Subgroups — C₂×C₃×#5674 #11900998

Order 1152.

3957 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5674	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#884	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#882	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×#874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#535	—	3	1	no	maximal
12	C₂×#5674	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₂⁴×C₃×D₃	C₂²	1	2	yes	—
14	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#67	C₂²	1	2	yes	—
17	C₂²×C₃×#67	C₂²	1	4	yes	complemented
18	C₂×C₃×#239	—	2	8	no	—
19	C₂×C₃×#239	C₂²	1	8	yes	complemented
20	C₂×C₃×D₃×D₄	—	2	8	no	—
21	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
22	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
23	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
24	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×D₁₂	C₂²	1	4	yes	complemented
26	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
28	C₃²×#124	C₂²	1	8	yes	complemented
29	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	complemented
30	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
31	C₃×#947	C₂²	1	8	yes	complemented
32	C₃×#940	C₂²	1	8	yes	complemented
33	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
35	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₃×#884	C₂²	1	32	yes	complemented
38	C₃×#882	C₂²	1	32	yes	complemented
39	C₃×#874	C₂²	1	8	yes	complemented
40	C₃×#872	C₂²	1	8	yes	complemented
41	C₂²×C₃×#41	—	3	1	no	—
42	C₂³×C₃×D₄	—	3	1	no	—
43	C₂²×#239	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#535	—	3	16	no	—
46	C₂×C₃×#127	—	3	1	no	—
47	C₂×C₃×#127	—	3	1	no	—
48	C₂×C₃×#124	—	2	1	no	—
49	C₂×C₃×#124	—	3	1	no	—
50	C₂×C₃×#124	D₃	1	1	yes	characteristic, complemented
51	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₃×#121	—	3	4	no	—
53	C₂×C₃×#120	—	3	4	no	—
54	C₂×C₃×#117	—	3	1	no	—
55	C₂×#947	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#940	C₂×C₃	1	1	yes	characteristic, complemented
57	#5674	C₂×C₃	1	16	yes	direct product factor
58	C₂×#884	C₂×C₃	1	4	yes	complemented
59	C₂×#882	C₂×C₃	1	4	yes	complemented
60	C₂×#874	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×#872	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂⁴×C₃²	C₂³	1	2	yes	—
63	C₂³×C₃×D₃	—	2	8	no	—
64	C₂³×C₃×D₃	—	4	8	no	—
65	C₂³×C₃×D₃	C₂³	1	2	yes	—
66	C₂³×C₃×D₃	C₂³	1	2	yes	—
67	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
68	C₂³×C₃×D₃	C₂³	1	8	yes	—
69	C₂×C₃²×Q₈	—	2	4	no	—
70	C₂×C₃²×Q₈	C₂³	1	4	yes	complemented
71	C₂×C₃²×D₄	—	2	4	no	—
72	C₂×C₃²×D₄	C₂³	1	4	yes	—
73	C₂²×C₃²×C₄	C₂³	1	2	yes	—
74	C₂²×C₃²×C₄	C₂³	1	2	yes	—
75	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
76	C₂×C₃×#67	—	2	8	no	—
77	C₂×C₃×#67	—	4	8	no	—
78	C₂×C₃×#67	C₂³	1	8	yes	—
79	C₂×C₃×#67	C₂³	1	16	yes	complemented
80	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
81	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
82	C₃×#239	—	2	32	no	—
