Subgroups — C₂×C₃×#5532 #11903304

Order 1152.

2645 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#930	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5532	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#895	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#893	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#888	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#885	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#884	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#875	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×#872	C₂	1	2	yes	maximal, complemented
13	C₂×C₃×#555	—	3	1	no	maximal
14	C₂×#5532	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#67	C₂²	1	2	yes	—
18	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
20	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
21	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
23	C₃²×#117	C₂²	1	8	yes	complemented
24	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃²×C₄²	C₂²	1	2	yes	—
28	C₂×C₃×#217	C₂²	1	1	yes	characteristic
29	C₃×#930	C₂²	1	8	yes	complemented
30	C₃×C₄×#67	C₂²	1	8	yes	complemented
31	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
36	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
40	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
41	C₃×#895	C₂²	1	8	yes	complemented
42	C₃×#893	C₂²	1	8	yes	complemented
43	C₃×#892	C₂²	1	8	yes	complemented
44	C₃×#888	C₂²	1	8	yes	complemented
45	C₃×#885	C₂²	1	16	yes	complemented
46	C₃×#884	C₂²	1	16	yes	complemented
47	C₃×#875	C₂²	1	16	yes	complemented
48	C₃×#872	C₂²	1	16	yes	complemented
49	C₃×#555	—	3	16	no	—
50	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
51	C₂×C₃×#124	—	3	2	no	—
52	C₂×C₃×#124	—	3	2	no	—
53	C₂×C₃×#121	—	3	1	no	—
54	C₂×C₃×#121	—	3	1	no	—
55	C₂×C₃×#121	—	3	2	no	—
56	C₂×C₃×C₄×D₄	—	3	1	no	—
57	C₂×C₃×C₄×D₄	—	3	1	no	—
58	C₂×C₃×#117	—	2	1	no	—
59	C₂×C₃×#117	—	3	1	no	—
60	C₂×C₃×#117	—	3	2	no	—
61	C₂×C₃×#117	D₃	1	1	yes	characteristic, complemented
62	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×#930	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×C₄×#67	C₂×C₃	1	1	yes	characteristic, complemented
65	#5532	C₂×C₃	1	16	yes	direct product factor
66	C₂×#895	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×#893	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#892	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂×#888	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂×#885	C₂×C₃	1	2	yes	complemented
71	C₂×#884	C₂×C₃	1	2	yes	complemented
72	C₂×#875	C₂×C₃	1	2	yes	complemented
73	C₂×#872	C₂×C₃	1	2	yes	complemented
74	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
75	C₂³×C₃×D₃	C₂³	1	2	yes	—
76	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
77	C₂²×C₃²×C₄	—	2	4	no	—
78	C₂²×C₃²×C₄	C₂³	1	2	yes	—
79	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂³	1	2	yes	—
81	C₂²×C₃²×C₄	C₂³	1	4	yes	—
82	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
83	C₂×C₃×#67	—	2	4	no	—
84	C₂×C₃×#67	—	4	4	no	—
