃×M₁₆	—	3	1	no	—
49	C₃×#525	—	3	1	no	—
50	#5828	C₂×C₃	1	1	yes	characteristic
51	C₂×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×#436	—	3	2	no	—
53	C₃×#435	—	3	2	no	—
54	C₃×#435	—	3	2	no	—
55	C₃×C₈×D₄	—	3	2	no	—
56	C₃×#424	—	3	1	no	—
57	C₃×#408	—	3	1	no	—
58	C₂×C₃×C₂²⋊C₈	—	3	1	no	—
59	C₃×#405	—	3	1	no	—
60	#5234	C₂×C₃	1	1	yes	characteristic, complemented
61	#5128	C₂×C₃	1	2	yes	complemented
62	#5127	C₂×C₃	1	2	yes	complemented
63	#5122	C₂×C₃	1	1	yes	characteristic, complemented
64	#5111	C₂×C₃	1	2	yes	complemented
65	C₈×#67	C₂×C₃	1	2	yes	complemented
66	C₂×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
67	#5102	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
69	C₃²×#41	—	2	2	no	—
70	C₃²×#41	—	2	2	no	—
71	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
73	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₃²×C₄	C₂³	1	2	yes	—
75	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
76	C₂×C₃×#67	C₂×C₄	1	2	yes	—
77	C₂×C₃×#67	C₂×C₄	1	2	yes	—
78	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄×D₃	—	2	2	no	—
80	C₂×C₃×C₄×D₃	—	2	2	no	—
81	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
85	C₃²×M₁₆	—	2	4	no	—
86	C₃²×M₁₆	D₄	1	4	yes	complemented
87	C₂×C₃²×C₈	—	2	2	no	—
88	C₂×C₃²×C₈	—	2	4	no	—
89	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
90	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃²×C₈	C₂³	1	2	yes	—
92	C₃×#217	C₂×C₄	1	2	yes	—
93	C₃×#217	C₂×C₄	1	2	yes	—
94	C₃×#217	C₂×C₄	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
96	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
97	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
98	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
99	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
100	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
101	C₃×C₄×Dic₃	C₂³	1	2	yes	—
102	C₃×#208	—	2	2	no	—
103	C₂×C₃×C₃⋊C₈	—	2	2	no	—
104	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
105	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
107	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
108	C₃×D₃×C₈	—	2	4	no	—
109	#2933	—	3	1	no	Sylow
110	C₂×C₃×#41	—	2	1	no	—
111	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
112	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂³×C₃×C₄	—	3	1	no	—
114	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
115	C₃×#131	—	2	8	no	—
116	C₃×#131	—	2	4	no	—
117	C₃×#131	—	2	4	no	—
118	C₂×C₃×M₁₆	—	2	1	no	—
119	C₂×C₃×M₁₆	—	2	2	no	—
120	C₂×C₃×M₁₆	—	3	1	no	—
121	C₂×C₃×M₁₆	—	3	2	no	—
122	C₂×C₃×M₁₆	—	6	4	no	—
123	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
124	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	complemented
125	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	complemented
127	C₂²×C₃×C₈	—	2	1	no	—
128	C₂²×C₃×C₈	—	2	2	no	—
129	C₂²×C₃×C₈	—	3	1	no	—
130	C₂²×C₃×C₈	—	3	2	no	—