83	C₃×D₃×D₄	—	2	32	no	—
84	C₂×C₃×D₁₂	—	2	8	no	—
85	C₂×C₃×D₁₂	—	2	4	no	—
86	C₂×C₃×D₁₂	—	2	4	no	—
87	C₂×C₃×D₁₂	—	4	8	no	—
88	C₂×C₃×D₁₂	C₂³	1	8	yes	—
89	C₂×C₃×D₁₂	C₂³	1	4	yes	—
90	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
91	C₂×C₃×D₁₂	C₂³	1	16	yes	complemented
92	C₂×C₃×C₄×D₃	—	2	8	no	—
93	C₂×C₃×C₄×D₃	D₄	1	8	yes	complemented
94	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
95	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
96	C₃²×C₂²⋊C₄	C₂³	1	16	yes	complemented
97	C₃²×C₄²	C₂³	1	4	yes	complemented
98	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
99	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
100	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
101	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
102	C₂×#535	—	3	1	no	Sylow
103	C₂⁵×C₃	—	3	2	no	—
104	C₂⁴×D₃	C₂²×C₃	1	2	yes	—
105	C₂×C₃×#41	—	3	8	no	—
106	C₂×C₃×#41	—	6	8	no	—
107	C₂²×C₃×Q₈	—	2	1	no	—
108	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
109	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₂²×C₃×D₄	—	2	1	no	—
111	C₂²×C₃×D₄	—	3	2	no	—
112	C₂²×C₃×D₄	—	3	4	no	—
113	C₂²×C₃×D₄	—	3	8	no	—
114	C₂²×C₃×D₄	—	3	1	no	—
115	C₂²×C₃×D₄	—	3	2	no	—
116	C₂²×C₃×D₄	—	3	1	no	—
117	C₂²×C₃×D₄	—	3	4	no	—
118	C₂²×C₃×D₄	—	6	8	no	—
119	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
120	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₂³×C₃×C₄	—	3	1	no	—
122	C₂³×C₃×C₄	—	3	2	no	—
123	C₂²×#67	C₂²×C₃	1	2	yes	—
124	C₂²×#67	C₂²×C₃	1	4	yes	complemented
125	C₂×#239	—	2	8	no	—
126	C₂×#239	C₂²×C₃	1	8	yes	complemented
127	C₂×D₃×D₄	—	2	8	no	—
128	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
129	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
130	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
131	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₂²×D₁₂	C₂²×C₃	1	4	yes	complemented
133	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
134	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
135	C₃×#127	—	3	8	no	—
136	C₃×#127	—	3	8	no	—
137	C₃×#124	—	2	8	no	—
138	C₃×#124	—	3	8	no	—
139	C₃×#124	C₂×D₃	1	8	yes	complemented
140	C₃×#124	C₂²×C₃	1	8	yes	complemented
141	C₃×#121	—	3	32	no	—
142	C₃×#120	—	3	32	no	—
143	C₃×#117	—	3	8	no	—
144	C₂×C₃×C₄⋊C₄	—	3	2	no	—
145	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
146	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
147	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
148	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
149	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
150	C₂×C₃×C₄²	—	2	1	no	—
151	C₂×C₃×C₄²	—	3	1	no	—
152	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
153	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
154	#947	C₂²×C₃	1	8	yes	complemented
155	#940	C₂²×C₃	1	8	yes	complemented
156	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
157	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	complemented
158	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
