Subgroups — C₂²×C₃×#1004 #11919213

Order 1152.

13801 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#67	C₂	1	4	yes	maximal, complemented
3	C₂×C₃×#1004	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₃×#237	C₂	1	4	yes	maximal, complemented
5	C₂²×C₃×D₃×D₄	C₂	1	4	yes	maximal, complemented
6	C₂²×C₃×#235	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃×H(5,𝔽₂)	—	3	1	no	maximal
8	C₂²×#1004	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	2	yes	complemented
10	C₂⁴×C₃×D₃	C₂²	1	4	yes	complemented
11	C₂²×C₃²×D₄	C₂²	1	4	yes	complemented
12	C₂²×C₃²×D₄	C₂²	1	24	yes	complemented
13	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×#67	C₂²	1	4	yes	complemented
15	C₂²×C₃×#67	C₂²	1	8	yes	complemented
16	C₂²×C₃×#67	C₂²	1	96	yes	complemented
17	C₂³×C₃×Dic₃	C₂²	1	4	yes	complemented
18	C₃×#1004	C₂²	1	256	yes	direct product factor
19	C₂×C₃×#237	C₂²	1	96	yes	complemented
20	C₂×C₃×D₃×D₄	C₂²	1	96	yes	complemented
21	C₂×C₃×#235	C₂²	1	48	yes	complemented
22	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₄×D₃	C₂²	1	4	yes	complemented
24	C₂²×C₃×Dic₆	C₂²	1	2	yes	complemented
25	C₂×C₃×H(5,𝔽₂)	—	3	48	no	—
26	C₂²×C₃×#41	—	3	4	no	—
27	C₂²×C₃×#41	—	3	2	no	—
28	C₂³×C₃×D₄	—	2	1	no	—
29	C₂³×C₃×D₄	—	3	4	no	—
30	C₂³×C₃×D₄	—	3	4	no	—
31	C₂³×C₃×D₄	D₃	1	1	yes	characteristic, complemented
32	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂³×#67	C₂×C₃	1	4	yes	complemented
34	C₂×#1004	C₂×C₃	1	48	yes	direct product factor
35	C₂²×#237	C₂×C₃	1	4	yes	complemented
36	C₂²×D₃×D₄	C₂×C₃	1	4	yes	complemented
37	C₂²×#235	C₂×C₃	1	2	yes	complemented
38	C₂⁴×C₃²	—	4	8	no	—
39	C₂⁴×C₃²	C₂³	1	4	yes	—
40	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
41	C₂⁴×C₃²	C₂³	1	24	yes	complemented
42	C₂³×C₃×D₃	—	4	16	no	—
43	C₂³×C₃×D₃	C₂³	1	4	yes	—
44	C₂³×C₃×D₃	C₂³	1	48	yes	complemented
45	C₂×C₃²×D₄	C₂³	1	48	yes	complemented
46	C₂×C₃²×D₄	C₂³	1	64	yes	complemented
47	C₂²×C₃²×C₄	C₂³	1	2	yes	—
48	C₂²×C₃²×C₄	C₂³	1	12	yes	complemented
49	C₂×C₃×#67	C₂³	1	48	yes	complemented
50	C₂×C₃×#67	C₂³	1	96	yes	complemented
51	C₂×C₃×#67	C₂³	1	256	yes	complemented
52	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
53	C₂²×C₃×Dic₃	C₂³	1	48	yes	complemented
54	C₃×#237	C₂³	1	256	yes	complemented
55	C₃×D₃×D₄	C₂³	1	256	yes	complemented
56	C₃×#235	C₂³	1	128	yes	complemented
57	C₂×C₃×D₁₂	C₂³	1	24	yes	complemented