85	C₂×C₃×#67	C₂³	1	4	yes	—
86	C₂×C₃×#67	C₂³	1	8	yes	—
87	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
88	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
89	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
90	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
91	C₂×C₃×D₁₂	—	2	4	no	—
92	C₂×C₃×D₁₂	—	4	4	no	—
93	C₂×C₃×D₁₂	C₂³	1	4	yes	—
94	C₂×C₃×D₁₂	C₂³	1	8	yes	—
95	C₂×C₃×C₄×D₃	—	2	4	no	—
96	C₂×C₃×C₄×D₃	—	2	8	no	—
97	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
98	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
99	C₂×C₃×Dic₆	—	4	4	no	—
100	C₂×C₃×Dic₆	C₂³	1	8	yes	—
101	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
102	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
103	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₃²×C₄²	C₂³	1	8	yes	—
105	C₃×#217	C₂³	1	4	yes	—
106	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
107	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
108	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
109	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
110	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
111	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
112	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
113	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
114	C₃×C₄×Dic₃	C₂³	1	8	yes	—
115	C₃×C₄×Dic₃	C₂³	1	4	yes	—
116	C₂×#555	—	3	1	no	Sylow
117	C₂²×C₃×Q₈	—	3	2	no	—
118	C₂²×C₃×D₄	—	3	1	no	—
119	C₂²×C₃×D₄	—	3	2	no	—
120	C₂²×C₃×D₄	—	3	1	no	—
121	C₂²×C₃×D₄	—	3	2	no	—
122	C₂³×C₃×C₄	—	2	1	no	—
123	C₂³×C₃×C₄	—	3	2	no	—
124	C₂³×C₃×C₄	—	3	1	no	—
125	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
126	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
128	C₂²×#67	C₂²×C₃	1	2	yes	—
129	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
130	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
131	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
132	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
133	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
134	C₃×C₄⋊Q₈	—	3	8	no	—
135	C₃×#124	—	3	16	no	—
136	C₃×#124	—	3	16	no	—
137	C₃×#121	—	3	8	no	—
138	C₃×#121	—	3	8	no	—
139	C₃×#121	—	3	16	no	—
140	C₃×C₄×D₄	—	3	8	no	—
141	C₃×C₄×D₄	—	3	8	no	—
142	C₃×#117	—	2	8	no	—
143	C₃×#117	—	3	8	no	—
144	C₃×#117	—	3	16	no	—
145	C₃×#117	C₂×D₃	1	8	yes	complemented
146	C₃×#117	C₂²×C₃	1	8	yes	complemented
147	C₂×C₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₃×C₄⋊C₄	—	3	1	no	—
150	C₂×C₃×C₄⋊C₄	—	3	2	no	—
151	C₂×C₃×C₄⋊C₄	—	3	1	no	—
152	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
157	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
158	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
159	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
160	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
161	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
162	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
163	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