159	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
160	#884	C₂²×C₃	1	32	yes	complemented
161	#882	C₂²×C₃	1	32	yes	complemented
162	#874	C₂²×C₃	1	8	yes	complemented
163	#872	C₂²×C₃	1	8	yes	complemented
164	C₂³×C₃²	—	2	4	no	—
165	C₂³×C₃²	—	2	8	no	—
166	C₂³×C₃²	C₂⁴	1	4	yes	—
167	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
168	C₂²×C₃×D₃	—	2	4	no	—
169	C₂²×C₃×D₃	—	2	4	no	—
170	C₂²×C₃×D₃	—	2	4	no	—
171	C₂²×C₃×D₃	—	2	8	no	—
172	C₂²×C₃×D₃	—	2	8	no	—
173	C₂²×C₃×D₃	—	2	16	no	—
174	C₂²×C₃×D₃	—	4	16	no	—
175	C₂²×C₃×D₃	—	4	32	no	—
176	C₂²×C₃×D₃	C₂×D₄	1	4	yes	—
177	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
178	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
179	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
180	C₃²×Q₈	—	2	8	no	—
181	C₃²×D₄	—	2	8	no	—
182	C₂×C₃²×C₄	—	2	4	no	—
183	C₂×C₃²×C₄	—	2	4	no	—
184	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
185	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
186	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
187	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
188	C₃×#67	—	2	16	no	—
189	C₃×#67	—	4	16	no	—
190	C₂×C₃×Dic₃	—	2	4	no	—
191	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
192	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
193	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
194	C₃×D₁₂	—	2	16	no	—
195	C₃×D₁₂	—	2	8	no	—
196	C₃×D₁₂	—	2	8	no	—
197	C₃×D₁₂	—	4	16	no	—
198	C₃×C₄×D₃	—	2	16	no	—
199	C₃×C₄×D₃	C₂×D₄	1	16	yes	complemented
200	C₂²×#41	—	3	1	no	—
201	C₂³×D₄	—	3	1	no	—
202	#535	—	3	16	no	—
203	C₂×#127	—	3	1	no	—
204	C₂×#127	—	3	1	no	—
205	C₂×#124	—	3	1	no	—
206	C₂×#124	C₃×D₃	1	1	yes	characteristic, complemented
207	C₂×#121	—	3	4	no	—
208	C₂×#120	—	3	4	no	—
209	C₂×#117	—	3	1	no	—
210	C₂⁴×C₃	—	2	2	no	—
211	C₂⁴×C₃	—	3	1	no	—
212	C₂⁴×C₃	—	3	2	no	—
213	C₂⁴×C₃	—	3	2	no	—
214	C₂⁴×C₃	—	3	8	no	—
215	C₂⁴×C₃	—	6	8	no	—
216	C₂⁴×C₃	—	12	8	no	—
217	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
218	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
219	C₂³×D₃	—	2	8	no	—
220	C₂³×D₃	—	4	8	no	—
221	C₂³×D₃	C₂³×C₃	1	2	yes	—
222	C₂³×D₃	C₂³×C₃	1	2	yes	—
223	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
224	C₂³×D₃	C₂³×C₃	1	8	yes	—
225	C₃×#41	—	6	32	no	—
226	C₂×C₃×Q₈	—	2	4	no	—
227	C₂×C₃×Q₈	—	2	4	no	—
228	C₂×C₃×Q₈	—	2	4	no	—
229	C₂×C₃×Q₈	—	4	4	no	—
230	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	complemented
231	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	complemented
232	C₂×C₃×D₄	—	2	4	no	—
233	C₂×C₃×D₄	—	2	4	no	—
234	C₂×C₃×D₄	—	2	4	no	—
235	C₂×C₃×D₄	—	3	8	no	—
236	C₂×C₃×D₄	—	3	16	no	—
237	C₂×C₃×D₄	—	3	8	no	—
238	C₂×C₃×D₄	—	3	4	no	—
239	C₂×C₃×D₄	—	3	4	no	—
240	C₂×C₃×D₄	—	3	16	no	—
241	C₂×C₃×D₄	—	4	4	no	—
242	C₂×C₃×D₄	—	6	8	no	—
243	C₂×C₃×D₄	—	6	32	no	—
244	C₂×C₃×D₄	—	6	8	no	—
245	C₂×C₃×D₄	—	6	4	no	—
246	C₂×C₃×D₄	—	6	4	no	—
247	C₂×C₃×D₄	—	12	8	no	—
248	C₂×C₃×D₄	—	12	8	no	—
249	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