58	C₂×C₃×C₄×D₃	C₂³	1	48	yes	complemented
59	C₂×C₃×Dic₆	C₂³	1	24	yes	complemented
60	C₂²×H(5,𝔽₂)	—	3	1	no	Sylow
61	C₂⁵×C₃	—	2	2	no	—
62	C₂⁵×C₃	—	3	4	no	—
63	C₂⁵×C₃	C₂×D₃	1	2	yes	complemented
64	C₂⁵×C₃	C₂²×C₃	1	2	yes	complemented
65	C₂⁴×D₃	C₂²×C₃	1	4	yes	complemented
66	C₃×H(5,𝔽₂)	—	3	256	no	—
67	C₂×C₃×#41	—	3	96	no	—
68	C₂×C₃×#41	—	3	48	no	—
69	C₂²×C₃×Q₈	—	3	2	no	—
70	C₂²×C₃×D₄	—	2	4	no	—
71	C₂²×C₃×D₄	—	2	24	no	—
72	C₂²×C₃×D₄	—	3	8	no	—
73	C₂²×C₃×D₄	—	3	4	no	—
74	C₂²×C₃×D₄	—	3	96	no	—
75	C₂²×C₃×D₄	—	3	96	no	—
76	C₂²×C₃×D₄	—	3	2	no	—
77	C₂²×C₃×D₄	C₂×D₃	1	4	yes	complemented
78	C₂²×C₃×D₄	C₂×D₃	1	24	yes	complemented
79	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	complemented
80	C₂²×C₃×D₄	C₂²×C₃	1	24	yes	complemented
81	C₂³×C₃×C₄	—	2	1	no	—
82	C₂³×C₃×C₄	—	3	4	no	—
83	C₂³×C₃×C₄	—	3	4	no	—
84	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
85	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₂²×#67	C₂²×C₃	1	4	yes	complemented
87	C₂²×#67	C₂²×C₃	1	8	yes	complemented
88	C₂²×#67	C₂²×C₃	1	96	yes	complemented
89	C₂³×Dic₃	C₂²×C₃	1	4	yes	complemented
90	#1004	C₂²×C₃	1	256	yes	direct product factor
91	C₂×#237	C₂²×C₃	1	96	yes	complemented
92	C₂×D₃×D₄	C₂²×C₃	1	96	yes	complemented
93	C₂×#235	C₂²×C₃	1	48	yes	complemented
94	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
95	C₂²×C₄×D₃	C₂²×C₃	1	4	yes	complemented
96	C₂²×Dic₆	C₂²×C₃	1	2	yes	complemented
97	C₂³×C₃²	—	2	4	no	—
98	C₂³×C₃²	—	2	16	no	—
99	C₂³×C₃²	—	4	48	no	—
100	C₂³×C₃²	C₂⁴	1	24	yes	—
101	C₂³×C₃²	C₂⁴	1	6	yes	—
102	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
103	C₂³×C₃²	C₂⁴	1	32	yes	complemented
104	C₂²×C₃×D₃	—	2	16	no	—
105	C₂²×C₃×D₃	—	4	96	no	—
106	C₂²×C₃×D₃	C₂⁴	1	24	yes	—
107	C₂²×C₃×D₃	C₂⁴	1	64	yes	complemented
108	C₃²×D₄	C₂⁴	1	64	yes	complemented
109	C₂×C₃²×C₄	C₂⁴	1	12	yes	—
110	C₂×C₃²×C₄	C₂⁴	1	16	yes	complemented
111	C₃×#67	C₂⁴	1	64	yes	complemented
112	C₃×#67	C₂⁴	1	128	yes	complemented
113	C₂×C₃×Dic₃	C₂⁴	1	24	yes	—
114	C₂×C₃×Dic₃	C₂⁴	1	64	yes	complemented
115	C₃×D₁₂	C₂⁴	1	32	yes	complemented
116	C₃×C₄×D₃	C₂⁴	1	64	yes	complemented
117	C₃×Dic₆	C₂⁴	1	32	yes	complemented
118	C₂×H(5,𝔽₂)	—	3	48	no	—
119	C₂²×#41	—	3	4	no	—
120	C₂²×#41	—	3	2	no	—
121	C₂³×D₄	—	3	4	no	—
122	C₂³×D₄	—	3	4	no	—
123	C₂³×D₄	C₃×D₃	1	1	yes	characteristic, complemented
124	C₂⁴×C₃	—	2	1	no	—
125	C₂⁴×C₃	—	2	4	no	—
126	C₂⁴×C₃	—	2	24	no	—
127	C₂⁴×C₃	—	3	4	no	—