131	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₈	C₂×D₃	1	2	yes	complemented
133	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
134	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	complemented
135	C₃×#123	—	3	2	no	—
136	C₃×C₂²⋊Q₈	—	3	1	no	—
137	C₃×C₂²⋊Q₈	—	3	1	no	—
138	C₃×#121	—	3	1	no	—
139	C₃×#121	—	3	1	no	—
140	C₃×#120	—	3	2	no	—
141	C₃×C₄×D₄	—	3	2	no	—
142	C₃×C₄×D₄	—	3	2	no	—
143	C₃×#117	—	3	1	no	—
144	#946	C₃×C₄	1	1	yes	characteristic
145	#946	C₃×C₄	1	1	yes	characteristic
146	#938	C₃×C₄	1	1	yes	characteristic
147	#938	C₃×C₄	1	1	yes	characteristic
148	#937	C₃×C₄	1	2	yes	—
149	#935	C₃×C₄	1	2	yes	—
150	C₄×#67	C₂²×C₃	1	2	yes	—
151	C₄×#67	C₂²×C₃	1	2	yes	—
152	#926	C₂²×C₃	1	1	yes	characteristic
153	C₂×#208	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
155	D₃×M₁₆	—	2	4	no	—
156	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
157	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
158	C₃×C₄⋊C₈	—	3	2	no	—
159	C₃×C₄⋊C₈	—	3	2	no	—
160	C₃×C₂²⋊C₈	—	3	2	no	—
161	C₃×C₂²⋊C₈	—	3	2	no	—
162	C₃×C₂²⋊C₈	—	3	1	no	—
163	C₃×C₂²⋊C₈	—	3	1	no	—
164	C₃×C₂²⋊C₈	—	3	1	no	—
165	C₃×C₂²⋊C₈	—	3	1	no	—
166	C₃×#97	—	3	2	no	—
167	C₃×C₄×C₈	—	3	2	no	—
168	#830	C₂²×C₃	1	2	yes	complemented
169	#830	C₂²×C₃	1	2	yes	complemented
170	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
172	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
173	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
174	#815	C₂²×C₃	1	2	yes	complemented
175	Dic₃⋊C₈	C₂²×C₃	1	2	yes	complemented
176	Dic₃⋊C₈	C₂²×C₃	1	2	yes	complemented
177	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
178	C₂³×C₃²	C₂²×C₄	1	2	yes	—
179	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₃×D₃	—	2	2	no	—
181	C₂²×C₃×D₃	—	2	2	no	—
182	C₂²×C₃×D₃	—	4	1	no	—
183	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
185	C₃²×Q₈	—	2	2	no	—
186	C₃²×D₄	—	2	4	no	—
187	C₃²×D₄	—	2	2	no	—
188	C₂×C₃²×C₄	—	2	2	no	—
189	C₂×C₃²×C₄	—	2	2	no	—
190	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
191	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
193	C₂×C₃²×C₄	#41	1	2	yes	—
194	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
195	C₃×#67	—	2	4	no	—
196	C₃×#67	—	4	2	no	—
197	C₂×C₃×Dic₃	—	2	2	no	—
198	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
199	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
200	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
202	C₃×C₄×D₃	—	2	2	no	—
203	C₃×C₄×D₃	—	2	2	no	—
204	C₃×C₄×D₃	—	2	1	no	—
205	C₃×C₄×D₃	—	2	1	no	—
206	C₃×C₄×D₃	—	2	1	no	—
207	C₃×C₄×D₃	—	2	1	no	—
208	C₃²×C₈	—	2	1	no	—
209	C₃²×C₈	—	2	1	no	—
210	C₃²×C₈	C₂×D₄	1	4	yes	—
211	C₃×C₃⋊C₈	—	2	2	no	—
212	C₃×C₃⋊C₈	—	2	1	no	—
213	C₃×C₃⋊C₈	—	2	1	no	—
214	C₂×#131	C₃×D₃	1	1	yes	characteristic, complemented
215	C₂²×M₁₆	—	3	1	no	—
216	#525	—	3	1	no	—
217	#436	—	3	2	no	—
218	#435	—	3	2	no	—
219	#435	—	3	2	no	—