250	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
251	C₂²×C₃×C₄	—	2	1	no	—
252	C₂²×C₃×C₄	—	2	2	no	—
253	C₂²×C₃×C₄	—	2	2	no	—
254	C₂²×C₃×C₄	—	3	1	no	—
255	C₂²×C₃×C₄	—	3	8	no	—
256	C₂²×C₃×C₄	—	3	4	no	—
257	C₂²×C₃×C₄	—	3	2	no	—
258	C₂²×C₃×C₄	—	3	8	no	—
259	C₂²×C₃×C₄	—	6	8	no	—
260	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
261	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
262	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
264	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
265	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
266	C₂×#67	—	2	8	no	—
267	C₂×#67	—	4	8	no	—
268	C₂×#67	C₂³×C₃	1	8	yes	—
269	C₂×#67	C₂³×C₃	1	16	yes	complemented
270	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
271	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
272	#239	—	2	32	no	—
273	D₃×D₄	—	2	32	no	—
274	C₂×D₁₂	—	2	8	no	—
275	C₂×D₁₂	—	2	4	no	—
276	C₂×D₁₂	—	2	4	no	—
277	C₂×D₁₂	—	4	8	no	—
278	C₂×D₁₂	C₂³×C₃	1	4	yes	—
279	C₂×D₁₂	C₂³×C₃	1	8	yes	—
280	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
281	C₂×D₁₂	C₂³×C₃	1	16	yes	complemented
282	C₂×C₄×D₃	—	2	8	no	—
283	C₂×C₄×D₃	C₃×D₄	1	8	yes	complemented
284	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
285	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
286	C₃×C₄⋊C₄	—	3	8	no	—
287	C₃×C₂²⋊C₄	—	2	16	no	—
288	C₃×C₂²⋊C₄	—	3	8	no	—
289	C₃×C₂²⋊C₄	—	3	16	no	—
290	C₃×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
291	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
292	C₃×C₄²	—	2	4	no	—
293	C₃×C₄²	—	3	4	no	—
294	C₃×C₄²	C₂²×D₃	1	4	yes	complemented
295	C₃×C₄²	C₂³×C₃	1	4	yes	complemented
296	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
297	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
298	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
299	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
300	C₂²×C₃²	—	2	4	no	—
301	C₂²×C₃²	—	2	8	no	—
302	C₂²×C₃²	—	4	8	no	—
303	C₂²×C₃²	C₂²×D₄	1	2	yes	—
304	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
305	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
306	C₂×C₃×D₃	—	2	8	no	—
307	C₂×C₃×D₃	—	2	4	no	—
308	C₂×C₃×D₃	—	2	4	no	—
309	C₂×C₃×D₃	—	2	4	no	—
310	C₂×C₃×D₃	—	2	8	no	—
311	C₂×C₃×D₃	—	2	8	no	—
312	C₂×C₃×D₃	—	4	32	no	—
313	C₂×C₃×D₃	—	4	8	no	—
314	C₂×C₃×D₃	—	4	8	no	—
315	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
316	C₃²×C₄	—	2	4	no	—
317	C₃²×C₄	—	2	4	no	—
318	C₃²×C₄	C₂²×D₄	1	4	yes	—
319	C₃×Dic₃	—	2	4	no	—
320	C₃×Dic₃	C₂²×D₄	1	4	yes	—
321	C₂⁵	—	3	2	no	—
322	C₂×#41	—	3	8	no	—
323	C₂×#41	—	6	8	no	—
324	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
325	C₂²×D₄	—	3	2	no	—
326	C₂²×D₄	—	3	4	no	—
327	C₂²×D₄	—	3	8	no	—
328	C₂²×D₄	—	3	2	no	—
329	C₂²×D₄	—	3	1	no	—
330	C₂²×D₄	—	3	1	no	—
331	C₂²×D₄	—	3	4	no	—
332	C₂²×D₄	—	6	8	no	—
333	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
334	C₂³×C₄	—	3	1	no	—
335	C₂³×C₄	—	3	2	no	—
336	#127	—	3	8	no	—
337	#127	—	3	8	no	—
338	#124	—	3	8	no	—