165	C₂×C₃×C₄²	—	2	2	no	—
166	C₂×C₃×C₄²	—	3	2	no	—
167	C₂×C₃×C₄²	—	3	1	no	—
168	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
169	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
170	C₂×#217	C₂²×C₃	1	1	yes	characteristic
171	#930	C₂²×C₃	1	8	yes	complemented
172	C₄×#67	C₂²×C₃	1	8	yes	complemented
173	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
174	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
175	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
177	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
178	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
179	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
181	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
182	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
183	#895	C₂²×C₃	1	8	yes	complemented
184	#893	C₂²×C₃	1	8	yes	complemented
185	#892	C₂²×C₃	1	8	yes	complemented
186	#888	C₂²×C₃	1	8	yes	complemented
187	#885	C₂²×C₃	1	16	yes	complemented
188	#884	C₂²×C₃	1	16	yes	complemented
189	#875	C₂²×C₃	1	16	yes	complemented
190	#872	C₂²×C₃	1	16	yes	complemented
191	C₂³×C₃²	—	2	2	no	—
192	C₂³×C₃²	—	2	2	no	—
193	C₂³×C₃²	—	2	2	no	—
194	C₂³×C₃²	C₂⁴	1	2	yes	—
195	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
196	C₂²×C₃×D₃	—	2	2	no	—
197	C₂²×C₃×D₃	—	2	4	no	—
198	C₂²×C₃×D₃	—	2	4	no	—
199	C₂²×C₃×D₃	—	2	2	no	—
200	C₂²×C₃×D₃	—	2	2	no	—
201	C₂²×C₃×D₃	—	2	4	no	—
202	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
203	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
204	C₂×C₃²×C₄	—	2	2	no	—
205	C₂×C₃²×C₄	—	2	8	no	—
206	C₂×C₃²×C₄	—	2	4	no	—
207	C₂×C₃²×C₄	—	2	4	no	—
208	C₂×C₃²×C₄	#41	1	4	yes	—
209	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
210	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
211	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
212	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
213	C₃×#67	—	2	8	no	—
214	C₃×#67	—	4	8	no	—
215	C₂×C₃×Dic₃	—	2	2	no	—
216	C₂×C₃×Dic₃	—	2	2	no	—
217	C₂×C₃×Dic₃	—	2	4	no	—
218	C₂×C₃×Dic₃	#41	1	4	yes	—
219	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
220	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
221	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
222	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
223	C₃×D₁₂	—	2	8	no	—
224	C₃×D₁₂	—	4	8	no	—
225	C₃×C₄×D₃	—	2	8	no	—
226	C₃×C₄×D₃	—	2	16	no	—
227	C₃×Dic₆	—	4	8	no	—
228	#555	—	3	16	no	—
229	C₂×C₄⋊Q₈	—	3	1	no	—
230	C₂×#124	—	3	2	no	—
231	C₂×#124	—	3	2	no	—
232	C₂×#121	—	3	1	no	—
233	C₂×#121	—	3	1	no	—
234	C₂×#121	—	3	2	no	—
235	C₂×C₄×D₄	—	3	1	no	—
236	C₂×C₄×D₄	—	3	1	no	—
237	C₂×#117	—	3	1	no	—
238	C₂×#117	—	3	2	no	—
239	C₂×#117	C₃×D₃	1	1	yes	characteristic, complemented
240	C₂⁴×C₃	—	2	1	no	—
241	C₂⁴×C₃	—	3	1	no	—
242	C₂⁴×C₃	—	3	2	no	—
243	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
244	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
245	C₂³×D₃	C₂³×C₃	1	2	yes	—
246	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₃×Q₈	—	3	8	no	—
248	C₂×C₃×Q₈	—	12	4	no	—