128	C₂⁴×C₃	—	3	48	no	—
129	C₂⁴×C₃	—	4	8	no	—
130	C₂⁴×C₃	—	4	8	no	—
131	C₂⁴×C₃	—	4	16	no	—
132	C₂⁴×C₃	—	12	16	no	—
133	C₂⁴×C₃	C₂²×D₃	1	4	yes	—
134	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
135	C₂⁴×C₃	C₂²×D₃	1	24	yes	complemented
136	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
137	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
138	C₂⁴×C₃	C₂³×C₃	1	24	yes	complemented
139	C₂³×D₃	—	4	16	no	—
140	C₂³×D₃	C₂³×C₃	1	4	yes	—
141	C₂³×D₃	C₂³×C₃	1	48	yes	complemented
142	C₃×#41	—	3	256	no	—
143	C₃×#41	—	3	128	no	—
144	C₂×C₃×Q₈	—	3	24	no	—
145	C₂×C₃×D₄	—	2	48	no	—
146	C₂×C₃×D₄	—	2	64	no	—
147	C₂×C₃×D₄	—	3	96	no	—
148	C₂×C₃×D₄	—	3	48	no	—
149	C₂×C₃×D₄	—	3	256	no	—
150	C₂×C₃×D₄	—	3	256	no	—
151	C₂×C₃×D₄	—	3	24	no	—
152	C₂×C₃×D₄	C₂²×D₃	1	48	yes	complemented
153	C₂×C₃×D₄	C₂²×D₃	1	64	yes	complemented
154	C₂×C₃×D₄	C₂³×C₃	1	48	yes	complemented
155	C₂×C₃×D₄	C₂³×C₃	1	64	yes	complemented
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	—	2	12	no	—
158	C₂²×C₃×C₄	—	3	48	no	—
159	C₂²×C₃×C₄	—	3	4	no	—
160	C₂²×C₃×C₄	—	3	48	no	—
161	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
162	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	complemented
163	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
164	C₂²×C₃×C₄	C₂³×C₃	1	12	yes	complemented
165	C₂×#67	C₂³×C₃	1	48	yes	complemented
166	C₂×#67	C₂³×C₃	1	96	yes	complemented
167	C₂×#67	C₂³×C₃	1	256	yes	complemented
168	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
169	C₂²×Dic₃	C₂³×C₃	1	48	yes	complemented
170	#237	C₂³×C₃	1	256	yes	complemented
171	D₃×D₄	C₂³×C₃	1	256	yes	complemented
172	#235	C₂³×C₃	1	128	yes	complemented
173	C₂×D₁₂	C₂³×C₃	1	24	yes	complemented
174	C₂×C₄×D₃	C₂³×C₃	1	48	yes	complemented
175	C₂×Dic₆	C₂³×C₃	1	24	yes	complemented
176	C₂²×C₃²	—	2	12	no	—
177	C₂²×C₃²	—	2	48	no	—
178	C₂²×C₃²	—	4	32	no	—
179	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	complemented
180	C₂²×C₃²	C₂⁵	1	16	yes	—
181	C₂²×C₃²	C₂⁵	1	4	yes	—
182	C₂²×C₃²	C₂⁵	1	3	yes	—
183	C₂×C₃×D₃	—	2	48	no	—
184	C₂×C₃×D₃	—	4	64	no	—
185	C₂×C₃×D₃	C₂⁵	1	16	yes	—
186	C₃²×C₄	C₂⁵	1	8	yes	—
187	C₃×Dic₃	C₂⁵	1	16	yes	—
188	C₂⁵	—	3	4	no	—
189	C₂⁵	C₂×C₃×D₃	1	2	yes	complemented
190	H(5,𝔽₂)	—	3	256	no	—
191	C₂×#41	—	3	96	no	—
192	C₂×#41	—	3	48	no	—
193	C₂²×Q₈	—	3	2	no	—
194	C₂²×D₄	—	3	8	no	—
195	C₂²×D₄	—	3	4	no	—
196	C₂²×D₄	—	3	96	no	—