220	C₈×D₄	—	3	2	no	—
221	#424	—	3	1	no	—
222	#408	—	3	1	no	—
223	C₂×C₂²⋊C₈	—	3	1	no	—
224	#405	—	3	1	no	—
225	C₂⁴×C₃	—	3	1	no	—
226	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
227	C₃×#41	—	2	4	no	—
228	C₃×#41	—	2	4	no	—
229	C₃×#41	—	2	2	no	—
230	C₃×#41	—	2	2	no	—
231	C₃×#41	—	2	2	no	—
232	C₃×#41	—	2	2	no	—
233	C₂×C₃×Q₈	—	2	1	no	—
234	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
235	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
236	C₂×C₃×D₄	—	2	2	no	—
237	C₂×C₃×D₄	—	2	1	no	—
238	C₂×C₃×D₄	—	3	2	no	—
239	C₂×C₃×D₄	—	3	2	no	—
240	C₂×C₃×D₄	C₄×D₃	1	2	yes	—
241	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
242	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
243	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
244	C₂²×C₃×C₄	—	2	2	no	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	—	3	1	no	—
247	C₂²×C₃×C₄	—	3	1	no	—
248	C₂²×C₃×C₄	—	3	1	no	—
249	C₂²×C₃×C₄	—	3	1	no	—
250	C₂²×C₃×C₄	—	3	1	no	—
251	C₂²×C₃×C₄	—	6	2	no	—
252	C₂²×C₃×C₄	—	6	2	no	—
253	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
254	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
256	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
257	C₂×#67	C₂×C₃×C₄	1	2	yes	—
258	C₂×#67	C₂×C₃×C₄	1	2	yes	—
259	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
260	C₂×C₄×D₃	—	2	2	no	—
261	C₂×C₄×D₃	—	2	2	no	—
262	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
263	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
264	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
266	C₃×M₁₆	—	2	8	no	—
267	C₃×M₁₆	—	2	4	no	—
268	C₃×M₁₆	—	2	4	no	—
269	C₃×M₁₆	—	2	4	no	—
270	C₃×M₁₆	—	6	2	no	—
271	C₃×M₁₆	—	6	4	no	—
272	C₃×M₁₆	#67	1	4	yes	complemented
273	C₃×M₁₆	C₃×D₄	1	4	yes	complemented
274	C₂×C₃×C₈	—	2	4	no	—
275	C₂×C₃×C₈	—	2	8	no	—
276	C₂×C₃×C₈	—	2	2	no	—
277	C₂×C₃×C₈	—	2	2	no	—
278	C₂×C₃×C₈	—	2	4	no	—
279	C₂×C₃×C₈	—	2	4	no	—
280	C₂×C₃×C₈	—	2	1	no	—
281	C₂×C₃×C₈	—	2	1	no	—
282	C₂×C₃×C₈	—	2	2	no	—
283	C₂×C₃×C₈	—	3	1	no	—
284	C₂×C₃×C₈	—	3	1	no	—
285	C₂×C₃×C₈	—	3	2	no	—
286	C₂×C₃×C₈	—	6	2	no	—
287	C₂×C₃×C₈	—	6	4	no	—
288	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
290	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
291	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
294	C₃×C₄⋊C₄	—	3	2	no	—
295	C₃×C₄⋊C₄	—	3	2	no	—
296	C₃×C₄⋊C₄	—	3	1	no	—
297	C₃×C₄⋊C₄	—	3	1	no	—
298	C₃×C₂²⋊C₄	—	3	2	no	—
299	C₃×C₂²⋊C₄	—	3	2	no	—
300	C₃×C₂²⋊C₄	—	3	2	no	—
301	C₃×C₂²⋊C₄	—	3	2	no	—
302	C₃×C₂²⋊C₄	—	3	2	no	—
303	C₃×C₄²	—	3	2	no	—
304	#217	C₂×C₃×C₄	1	2	yes	—
305	#217	C₂×C₃×C₄	1	2	yes	—
306	#217	C₂×C₃×C₄	1	2	yes	—
307	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
308	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
309	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
310	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
311	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