249	C₂×C₃×D₄	—	3	4	no	—
250	C₂×C₃×D₄	—	3	8	no	—
251	C₂×C₃×D₄	—	3	4	no	—
252	C₂×C₃×D₄	—	3	8	no	—
253	C₂×C₃×D₄	—	6	4	no	—
254	C₂×C₃×D₄	—	6	4	no	—
255	C₂×C₃×D₄	—	12	4	no	—
256	C₂×C₃×D₄	—	12	4	no	—
257	C₂²×C₃×C₄	—	2	8	no	—
258	C₂²×C₃×C₄	—	2	4	no	—
259	C₂²×C₃×C₄	—	2	4	no	—
260	C₂²×C₃×C₄	—	2	1	no	—
261	C₂²×C₃×C₄	—	2	1	no	—
262	C₂²×C₃×C₄	—	2	4	no	—
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	2	2	no	—
265	C₂²×C₃×C₄	—	3	1	no	—
266	C₂²×C₃×C₄	—	3	1	no	—
267	C₂²×C₃×C₄	—	3	1	no	—
268	C₂²×C₃×C₄	—	3	2	no	—
269	C₂²×C₃×C₄	—	3	8	no	—
270	C₂²×C₃×C₄	—	3	4	no	—
271	C₂²×C₃×C₄	—	6	8	no	—
272	C₂²×C₃×C₄	—	6	4	no	—
273	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
274	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
275	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
277	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
279	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
281	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
282	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
283	C₂×#67	—	2	4	no	—
284	C₂×#67	—	4	4	no	—
285	C₂×#67	C₂³×C₃	1	4	yes	—
286	C₂×#67	C₂³×C₃	1	8	yes	—
287	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
288	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
289	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
290	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
291	C₂×D₁₂	—	2	4	no	—
292	C₂×D₁₂	—	4	4	no	—
293	C₂×D₁₂	C₂³×C₃	1	4	yes	—
294	C₂×D₁₂	C₂³×C₃	1	8	yes	—
295	C₂×C₄×D₃	—	2	4	no	—
296	C₂×C₄×D₃	—	2	8	no	—
297	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
298	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
299	C₂×Dic₆	—	4	4	no	—
300	C₂×Dic₆	C₂³×C₃	1	8	yes	—
301	C₃×C₄⋊C₄	—	2	4	no	—
302	C₃×C₄⋊C₄	—	2	4	no	—
303	C₃×C₄⋊C₄	—	3	4	no	—
304	C₃×C₄⋊C₄	—	3	8	no	—
305	C₃×C₄⋊C₄	—	3	4	no	—
306	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
307	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
308	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
309	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
310	C₃×C₂²⋊C₄	—	2	8	no	—
311	C₃×C₂²⋊C₄	—	3	4	no	—
312	C₃×C₂²⋊C₄	—	3	8	no	—
313	C₃×C₂²⋊C₄	—	3	8	no	—
314	C₃×C₂²⋊C₄	—	3	8	no	—
315	C₃×C₂²⋊C₄	—	3	8	no	—
316	C₃×C₂²⋊C₄	—	3	4	no	—
317	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
318	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
319	C₃×C₄²	—	2	8	no	—
320	C₃×C₄²	—	3	8	no	—
321	C₃×C₄²	—	3	4	no	—
322	C₃×C₄²	C₂²×D₃	1	8	yes	—
323	C₃×C₄²	C₂³×C₃	1	8	yes	—
324	#217	C₂³×C₃	1	4	yes	—
325	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
326	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
327	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
328	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
329	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
330	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
331	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
332	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
333	C₄×Dic₃	C₂³×C₃	1	8	yes	—