339	#124	C₂×C₃×D₃	1	8	yes	complemented
340	#121	—	3	32	no	—
341	#120	—	3	32	no	—
342	#117	—	3	8	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	4	no	—
346	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
349	C₂³×C₃	—	2	4	no	—
350	C₂³×C₃	—	2	8	no	—
351	C₂³×C₃	—	2	4	no	—
352	C₂³×C₃	—	2	8	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	—	2	4	no	—
355	C₂³×C₃	—	3	4	no	—
356	C₂³×C₃	—	3	2	no	—
357	C₂³×C₃	—	3	4	no	—
358	C₂³×C₃	—	3	4	no	—
359	C₂³×C₃	—	4	4	no	—
360	C₂³×C₃	—	4	8	no	—
361	C₂³×C₃	—	6	16	no	—
362	C₂³×C₃	—	6	4	no	—
363	C₂³×C₃	—	6	4	no	—
364	C₂³×C₃	—	6	4	no	—
365	C₂³×C₃	—	6	8	no	—
366	C₂³×C₃	—	6	8	no	—
367	C₂³×C₃	—	12	16	no	—
368	C₂³×C₃	—	12	32	no	—
369	C₂³×C₃	C₂³×D₃	1	4	yes	—
370	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
371	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
372	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
373	C₂²×D₃	—	2	4	no	—
374	C₂²×D₃	—	2	4	no	—
375	C₂²×D₃	—	2	4	no	—
376	C₂²×D₃	—	2	8	no	—
377	C₂²×D₃	—	2	8	no	—
378	C₂²×D₃	—	2	16	no	—
379	C₂²×D₃	—	4	16	no	—
380	C₂²×D₃	—	4	32	no	—
381	C₂²×D₃	C₂×C₃×D₄	1	4	yes	—
382	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
383	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
384	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
385	C₃×Q₈	—	2	8	no	—
386	C₃×Q₈	—	2	8	no	—
387	C₃×Q₈	—	4	8	no	—
388	C₃×D₄	—	2	8	no	—
389	C₃×D₄	—	2	8	no	—
390	C₃×D₄	—	4	8	no	—
391	C₃×D₄	—	6	16	no	—
392	C₃×D₄	—	6	16	no	—
393	C₃×D₄	—	6	8	no	—
394	C₃×D₄	—	6	8	no	—
395	C₃×D₄	—	12	16	no	—
396	C₃×D₄	—	12	16	no	—
397	C₂×C₃×C₄	—	2	4	no	—
398	C₂×C₃×C₄	—	2	4	no	—
399	C₂×C₃×C₄	—	2	4	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	4	no	—
403	C₂×C₃×C₄	—	2	4	no	—
404	C₂×C₃×C₄	—	2	4	no	—
405	C₂×C₃×C₄	—	3	4	no	—
406	C₂×C₃×C₄	—	3	2	no	—
407	C₂×C₃×C₄	—	3	16	no	—
408	C₂×C₃×C₄	—	3	4	no	—
409	C₂×C₃×C₄	—	4	4	no	—
410	C₂×C₃×C₄	—	4	4	no	—
411	C₂×C₃×C₄	—	6	16	no	—
412	C₂×C₃×C₄	—	6	4	no	—
413	C₂×C₃×C₄	D₃×D₄	1	4	yes	—
414	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
415	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
416	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
417	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
418	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
419	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
420	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
421	#67	—	2	16	no	—
422	#67	—	4	16	no	—
423	C₂×Dic₃	—	2	4	no	—
424	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
425	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
426	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
427	D₁₂	—	2	16	no	—
428	D₁₂	—	2	8	no	—
429	D₁₂	—	2	8	no	—
430	D₁₂	—	4	16	no	—
431	C₄×D₃	—	2	16	no	—
432	C₄×D₃	C₂×C₃×D₄	1	16	yes	complemented
433	C₂×C₃²	—	4	4	no	—
434	C₂×C₃²	#535	1	4	yes	complemented
435	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
436	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
437	C₃×D₃	—	2	4	no	—
438	C₃×D₃	—	4	4	no	—