197	C₂²×D₄	—	3	96	no	—
198	C₂²×D₄	—	3	2	no	—
199	C₂²×D₄	C₂×C₃×D₃	1	4	yes	complemented
200	C₂²×D₄	C₂×C₃×D₃	1	24	yes	complemented
201	C₂³×C₄	—	3	4	no	—
202	C₂³×C₄	—	3	4	no	—
203	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
204	C₂³×C₃	—	2	8	no	—
205	C₂³×C₃	—	2	4	no	—
206	C₂³×C₃	—	2	16	no	—
207	C₂³×C₃	—	2	16	no	—
208	C₂³×C₃	—	2	4	no	—
209	C₂³×C₃	—	2	6	no	—
210	C₂³×C₃	—	2	1	no	—
211	C₂³×C₃	—	2	24	no	—
212	C₂³×C₃	—	2	32	no	—
213	C₂³×C₃	—	3	24	no	—
214	C₂³×C₃	—	3	64	no	—
215	C₂³×C₃	—	4	16	no	—
216	C₂³×C₃	—	4	48	no	—
217	C₂³×C₃	—	4	48	no	—
218	C₂³×C₃	—	4	96	no	—
219	C₂³×C₃	—	6	16	no	—
220	C₂³×C₃	—	12	96	no	—
221	C₂³×C₃	C₂³×D₃	1	24	yes	—
222	C₂³×C₃	C₂³×D₃	1	6	yes	—
223	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
224	C₂³×C₃	C₂³×D₃	1	32	yes	complemented
225	C₂³×C₃	C₂⁴×C₃	1	24	yes	—
226	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
227	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
228	C₂³×C₃	C₂⁴×C₃	1	32	yes	complemented
229	C₂²×D₃	—	2	16	no	—
230	C₂²×D₃	—	4	96	no	—
231	C₂²×D₃	C₂⁴×C₃	1	24	yes	—
232	C₂²×D₃	C₂⁴×C₃	1	64	yes	complemented
233	C₃×Q₈	—	3	32	no	—
234	C₃×D₄	—	2	64	no	—
235	C₃×D₄	—	3	128	no	—
236	C₃×D₄	—	3	64	no	—
237	C₃×D₄	—	3	32	no	—
238	C₃×D₄	C₂³×D₃	1	64	yes	complemented
239	C₃×D₄	C₂⁴×C₃	1	64	yes	complemented
240	C₂×C₃×C₄	—	2	12	no	—
241	C₂×C₃×C₄	—	2	16	no	—
242	C₂×C₃×C₄	—	3	24	no	—
243	C₂×C₃×C₄	—	3	64	no	—
244	C₂×C₃×C₄	—	3	64	no	—
245	C₂×C₃×C₄	C₂³×D₃	1	12	yes	—
246	C₂×C₃×C₄	C₂³×D₃	1	16	yes	complemented
247	C₂×C₃×C₄	C₂⁴×C₃	1	12	yes	—
248	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	complemented
249	#67	C₂⁴×C₃	1	64	yes	complemented
250	#67	C₂⁴×C₃	1	128	yes	complemented
251	C₂×Dic₃	C₂⁴×C₃	1	24	yes	—
252	C₂×Dic₃	C₂⁴×C₃	1	64	yes	complemented
253	D₁₂	C₂⁴×C₃	1	32	yes	complemented
254	C₄×D₃	C₂⁴×C₃	1	64	yes	complemented
255	Dic₆	C₂⁴×C₃	1	32	yes	complemented
256	C₂×C₃²	—	2	4	no	—
257	C₂×C₃²	—	2	16	no	—
258	C₂×C₃²	C₂×H(5,𝔽₂)	1	6	yes	complemented
259	C₂×C₃²	C₂⁶	1	1	yes	characteristic
260	C₃×D₃	—	2	16	no	—
261	C₂⁴	—	3	4	no	—
262	C₂⁴	—	3	48	no	—
263	C₂⁴	—	4	8	no	—
264	C₂⁴	—	12	16	no	—
265	C₂⁴	C₂²×C₃×D₃	1	4	yes	—
266	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
267	C₂⁴	C₂²×C₃×D₃	1	24	yes	complemented
268	#41	—	3	256	no	—
269	#41	—	3	128	no	—
270	C₂×Q₈	—	3	24	no	—
271	C₂×D₄	—	3	96	no	—
272	C₂×D₄	—	3	48	no	—
273	C₂×D₄	—	3	256	no	—
274	C₂×D₄	—	3	256	no	—