334	C₄×Dic₃	C₂³×C₃	1	4	yes	—
335	C₂²×C₃²	—	2	2	no	—
336	C₂²×C₃²	—	2	2	no	—
337	C₂²×C₃²	—	2	2	no	—
338	C₂²×C₃²	—	4	4	no	—
339	C₂²×C₃²	C₂×#41	1	2	yes	—
340	C₂²×C₃²	C₂×#41	1	2	yes	—
341	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
342	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
343	C₂×C₃×D₃	—	2	2	no	—
344	C₂×C₃×D₃	—	2	4	no	—
345	C₂×C₃×D₃	—	2	4	no	—
346	C₂×C₃×D₃	—	2	2	no	—
347	C₂×C₃×D₃	—	2	2	no	—
348	C₂×C₃×D₃	—	2	4	no	—
349	C₂×C₃×D₃	—	4	8	no	—
350	C₂×C₃×D₃	—	4	4	no	—
351	C₃²×C₄	—	2	2	no	—
352	C₃²×C₄	—	2	4	no	—
353	C₃²×C₄	—	2	4	no	—
354	C₃²×C₄	C₂×#41	1	4	yes	—
355	C₃×Dic₃	—	2	2	no	—
356	C₃×Dic₃	—	2	2	no	—
357	C₃×Dic₃	—	2	4	no	—
358	C₃×Dic₃	C₂×#41	1	4	yes	—
359	C₂²×Q₈	—	3	2	no	—
360	C₂²×D₄	—	3	1	no	—
361	C₂²×D₄	—	3	2	no	—
362	C₂²×D₄	—	3	1	no	—
363	C₂²×D₄	—	3	2	no	—
364	C₂³×C₄	—	3	2	no	—
365	C₂³×C₄	—	3	1	no	—
366	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
367	C₄⋊Q₈	—	3	8	no	—
368	#124	—	3	16	no	—
369	#124	—	3	16	no	—
370	#121	—	3	8	no	—
371	#121	—	3	8	no	—
372	#121	—	3	16	no	—
373	C₄×D₄	—	3	8	no	—
374	C₄×D₄	—	3	8	no	—
375	#117	—	3	8	no	—
376	#117	—	3	16	no	—
377	#117	C₂×C₃×D₃	1	8	yes	complemented
378	C₂×C₄⋊C₄	—	3	1	no	—
379	C₂×C₄⋊C₄	—	3	2	no	—
380	C₂×C₄⋊C₄	—	3	1	no	—
381	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	—	3	1	no	—
384	C₂×C₂²⋊C₄	—	3	2	no	—
385	C₂×C₂²⋊C₄	—	3	2	no	—
386	C₂×C₂²⋊C₄	—	3	2	no	—
387	C₂×C₂²⋊C₄	—	3	2	no	—
388	C₂×C₂²⋊C₄	—	3	1	no	—
389	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
390	C₂×C₄²	—	3	2	no	—
391	C₂×C₄²	—	3	1	no	—
392	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
393	C₂³×C₃	—	2	4	no	—
394	C₂³×C₃	—	2	2	no	—
395	C₂³×C₃	—	2	2	no	—
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	2	no	—
398	C₂³×C₃	—	2	2	no	—
399	C₂³×C₃	—	2	2	no	—
400	C₂³×C₃	—	2	1	no	—
401	C₂³×C₃	—	2	2	no	—
402	C₂³×C₃	—	3	2	no	—
403	C₂³×C₃	—	3	4	no	—
404	C₂³×C₃	—	4	2	no	—
405	C₂³×C₃	—	4	2	no	—
406	C₂³×C₃	—	6	2	no	—
407	C₂³×C₃	—	6	4	no	—
408	C₂³×C₃	—	6	4	no	—
409	C₂³×C₃	—	6	2	no	—
410	C₂³×C₃	—	6	2	no	—
411	C₂³×C₃	—	6	4	no	—
412	C₂³×C₃	C₂³×D₃	1	2	yes	—
413	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
414	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
415	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
416	C₂²×D₃	—	2	2	no	—
417	C₂²×D₃	—	2	4	no	—
418	C₂²×D₃	—	2	4	no	—
419	C₂²×D₃	—	2	2	no	—
420	C₂²×D₃	—	2	2	no	—
421	C₂²×D₃	—	2	4	no	—
422	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
423	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
424	C₃×Q₈	—	12	8	no	—
425	C₃×D₄	—	6	8	no	—
426	C₃×D₄	—	6	8	no	—
427	C₃×D₄	—	12	8	no	—
428	C₃×D₄	—	12	8	no	—
429	C₂×C₃×C₄	—	2	4	no	—
430	C₂×C₃×C₄	—	2	16	no	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	—	2	4	no	—
433	C₂×C₃×C₄	—	2	4	no	—
434	C₂×C₃×C₄	—	2	4	no	—
435	C₂×C₃×C₄	—	2	2	no	—
436	C₂×C₃×C₄	—	2	4	no	—
437	C₂×C₃×C₄	—	2	8	no	—
438	C₂×C₃×C₄	—	2	8	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	2	no	—
441	C₂×C₃×C₄	—	2	4	no	—
442	C₂×C₃×C₄	—	2	4	no	—
443	C₂×C₃×C₄	—	2	4	no	—
444	C₂×C₃×C₄	—	3	4	no	—