312	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
313	C₄×Dic₃	C₂³×C₃	1	2	yes	—
314	#208	—	2	2	no	—
315	C₂×C₃⋊C₈	—	2	2	no	—
316	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
317	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
318	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
319	ΓL(1,𝔽₂₅)	—	2	4	no	—
320	D₃×C₈	—	2	4	no	—
321	C₂²×C₃²	—	2	2	no	—
322	C₂²×C₃²	—	2	1	no	—
323	C₂²×C₃²	—	2	1	no	—
324	C₂²×C₃²	—	2	2	no	—
325	C₂²×C₃²	—	2	2	no	—
326	C₂²×C₃²	C₄×D₄	1	2	yes	—
327	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
328	C₂×C₃×D₃	—	2	1	no	—
329	C₂×C₃×D₃	—	2	1	no	—
330	C₂×C₃×D₃	—	2	1	no	—
331	C₂×C₃×D₃	—	2	1	no	—
332	C₂×C₃×D₃	—	2	1	no	—
333	C₂×C₃×D₃	—	4	4	no	—
334	C₂×C₃×D₃	#131	1	2	yes	complemented
335	C₃²×C₄	—	2	2	no	—
336	C₃²×C₄	C₄×D₄	1	2	yes	—
337	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
338	C₃²×C₄	C₂×#41	1	1	yes	characteristic
339	C₃×Dic₃	—	2	1	no	—
340	C₃×Dic₃	—	2	1	no	—
341	C₃×Dic₃	—	2	2	no	—
342	C₃×Dic₃	—	2	2	no	—
343	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
344	C₂³×C₄	—	3	1	no	—
345	#131	—	2	4	no	—
346	C₂×M₁₆	—	3	1	no	—
347	C₂×M₁₆	—	3	2	no	—
348	C₂×M₁₆	—	6	4	no	—
349	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
350	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	complemented
351	C₂²×C₈	—	3	1	no	—
352	C₂²×C₈	—	3	2	no	—
353	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
354	C₂²×C₈	C₂×C₃×D₃	1	2	yes	complemented
355	#123	—	3	2	no	—
356	C₂²⋊Q₈	—	3	1	no	—
357	C₂²⋊Q₈	—	3	1	no	—
358	#121	—	3	1	no	—
359	#121	—	3	1	no	—
360	#120	—	3	2	no	—
361	C₄×D₄	—	3	2	no	—
362	C₄×D₄	—	3	2	no	—
363	#117	—	3	1	no	—
364	C₄⋊C₈	—	3	2	no	—
365	C₄⋊C₈	—	3	2	no	—
366	C₂²⋊C₈	—	3	2	no	—
367	C₂²⋊C₈	—	3	2	no	—
368	C₂²⋊C₈	—	3	1	no	—
369	C₂²⋊C₈	—	3	1	no	—
370	C₂²⋊C₈	—	3	1	no	—
371	C₂²⋊C₈	—	3	1	no	—
372	#97	—	3	2	no	—
373	C₄×C₈	—	3	2	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	2	1	no	—
376	C₂³×C₃	—	3	1	no	—
377	C₂³×C₃	—	3	1	no	—
378	C₂³×C₃	—	6	2	no	—
379	C₂³×C₃	—	6	2	no	—
380	C₂³×C₃	—	12	1	no	—
381	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
382	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
383	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
384	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
385	C₂²×D₃	—	2	2	no	—
386	C₂²×D₃	—	2	2	no	—
387	C₂²×D₃	—	4	1	no	—
388	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
389	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
390	C₃×Q₈	—	2	4	no	—
391	C₃×Q₈	—	2	2	no	—
392	C₃×Q₈	—	2	2	no	—
393	C₃×D₄	—	2	8	no	—
394	C₃×D₄	—	2	4	no	—
395	C₃×D₄	—	2	4	no	—
396	C₃×D₄	—	2	4	no	—
397	C₃×D₄	—	2	2	no	—
398	C₃×D₄	—	2	2	no	—
399	C₃×D₄	—	6	4	no	—
400	C₃×D₄	—	12	2	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	2	4	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	3	2	no	—
413	C₂×C₃×C₄	—	3	2	no	—