439	C₃×D₃	—	4	4	no	—
440	C₂⁴	—	3	1	no	—
441	C₂⁴	—	3	2	no	—
442	C₂⁴	—	3	2	no	—
443	C₂⁴	—	3	8	no	—
444	C₂⁴	—	6	8	no	—
445	C₂⁴	—	12	8	no	—
446	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
447	#41	—	6	32	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	complemented
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	3	8	no	—
452	C₂×D₄	—	3	16	no	—
453	C₂×D₄	—	3	8	no	—
454	C₂×D₄	—	3	4	no	—
455	C₂×D₄	—	3	4	no	—
456	C₂×D₄	—	3	16	no	—
457	C₂×D₄	—	6	8	no	—
458	C₂×D₄	—	6	32	no	—
459	C₂×D₄	—	6	8	no	—
460	C₂×D₄	—	6	4	no	—
461	C₂×D₄	—	6	4	no	—
462	C₂×D₄	—	12	8	no	—
463	C₂×D₄	—	12	8	no	—
464	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	3	4	no	—
467	C₂²×C₄	—	3	8	no	—
468	C₂²×C₄	—	3	2	no	—
469	C₂²×C₄	—	3	8	no	—
470	C₂²×C₄	—	6	8	no	—
471	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
472	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
473	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
474	C₄⋊C₄	—	3	8	no	—
475	C₂²⋊C₄	—	3	8	no	—
476	C₂²⋊C₄	—	3	16	no	—
477	C₂²⋊C₄	C₂²×C₃×D₃	1	16	yes	complemented
478	C₄²	—	3	4	no	—
479	C₄²	C₂²×C₃×D₃	1	4	yes	complemented
480	C₂²×C₃	—	2	4	no	—
481	C₂²×C₃	—	2	8	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	2	8	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	2	4	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	3	4	no	—
488	C₂²×C₃	—	4	4	no	—
489	C₂²×C₃	—	4	8	no	—
490	C₂²×C₃	—	4	8	no	—
491	C₂²×C₃	—	4	8	no	—
492	C₂²×C₃	—	6	8	no	—
493	C₂²×C₃	—	6	4	no	—
494	C₂²×C₃	—	6	4	no	—
495	C₂²×C₃	—	6	4	no	—
496	C₂²×C₃	—	6	8	no	—
497	C₂²×C₃	—	6	8	no	—
498	C₂²×C₃	—	8	8	no	—
499	C₂²×C₃	—	12	32	no	—
500	C₂²×C₃	—	12	8	no	—
501	C₂²×C₃	—	12	8	no	—
502	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
503	C₂²×C₃	#1009	1	4	yes	—
504	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
505	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
506	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
507	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
508	C₂×D₃	—	2	4	no	—
509	C₂×D₃	—	2	8	no	—
510	C₂×D₃	—	2	4	no	—
511	C₂×D₃	—	2	4	no	—
512	C₂×D₃	—	2	8	no	—
513	C₂×D₃	—	2	8	no	—
514	C₂×D₃	—	4	32	no	—
515	C₂×D₃	—	4	8	no	—
516	C₂×D₃	—	4	8	no	—
517	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
518	C₃×C₄	—	2	4	no	—
519	C₃×C₄	—	2	4	no	—
520	C₃×C₄	—	2	4	no	—
521	C₃×C₄	—	2	4	no	—
522	C₃×C₄	—	2	4	no	—
523	C₃×C₄	—	3	4	no	—
524	C₃×C₄	—	4	4	no	—
525	C₃×C₄	—	4	4	no	—
526	C₃×C₄	—	6	4	no	—
527	C₃×C₄	C₂×D₃×D₄	1	4	yes	—
528	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
529	Dic₃	—	2	4	no	—
530	Dic₃	C₂²×C₃×D₄	1	4	yes	—
531	C₃²	C₂×#535	1	1	yes	characteristic, complemented, Sylow
532	C₂³	—	2	4	no	—
533	C₂³	—	2	8	no	—
534	C₂³	—	3	4	no	—
535	C₂³	—	3	2	no	—
536	C₂³	—	3	4	no	—
537	C₂³	—	3	4	no	—
538	C₂³	—	6	16	no	—
539	C₂³	—	6	4	no	—
540	C₂³	—	6	4	no	—
541	C₂³	—	6	4	no	—
542	C₂³	—	6	8	no	—
543	C₂³	—	6	8	no	—
544	C₂³	—	12	16	no	—
545	C₂³	—	12	32	no	—
546	C₂³	C₂³×C₃×D₃	1	4	yes	—
547	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