445	C₂×C₃×C₄	—	3	2	no	—
446	C₂×C₃×C₄	—	3	2	no	—
447	C₂×C₃×C₄	—	3	2	no	—
448	C₂×C₃×C₄	—	3	4	no	—
449	C₂×C₃×C₄	—	4	4	no	—
450	C₂×C₃×C₄	—	4	4	no	—
451	C₂×C₃×C₄	—	6	16	no	—
452	C₂×C₃×C₄	—	6	2	no	—
453	C₂×C₃×C₄	—	6	4	no	—
454	C₂×C₃×C₄	—	6	2	no	—
455	C₂×C₃×C₄	—	6	8	no	—
456	C₂×C₃×C₄	#235	1	4	yes	—
457	C₂×C₃×C₄	C₃×#41	1	4	yes	—
458	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
459	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
460	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
461	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
462	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
463	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
464	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
465	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
466	#67	—	2	8	no	—
467	#67	—	4	8	no	—
468	C₂×Dic₃	—	2	2	no	—
469	C₂×Dic₃	—	2	2	no	—
470	C₂×Dic₃	—	2	4	no	—
471	C₂×Dic₃	C₃×#41	1	4	yes	—
472	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
473	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
474	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
475	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
476	D₁₂	—	2	8	no	—
477	D₁₂	—	4	8	no	—
478	C₄×D₃	—	2	8	no	—
479	C₄×D₃	—	2	16	no	—
480	Dic₆	—	4	8	no	—
481	C₂×C₃²	—	4	2	no	—
482	C₂×C₃²	#555	1	4	yes	complemented
483	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
484	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
485	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	C₃×D₃	—	4	4	no	—
487	C₃×D₃	—	4	2	no	—
488	C₂⁴	—	3	1	no	—
489	C₂⁴	—	3	2	no	—
490	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
491	C₂×Q₈	—	3	8	no	—
492	C₂×Q₈	—	12	4	no	—
493	C₂×D₄	—	3	4	no	—
494	C₂×D₄	—	3	8	no	—
495	C₂×D₄	—	3	4	no	—
496	C₂×D₄	—	3	8	no	—
497	C₂×D₄	—	6	4	no	—
498	C₂×D₄	—	6	4	no	—
499	C₂×D₄	—	12	4	no	—
500	C₂×D₄	—	12	4	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	3	1	no	—
503	C₂²×C₄	—	3	1	no	—
504	C₂²×C₄	—	3	1	no	—
505	C₂²×C₄	—	3	2	no	—
506	C₂²×C₄	—	3	8	no	—
507	C₂²×C₄	—	3	4	no	—
508	C₂²×C₄	—	6	8	no	—
509	C₂²×C₄	—	6	4	no	—
510	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
511	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
512	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
513	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
514	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
515	C₄⋊C₄	—	3	4	no	—
516	C₄⋊C₄	—	3	8	no	—
517	C₄⋊C₄	—	3	4	no	—
518	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
519	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
520	C₂²⋊C₄	—	3	4	no	—
521	C₂²⋊C₄	—	3	8	no	—
522	C₂²⋊C₄	—	3	8	no	—
523	C₂²⋊C₄	—	3	8	no	—
524	C₂²⋊C₄	—	3	8	no	—
525	C₂²⋊C₄	—	3	4	no	—
526	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
527	C₄²	—	3	8	no	—
528	C₄²	—	3	4	no	—
529	C₄²	C₂²×C₃×D₃	1	8	yes	—
530	C₂²×C₃	—	2	4	no	—
531	C₂²×C₃	—	2	2	no	—
532	C₂²×C₃	—	2	2	no	—
533	C₂²×C₃	—	2	2	no	—
534	C₂²×C₃	—	2	2	no	—
535	C₂²×C₃	—	2	2	no	—
536	C₂²×C₃	—	2	2	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	2	no	—