414	C₂×C₃×C₄	—	3	1	no	—
415	C₂×C₃×C₄	—	3	1	no	—
416	C₂×C₃×C₄	—	6	2	no	—
417	C₂×C₃×C₄	—	6	2	no	—
418	C₂×C₃×C₄	—	6	2	no	—
419	C₂×C₃×C₄	—	6	1	no	—
420	C₂×C₃×C₄	—	6	1	no	—
421	C₂×C₃×C₄	—	6	1	no	—
422	C₂×C₃×C₄	—	6	1	no	—
423	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
424	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
425	C₂×C₃×C₄	#235	1	2	yes	—
426	C₂×C₃×C₄	C₂×#67	1	2	yes	—
427	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
428	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
429	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
430	C₂×C₃×C₄	C₃×#41	1	2	yes	—
431	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
433	#67	—	2	4	no	—
434	#67	—	4	2	no	—
435	C₂×Dic₃	—	2	2	no	—
436	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
437	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
438	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
439	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
440	C₄×D₃	—	2	2	no	—
441	C₄×D₃	—	2	2	no	—
442	C₄×D₃	—	2	1	no	—
443	C₄×D₃	—	2	1	no	—
444	C₄×D₃	—	2	1	no	—
445	C₄×D₃	—	2	1	no	—
446	C₃×C₈	—	2	2	no	—
447	C₃×C₈	—	2	2	no	—
448	C₃×C₈	—	2	1	no	—
449	C₃×C₈	—	2	1	no	—
450	C₃×C₈	—	2	1	no	—
451	C₃×C₈	—	2	1	no	—
452	C₃×C₈	—	2	4	no	—
453	C₃×C₈	—	6	1	no	—
454	C₃×C₈	—	6	1	no	—
455	C₃×C₈	—	6	2	no	—
456	C₃×C₈	C₂×#67	1	4	yes	—
457	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
458	C₃⋊C₈	—	2	2	no	—
459	C₃⋊C₈	—	2	1	no	—
460	C₃⋊C₈	—	2	1	no	—
461	C₂×C₃²	—	2	2	no	—
462	C₂×C₃²	—	4	2	no	—
463	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
464	C₂×C₃²	C₂×#131	1	1	yes	characteristic
465	C₂×C₃²	#568	1	1	yes	characteristic
466	C₃×D₃	—	2	2	no	—
467	C₃×D₃	—	4	1	no	—
468	C₂⁴	—	3	1	no	—
469	#41	—	2	2	no	—
470	#41	—	2	2	no	—
471	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
472	C₂×D₄	—	3	2	no	—
473	C₂×D₄	—	3	2	no	—
474	C₂×D₄	C₃×C₄×D₃	1	2	yes	—
475	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
476	C₂²×C₄	—	3	1	no	—
477	C₂²×C₄	—	3	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	3	1	no	—
480	C₂²×C₄	—	3	1	no	—
481	C₂²×C₄	—	6	2	no	—
482	C₂²×C₄	—	6	2	no	—
483	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
484	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
485	M₁₆	—	2	4	no	—
486	M₁₆	—	6	2	no	—
487	M₁₆	—	6	4	no	—
488	M₁₆	C₃×#67	1	4	yes	complemented
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	4	no	—
491	C₂×C₈	—	3	1	no	—
492	C₂×C₈	—	3	1	no	—
493	C₂×C₈	—	3	2	no	—
494	C₂×C₈	—	6	2	no	—
495	C₂×C₈	—	6	4	no	—
496	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
497	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
498	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
499	C₄⋊C₄	—	3	1	no	—
500	C₄⋊C₄	—	3	1	no	—
501	C₄⋊C₄	—	3	2	no	—
502	C₄⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	2	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₄²	—	3	2	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	4	no	—