548	Q₈	—	2	8	no	—
549	D₄	—	2	8	no	—
550	D₄	—	6	16	no	—
551	D₄	—	6	16	no	—
552	D₄	—	6	8	no	—
553	D₄	—	6	8	no	—
554	D₄	—	12	16	no	—
555	D₄	—	12	16	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	3	4	no	—
559	C₂×C₄	—	3	2	no	—
560	C₂×C₄	—	3	16	no	—
561	C₂×C₄	—	3	4	no	—
562	C₂×C₄	—	6	16	no	—
563	C₂×C₄	—	6	4	no	—
564	C₂×C₄	C₃×D₃×D₄	1	4	yes	—
565	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
566	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
567	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
568	C₂×C₃	—	2	1	no	—
569	C₂×C₃	—	2	2	no	—
570	C₂×C₃	—	2	4	no	—
571	C₂×C₃	—	4	4	no	—
572	C₂×C₃	—	4	4	no	—
573	C₂×C₃	—	6	4	no	—
574	C₂×C₃	—	8	4	no	—
575	C₂×C₃	—	12	4	no	—
576	C₂×C₃	—	12	4	no	—
577	C₂×C₃	#5674	1	4	yes	direct product factor
578	C₂×C₃	C₃×#535	1	4	yes	complemented
579	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
580	C₂×C₃	C₂×#1009	1	2	yes	—
581	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
582	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
583	D₃	—	2	4	no	—
584	D₃	—	4	4	no	—
585	D₃	—	4	4	no	—
586	C₂²	—	2	4	no	—
587	C₂²	—	2	8	no	—
588	C₂²	—	3	4	no	—
589	C₂²	—	4	8	no	—
590	C₂²	—	6	4	no	—
591	C₂²	—	6	8	no	—
592	C₂²	—	6	4	no	—
593	C₂²	—	6	4	no	—
594	C₂²	—	6	8	no	—
595	C₂²	—	6	8	no	—
596	C₂²	—	12	32	no	—
597	C₂²	—	12	8	no	—
598	C₂²	—	12	8	no	—
599	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
600	C₂²	C₃×#1009	1	4	yes	—
601	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
602	C₄	—	2	4	no	—
603	C₄	—	2	4	no	—
604	C₄	—	3	4	no	—
605	C₄	—	6	4	no	—
606	C₄	C₂×C₃×D₃×D₄	1	4	yes	—
607	C₃	—	2	1	no	—
608	C₃	C₂×#5674	1	1	yes	characteristic, direct product factor
609	C₃	C₂×C₃×#535	1	1	yes	characteristic, complemented
610	C₂	—	4	4	no	—
611	C₂	—	6	4	no	—
612	C₂	—	12	4	no	—
613	C₂	—	12	4	no	—
614	C₂	C₃×#5674	1	4	yes	direct product factor
615	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
616	C₂	C₂×C₃×#1009	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#124	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#124	D₃
hypocenter	C₃	C₂×C₃×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#239	C₂	semidirect
2. C₂²×C₃×D₃×D₄	C₂	semidirect
3. C₂×C₃²×#124	C₂	semidirect
4. C₂×C₃×#947	C₂	semidirect
5. C₂×C₃×#940	C₂	semidirect
6. C₃×#5674	C₂	direct (N × H)
7. C₂×C₃×#884	C₂	semidirect
8. C₂×C₃×#882	C₂	semidirect
9. C₂×C₃×#874	C₂	semidirect
10. C₂×C₃×#872	C₂	semidirect
12. C₂×#5674	C₃	direct (N × H)
14. C₂²×C₃²×Q₈	C₂²	semidirect
17. C₂²×C₃×#67	C₂²	semidirect
19. C₂×C₃×#239	C₂²	semidirect
21. C₂×C₃×D₃×D₄	C₂²	semidirect
24. C₂²×C₃×D₁₂	C₂²	semidirect
25. C₂²×C₃×D₁₂	C₂²	semidirect
27. C₂²×C₃×C₄×D₃	C₂²	semidirect
28. C₃²×#124	C₂²	semidirect
29. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
30. C₂×C₃²×C₄²	C₂²	semidirect
31. C₃×#947	C₂²	semidirect
32. C₃×#940	C₂²	semidirect
34. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
36. C₂×C₃×C₄×Dic₃	C₂²	semidirect
37. C₃×#884	C₂²	semidirect
38. C₃×#882	C₂²	semidirect