539	C₂²×C₃	—	2	2	no	—
540	C₂²×C₃	—	2	1	no	—
541	C₂²×C₃	—	4	2	no	—
542	C₂²×C₃	—	4	2	no	—
543	C₂²×C₃	—	4	8	no	—
544	C₂²×C₃	—	4	4	no	—
545	C₂²×C₃	—	4	4	no	—
546	C₂²×C₃	—	6	2	no	—
547	C₂²×C₃	—	6	4	no	—
548	C₂²×C₃	—	6	4	no	—
549	C₂²×C₃	—	6	2	no	—
550	C₂²×C₃	—	6	2	no	—
551	C₂²×C₃	—	6	4	no	—
552	C₂²×C₃	—	12	4	no	—
553	C₂²×C₃	—	12	8	no	—
554	C₂²×C₃	C₂×#235	1	2	yes	—
555	C₂²×C₃	D₃×#41	1	2	yes	—
556	C₂²×C₃	#1009	1	2	yes	—
557	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
558	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
559	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
560	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
561	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
562	C₂×D₃	—	2	2	no	—
563	C₂×D₃	—	2	4	no	—
564	C₂×D₃	—	2	4	no	—
565	C₂×D₃	—	2	2	no	—
566	C₂×D₃	—	2	2	no	—
567	C₂×D₃	—	2	4	no	—
568	C₂×D₃	—	4	8	no	—
569	C₂×D₃	—	4	4	no	—
570	C₃×C₄	—	2	4	no	—
571	C₃×C₄	—	2	2	no	—
572	C₃×C₄	—	2	4	no	—
573	C₃×C₄	—	2	4	no	—
574	C₃×C₄	—	2	4	no	—
575	C₃×C₄	—	2	2	no	—
576	C₃×C₄	—	2	4	no	—
577	C₃×C₄	—	2	4	no	—
578	C₃×C₄	—	3	4	no	—
579	C₃×C₄	—	4	4	no	—
580	C₃×C₄	—	4	4	no	—
581	C₃×C₄	—	6	2	no	—
582	C₃×C₄	—	6	4	no	—
583	C₃×C₄	—	6	2	no	—
584	C₃×C₄	C₂×#235	1	4	yes	—
585	C₃×C₄	C₂×C₃×#41	1	4	yes	—
586	Dic₃	—	2	2	no	—
587	Dic₃	—	2	2	no	—
588	Dic₃	—	2	4	no	—
589	Dic₃	C₂×C₃×#41	1	4	yes	—
590	C₃²	C₂×#555	1	1	yes	characteristic, complemented, Sylow
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	3	2	no	—
595	C₂³	—	3	4	no	—
596	C₂³	—	6	2	no	—
597	C₂³	—	6	4	no	—
598	C₂³	—	6	4	no	—
599	C₂³	—	6	2	no	—
600	C₂³	—	6	2	no	—
601	C₂³	—	6	4	no	—
602	C₂³	C₂³×C₃×D₃	1	2	yes	—
603	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
604	Q₈	—	12	8	no	—
605	D₄	—	6	8	no	—
606	D₄	—	6	8	no	—
607	D₄	—	12	8	no	—
608	D₄	—	12	8	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	3	4	no	—
614	C₂×C₄	—	3	2	no	—
615	C₂×C₄	—	3	2	no	—
616	C₂×C₄	—	3	2	no	—
617	C₂×C₄	—	3	4	no	—
618	C₂×C₄	—	6	16	no	—
619	C₂×C₄	—	6	2	no	—
620	C₂×C₄	—	6	4	no	—
621	C₂×C₄	—	6	2	no	—
622	C₂×C₄	—	6	8	no	—
623	C₂×C₄	C₃×#235	1	4	yes	—
624	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
625	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
626	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
627	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
628	C₂×C₃	—	2	4	no	—
629	C₂×C₃	—	2	1	no	—
630	C₂×C₃	—	2	1	no	—
631	C₂×C₃	—	2	1	no	—
632	C₂×C₃	—	4	4	no	—
633	C₂×C₃	—	4	2	no	—
634	C₂×C₃	—	4	2	no	—
635	C₂×C₃	—	12	2	no	—
636	C₂×C₃	—	12	4	no	—
637	C₂×C₃	#5532	1	4	yes	direct product factor
638	C₂×C₃	C₃×#555	1	4	yes	complemented
639	C₂×C₃	C₂²×#235	1	1	yes	characteristic
640	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
641	C₂×C₃	C₂×#1009	1	1	yes	characteristic
642	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
643	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
644	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
645	D₃	—	4	4	no	—
646	D₃	—	4	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	6	2	no	—