514	C₂²×C₃	—	2	2	no	—
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	—	2	2	no	—
517	C₂²×C₃	—	2	2	no	—
518	C₂²×C₃	—	2	2	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	3	2	no	—
523	C₂²×C₃	—	4	1	no	—
524	C₂²×C₃	—	4	1	no	—
525	C₂²×C₃	—	4	2	no	—
526	C₂²×C₃	—	4	2	no	—
527	C₂²×C₃	—	6	1	no	—
528	C₂²×C₃	—	6	1	no	—
529	C₂²×C₃	—	6	1	no	—
530	C₂²×C₃	—	6	1	no	—
531	C₂²×C₃	—	6	1	no	—
532	C₂²×C₃	—	12	4	no	—
533	C₂²×C₃	C₄×#67	1	2	yes	—
534	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
535	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
536	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	2	1	no	—
540	C₂×D₃	—	2	1	no	—
541	C₂×D₃	—	2	1	no	—
542	C₂×D₃	—	4	4	no	—
543	C₂×D₃	C₃×#131	1	2	yes	complemented
544	C₃×C₄	—	2	4	no	—
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	—	2	2	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	6	2	no	—
551	C₃×C₄	—	6	2	no	—
552	C₃×C₄	—	6	1	no	—
553	C₃×C₄	—	6	1	no	—
554	C₃×C₄	C₄×#67	1	2	yes	—
555	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
556	C₃×C₄	C₂×#235	1	1	yes	characteristic
557	C₃×C₄	C₂²×#67	1	1	yes	characteristic
558	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
559	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
560	Dic₃	—	2	2	no	—
561	Dic₃	—	2	2	no	—
562	Dic₃	—	2	1	no	—
563	Dic₃	—	2	1	no	—
564	C₃²	#2933	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	3	1	no	—
566	C₂³	—	3	1	no	—
567	C₂³	—	6	2	no	—
568	C₂³	—	6	2	no	—
569	C₂³	—	12	1	no	—
570	C₂³	C₂×C₃×C₄×D₃	1	2	yes	—
571	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
572	Q₈	—	2	2	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	2	no	—
575	D₄	—	6	4	no	—
576	D₄	—	12	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	3	2	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	1	no	—
583	C₂×C₄	—	6	2	no	—
584	C₂×C₄	—	6	2	no	—
585	C₂×C₄	—	6	2	no	—
586	C₂×C₄	—	6	1	no	—
587	C₂×C₄	—	6	1	no	—
588	C₂×C₄	—	6	1	no	—
589	C₂×C₄	—	6	1	no	—
590	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
591	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
592	C₂×C₄	C₃×#235	1	2	yes	—
593	C₂×C₄	C₂×C₃×#67	1	2	yes	—
594	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
595	C₈	—	2	1	no	—
596	C₈	—	2	1	no	—
597	C₈	—	6	1	no	—
598	C₈	—	6	1	no	—
599	C₈	—	6	2	no	—
600	C₈	C₂×C₃×#67	1	4	yes	—
601	C₂×C₃	—	2	2	no	—
602	C₂×C₃	—	2	2	no	—
603	C₂×C₃	—	2	1	no	—
604	C₂×C₃	—	2	1	no	—
605	C₂×C₃	—	2	1	no	—
606	C₂×C₃	—	4	2	no	—
607	C₂×C₃	—	4	4	no	—
608	C₂×C₃	—	4	2	no	—
609	C₂×C₃	—	4	2	no	—
610	C₂×C₃	—	6	2	no	—
611	C₂×C₃	—	12	1	no	—
612	C₂×C₃	D₃×#131	1	1	yes	characteristic
613	C₂×C₃	#5750	1	1	yes	characteristic
614	C₂×C₃	C₂×C₄×#67	1	1	yes	characteristic
615	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
616	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
617	C₂×C₃	C₃×#568	1	1	yes	characteristic