39. C₃×#874	C₂²	semidirect
40. C₃×#872	C₂²	semidirect
43. C₂²×#239	C₂×C₃	semidirect
44. C₂²×D₃×D₄	C₂×C₃	semidirect
50. C₂×C₃×#124	D₃	semidirect
51. C₂×C₃×#124	C₂×C₃	semidirect
55. C₂×#947	C₂×C₃	semidirect
56. C₂×#940	C₂×C₃	semidirect
57. #5674	C₂×C₃	direct (N × H)
58. C₂×#884	C₂×C₃	semidirect
59. C₂×#882	C₂×C₃	semidirect
60. C₂×#874	C₂×C₃	semidirect
61. C₂×#872	C₂×C₃	semidirect
70. C₂×C₃²×Q₈	C₂³	semidirect
79. C₂×C₃×#67	C₂³	semidirect
90. C₂×C₃×D₁₂	C₂³	semidirect
91. C₂×C₃×D₁₂	C₂³	semidirect
93. C₂×C₃×C₄×D₃	D₄	semidirect
95. C₂×C₃×C₄×D₃	C₂³	semidirect
96. C₃²×C₂²⋊C₄	C₂³	semidirect
97. C₃²×C₄²	C₂³	semidirect
99. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
100. C₃×Dic₃⋊C₄	C₂³	semidirect
101. C₃×C₄×Dic₃	C₂³	semidirect
108. C₂²×C₃×Q₈	C₂×D₃	semidirect
109. C₂²×C₃×Q₈	C₂²×C₃	semidirect
124. C₂²×#67	C₂²×C₃	semidirect
126. C₂×#239	C₂²×C₃	semidirect
128. C₂×D₃×D₄	C₂²×C₃	semidirect
131. C₂²×D₁₂	C₂²×C₃	semidirect
132. C₂²×D₁₂	C₂²×C₃	semidirect
134. C₂²×C₄×D₃	C₂²×C₃	semidirect
139. C₃×#124	C₂×D₃	semidirect
140. C₃×#124	C₂²×C₃	semidirect
148. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
149. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
152. C₂×C₃×C₄²	C₂×D₃	semidirect
153. C₂×C₃×C₄²	C₂²×C₃	semidirect
154. #947	C₂²×C₃	semidirect
155. #940	C₂²×C₃	semidirect
157. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
158. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
159. C₂×C₄×Dic₃	C₂²×C₃	semidirect
160. #884	C₂²×C₃	semidirect
161. #882	C₂²×C₃	semidirect
162. #874	C₂²×C₃	semidirect
163. #872	C₂²×C₃	semidirect
199. C₃×C₄×D₃	C₂×D₄	semidirect
206. C₂×#124	C₃×D₃	semidirect
230. C₂×C₃×Q₈	C₂²×D₃	semidirect
231. C₂×C₃×Q₈	C₂³×C₃	semidirect
269. C₂×#67	C₂³×C₃	semidirect
280. C₂×D₁₂	C₂³×C₃	semidirect
281. C₂×D₁₂	C₂³×C₃	semidirect
283. C₂×C₄×D₃	C₃×D₄	semidirect
285. C₂×C₄×D₃	C₂³×C₃	semidirect
290. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
291. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
294. C₃×C₄²	C₂²×D₃	semidirect
295. C₃×C₄²	C₂³×C₃	semidirect
297. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
298. Dic₃⋊C₄	C₂³×C₃	semidirect
299. C₄×Dic₃	C₂³×C₃	semidirect
324. C₂²×Q₈	C₂×C₃×D₃	semidirect
339. #124	C₂×C₃×D₃	semidirect
346. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
348. C₂×C₄²	C₂×C₃×D₃	semidirect
432. C₄×D₃	C₂×C₃×D₄	semidirect
434. C₂×C₃²	#535	semidirect
449. C₂×Q₈	C₂²×C₃×D₃	semidirect
477. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
479. C₄²	C₂²×C₃×D₃	semidirect
531. C₃²	C₂×#535	semidirect
577. C₂×C₃	#5674	direct (N × H)
578. C₂×C₃	C₃×#535	semidirect
608. C₃	C₂×#5674	direct (N × H)
609. C₃	C₂×C₃×#535	semidirect
614. C₂	C₃×#5674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#239	2
C₂²×C₃×D₃×D₄	2
C₂×C₃²×#124	2
C₂×C₃×#947	2
C₂×C₃×#940	2
C₃×#5674	2
C₂×C₃×#884	2
C₂×C₃×#882	2
C₂×C₃×#874	2
C₂×C₃×#872	2
C₂×C₃×#535	3
C₂×#5674	3

Subgroups — C2×C3×#5674 #11900998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5674 #11900998