652	C₂²	—	6	4	no	—
653	C₂²	—	6	4	no	—
654	C₂²	—	6	2	no	—
655	C₂²	—	6	2	no	—
656	C₂²	—	6	4	no	—
657	C₂²	—	12	4	no	—
658	C₂²	—	12	8	no	—
659	C₂²	C₂×C₃×#235	1	2	yes	—
660	C₂²	C₃×D₃×#41	1	2	yes	—
661	C₂²	C₃×#1009	1	2	yes	—
662	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
663	C₄	—	2	2	no	—
664	C₄	—	2	4	no	—
665	C₄	—	2	4	no	—
666	C₄	—	3	4	no	—
667	C₄	—	6	2	no	—
668	C₄	—	6	4	no	—
669	C₄	—	6	2	no	—
670	C₄	C₂×C₃×#235	1	4	yes	—
671	C₃	—	2	1	no	—
672	C₃	C₂×#5532	1	1	yes	characteristic, direct product factor
673	C₃	C₂×C₃×#555	1	1	yes	characteristic, complemented
674	C₂	—	4	2	no	—
675	C₂	—	12	2	no	—
676	C₂	—	12	4	no	—
677	C₂	C₃×#5532	1	4	yes	direct product factor
678	C₂	C₂²×C₃×#235	1	1	yes	characteristic
679	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
680	C₂	C₂×C₃×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#117	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#117	D₃
hypocenter	C₃	C₂×C₃×#555
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#117	C₂	semidirect
2. C₂×C₃×#930	C₂	semidirect
3. C₂×C₃×C₄×#67	C₂	semidirect
4. C₃×#5532	C₂	direct (N × H)
5. C₂×C₃×#895	C₂	semidirect
6. C₂×C₃×#893	C₂	semidirect
7. C₂×C₃×#892	C₂	semidirect
8. C₂×C₃×#888	C₂	semidirect
9. C₂×C₃×#885	C₂	semidirect
10. C₂×C₃×#884	C₂	semidirect
11. C₂×C₃×#875	C₂	semidirect
12. C₂×C₃×#872	C₂	semidirect
14. C₂×#5532	C₃	direct (N × H)
23. C₃²×#117	C₂²	semidirect
29. C₃×#930	C₂²	semidirect
30. C₃×C₄×#67	C₂²	semidirect
41. C₃×#895	C₂²	semidirect
42. C₃×#893	C₂²	semidirect
43. C₃×#892	C₂²	semidirect
44. C₃×#888	C₂²	semidirect
45. C₃×#885	C₂²	semidirect
46. C₃×#884	C₂²	semidirect
47. C₃×#875	C₂²	semidirect
48. C₃×#872	C₂²	semidirect
61. C₂×C₃×#117	D₃	semidirect
62. C₂×C₃×#117	C₂×C₃	semidirect
63. C₂×#930	C₂×C₃	semidirect
64. C₂×C₄×#67	C₂×C₃	semidirect
65. #5532	C₂×C₃	direct (N × H)
66. C₂×#895	C₂×C₃	semidirect
67. C₂×#893	C₂×C₃	semidirect
68. C₂×#892	C₂×C₃	semidirect
69. C₂×#888	C₂×C₃	semidirect
70. C₂×#885	C₂×C₃	semidirect
71. C₂×#884	C₂×C₃	semidirect
72. C₂×#875	C₂×C₃	semidirect
73. C₂×#872	C₂×C₃	semidirect
145. C₃×#117	C₂×D₃	semidirect
146. C₃×#117	C₂²×C₃	semidirect
171. #930	C₂²×C₃	semidirect
172. C₄×#67	C₂²×C₃	semidirect
183. #895	C₂²×C₃	semidirect
184. #893	C₂²×C₃	semidirect
185. #892	C₂²×C₃	semidirect
186. #888	C₂²×C₃	semidirect
187. #885	C₂²×C₃	semidirect
188. #884	C₂²×C₃	semidirect
189. #875	C₂²×C₃	semidirect
190. #872	C₂²×C₃	semidirect
239. C₂×#117	C₃×D₃	semidirect
377. #117	C₂×C₃×D₃	semidirect
482. C₂×C₃²	#555	semidirect
590. C₃²	C₂×#555	semidirect
637. C₂×C₃	#5532	direct (N × H)
638. C₂×C₃	C₃×#555	semidirect
672. C₃	C₂×#5532	direct (N × H)
673. C₃	C₂×C₃×#555	semidirect
677. C₂	C₃×#5532	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#117	2
C₂×C₃×#930	2
C₂×C₃×C₄×#67	2
C₃×#5532	2
C₂×C₃×#895	2
C₂×C₃×#893	2
C₂×C₃×#892	2
C₂×C₃×#888	2
C₂×C₃×#885	2
C₂×C₃×#884	2
C₂×C₃×#875	2
C₂×C₃×#872	2
C₂×C₃×#555	3
C₂×#5532	3

Subgroups — C2×C3×#5532 #11903304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5532 #11903304