275	C₂×D₄	—	3	24	no	—
276	C₂×D₄	C₂²×C₃×D₃	1	48	yes	complemented
277	C₂×D₄	C₂²×C₃×D₃	1	64	yes	complemented
278	C₂²×C₄	—	3	4	no	—
279	C₂²×C₄	—	3	48	no	—
280	C₂²×C₄	—	3	48	no	—
281	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
282	C₂²×C₄	C₂²×C₃×D₃	1	12	yes	complemented
283	C₂²×C₃	—	2	24	no	—
284	C₂²×C₃	—	2	12	no	—
285	C₂²×C₃	—	2	48	no	—
286	C₂²×C₃	—	2	48	no	—
287	C₂²×C₃	—	2	12	no	—
288	C₂²×C₃	—	2	4	no	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	2	3	no	—
291	C₂²×C₃	—	2	16	no	—
292	C₂²×C₃	—	3	16	no	—
293	C₂²×C₃	—	4	48	no	—
294	C₂²×C₃	—	4	32	no	—
295	C₂²×C₃	—	4	32	no	—
296	C₂²×C₃	—	4	64	no	—
297	C₂²×C₃	—	6	48	no	—
298	C₂²×C₃	—	12	64	no	—
299	C₂²×C₃	#1004	1	4	yes	direct product factor
300	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	complemented
301	C₂²×C₃	C₂⁴×D₃	1	16	yes	—
302	C₂²×C₃	C₂⁴×D₃	1	4	yes	—
303	C₂²×C₃	C₂⁴×D₃	1	3	yes	—
304	C₂²×C₃	C₂⁵×C₃	1	16	yes	—
305	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
306	C₂²×C₃	C₂⁵×C₃	1	3	yes	—
307	C₂×D₃	—	2	48	no	—
308	C₂×D₃	—	4	64	no	—
309	C₂×D₃	C₂⁵×C₃	1	16	yes	—
310	C₃×C₄	—	2	8	no	—
311	C₃×C₄	—	3	16	no	—
312	C₃×C₄	C₂⁴×D₃	1	8	yes	—
313	C₃×C₄	C₂⁵×C₃	1	8	yes	—
314	Dic₃	C₂⁵×C₃	1	16	yes	—
315	C₃²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
316	C₂³	—	2	4	no	—
317	C₂³	—	2	16	no	—
318	C₂³	—	3	24	no	—
319	C₂³	—	3	64	no	—
320	C₂³	—	4	48	no	—
321	C₂³	—	6	16	no	—
322	C₂³	—	12	96	no	—
323	C₂³	C₂³×C₃×D₃	1	24	yes	—
324	C₂³	C₂³×C₃×D₃	1	6	yes	—
325	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
326	C₂³	C₂³×C₃×D₃	1	32	yes	complemented
327	Q₈	—	3	32	no	—
328	D₄	—	3	128	no	—
329	D₄	—	3	64	no	—
330	D₄	—	3	32	no	—
331	D₄	C₂³×C₃×D₃	1	64	yes	complemented
332	C₂×C₄	—	3	24	no	—
333	C₂×C₄	—	3	64	no	—
334	C₂×C₄	—	3	64	no	—
335	C₂×C₄	C₂³×C₃×D₃	1	12	yes	—
336	C₂×C₄	C₂³×C₃×D₃	1	16	yes	complemented
337	C₂×C₃	—	2	8	no	—
338	C₂×C₃	—	2	4	no	—
339	C₂×C₃	—	2	16	no	—
340	C₂×C₃	—	2	16	no	—
341	C₂×C₃	—	2	4	no	—
342	C₂×C₃	—	2	6	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	4	16	no	—
345	C₂×C₃	—	6	16	no	—
346	C₂×C₃	C₂×#1004	1	6	yes	direct product factor
347	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	6	yes	complemented
348	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
349	C₂×C₃	C₂⁶×C₃	1	1	yes	characteristic
350	D₃	—	2	16	no	—
351	C₂²	—	2	12	no	—
352	C₂²	—	2	48	no	—
353	C₂²	—	3	16	no	—
354	C₂²	—	4	32	no	—
355	C₂²	—	6	48	no	—