618	D₃	—	2	2	no	—
619	D₃	—	4	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	3	2	no	—
626	C₂²	—	6	1	no	—
627	C₂²	—	6	1	no	—
628	C₂²	—	6	1	no	—
629	C₂²	—	6	1	no	—
630	C₂²	—	6	1	no	—
631	C₂²	—	12	4	no	—
632	C₂²	C₃×C₄×#67	1	2	yes	—
633	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	6	2	no	—
636	C₄	—	6	2	no	—
637	C₄	—	6	1	no	—
638	C₄	—	6	1	no	—
639	C₄	C₃×C₄×#67	1	2	yes	—
640	C₄	C₂×C₃×#235	1	1	yes	characteristic
641	C₄	C₂²×C₃×#67	1	1	yes	characteristic
642	C₃	—	2	1	no	—
643	C₃	#83796	1	1	yes	characteristic, direct product factor
644	C₃	C₃×#2933	1	1	yes	characteristic, complemented
645	C₂	—	2	2	no	—
646	C₂	—	4	2	no	—
647	C₂	—	6	2	no	—
648	C₂	—	12	1	no	—
649	C₂	C₃×D₃×#131	1	1	yes	characteristic
650	C₂	C₃×#5750	1	1	yes	characteristic
651	C₂	C₂×C₃×C₄×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#131	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5828	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₃
hypocenter	C₃	C₃×#2933
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#131	C₂	semidirect
3. C₂×C₃×D₃×M₁₆	C₂	semidirect
4. C₃×#5234	C₂	semidirect
5. C₃×#5128	C₂	semidirect
6. C₃×#5127	C₂	semidirect
7. C₃×#5122	C₂	semidirect
8. C₃×#5111	C₂	semidirect
9. C₃×C₈×#67	C₂	semidirect
10. C₂×C₃×(C₂×D₃)⋊C₈	C₂	semidirect
11. C₃×#5102	C₂	semidirect
13. #83796	C₃	direct (N × H)
18. C₂×C₃²×M₁₆	C₂²	semidirect
20. C₂²×C₃²×C₈	C₂²	semidirect
35. C₃×#830	C₂²	semidirect
36. C₃×#830	C₂²	semidirect
41. C₃×#815	C₂²	semidirect
42. C₃×Dic₃⋊C₈	C₂²	semidirect
43. C₃×Dic₃⋊C₈	C₂²	semidirect
44. C₃×C₈×Dic₃	C₂²	semidirect
46. C₂×C₃×#131	D₃	semidirect
47. C₂×C₃×#131	C₂×C₃	semidirect
51. C₂×D₃×M₁₆	C₂×C₃	semidirect
60. #5234	C₂×C₃	semidirect
61. #5128	C₂×C₃	semidirect
62. #5127	C₂×C₃	semidirect
63. #5122	C₂×C₃	semidirect
64. #5111	C₂×C₃	semidirect
65. C₈×#67	C₂×C₃	semidirect
66. C₂×(C₂×D₃)⋊C₈	C₂×C₃	semidirect
67. #5102	C₂×C₃	semidirect
86. C₃²×M₁₆	D₄	semidirect
124. C₂×C₃×M₁₆	C₂×D₃	semidirect
126. C₂×C₃×M₁₆	C₂²×C₃	semidirect
132. C₂²×C₃×C₈	C₂×D₃	semidirect
134. C₂²×C₃×C₈	C₂²×C₃	semidirect
168. #830	C₂²×C₃	semidirect
169. #830	C₂²×C₃	semidirect
174. #815	C₂²×C₃	semidirect
175. Dic₃⋊C₈	C₂²×C₃	semidirect
176. Dic₃⋊C₈	C₂²×C₃	semidirect
177. C₈×Dic₃	C₂²×C₃	semidirect
214. C₂×#131	C₃×D₃	semidirect
272. C₃×M₁₆	#67	semidirect
273. C₃×M₁₆	C₃×D₄	semidirect
334. C₂×C₃×D₃	#131	semidirect
350. C₂×M₁₆	C₂×C₃×D₃	semidirect
354. C₂²×C₈	C₂×C₃×D₃	semidirect
488. M₁₆	C₃×#67	semidirect
543. C₂×D₃	C₃×#131	semidirect
564. C₃²	#2933	semidirect
643. C₃	#83796	direct (N × H)
644. C₃	C₃×#2933	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃²×#131	2
C₃×#5828	2
C₂×C₃×D₃×M₁₆	2
C₃×#5234	2
C₃×#5128	2
C₃×#5127	2
C₃×#5122	2
C₃×#5111	2
C₃×C₈×#67	2
C₂×C₃×(C₂×D₃)⋊C₈	2
C₃×#5102	2
C₃×#2933	3
#83796	3

Subgroups — C3×#83796 #11859566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83796 #11859566