356	C₂²	—	12	64	no	—
357	C₂²	C₃×#1004	1	4	yes	direct product factor
358	C₂²	C₂⁴×C₃×D₃	1	16	yes	—
359	C₂²	C₂⁴×C₃×D₃	1	4	yes	—
360	C₂²	C₂⁴×C₃×D₃	1	3	yes	—
361	C₄	—	3	16	no	—
362	C₄	C₂⁴×C₃×D₃	1	8	yes	—
363	C₃	—	2	1	no	—
364	C₃	C₂²×#1004	1	1	yes	characteristic, direct product factor
365	C₃	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
366	C₂	—	2	4	no	—
367	C₂	—	2	16	no	—
368	C₂	—	6	16	no	—
369	C₂	C₂×C₃×#1004	1	6	yes	direct product factor
370	C₂	C₂⁵×C₃×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂×C₃	C₂⁶×C₃
Frattini	C₂	C₂⁵×C₃×D₃
Fitting	C₂³×C₃²×D₄	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂³×C₃×D₄	D₃
hypocenter	C₃	C₂²×C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃²×D₄	C₂	semidirect
2. C₂³×C₃×#67	C₂	semidirect
3. C₂×C₃×#1004	C₂	direct (N × H)
4. C₂²×C₃×#237	C₂	semidirect
5. C₂²×C₃×D₃×D₄	C₂	semidirect
6. C₂²×C₃×#235	C₂	semidirect
8. C₂²×#1004	C₃	direct (N × H)
9. C₂⁵×C₃²	C₂²	semidirect
10. C₂⁴×C₃×D₃	C₂²	semidirect
11. C₂²×C₃²×D₄	C₂²	semidirect
12. C₂²×C₃²×D₄	C₂²	semidirect
13. C₂³×C₃²×C₄	C₂²	semidirect
14. C₂²×C₃×#67	C₂²	semidirect
15. C₂²×C₃×#67	C₂²	semidirect
16. C₂²×C₃×#67	C₂²	semidirect
17. C₂³×C₃×Dic₃	C₂²	semidirect
18. C₃×#1004	C₂²	direct (N × H)
19. C₂×C₃×#237	C₂²	semidirect
20. C₂×C₃×D₃×D₄	C₂²	semidirect
21. C₂×C₃×#235	C₂²	semidirect
22. C₂²×C₃×D₁₂	C₂²	semidirect
23. C₂²×C₃×C₄×D₃	C₂²	semidirect
24. C₂²×C₃×Dic₆	C₂²	semidirect
31. C₂³×C₃×D₄	D₃	semidirect
32. C₂³×C₃×D₄	C₂×C₃	semidirect
33. C₂³×#67	C₂×C₃	semidirect
34. C₂×#1004	C₂×C₃	direct (N × H)
35. C₂²×#237	C₂×C₃	semidirect
36. C₂²×D₃×D₄	C₂×C₃	semidirect
37. C₂²×#235	C₂×C₃	semidirect
41. C₂⁴×C₃²	C₂³	semidirect
44. C₂³×C₃×D₃	C₂³	semidirect
45. C₂×C₃²×D₄	C₂³	semidirect
46. C₂×C₃²×D₄	C₂³	semidirect
48. C₂²×C₃²×C₄	C₂³	semidirect
49. C₂×C₃×#67	C₂³	semidirect
50. C₂×C₃×#67	C₂³	semidirect
51. C₂×C₃×#67	C₂³	semidirect
53. C₂²×C₃×Dic₃	C₂³	semidirect
54. C₃×#237	C₂³	semidirect
55. C₃×D₃×D₄	C₂³	semidirect
56. C₃×#235	C₂³	semidirect
57. C₂×C₃×D₁₂	C₂³	semidirect
58. C₂×C₃×C₄×D₃	C₂³	semidirect
59. C₂×C₃×Dic₆	C₂³	semidirect
63. C₂⁵×C₃	C₂×D₃	semidirect
64. C₂⁵×C₃	C₂²×C₃	semidirect
65. C₂⁴×D₃	C₂²×C₃	semidirect
77. C₂²×C₃×D₄	C₂×D₃	semidirect
78. C₂²×C₃×D₄	C₂×D₃	semidirect
79. C₂²×C₃×D₄	C₂²×C₃	semidirect
80. C₂²×C₃×D₄	C₂²×C₃	semidirect
84. C₂³×C₃×C₄	C₂×D₃	semidirect
85. C₂³×C₃×C₄	C₂²×C₃	semidirect
86. C₂²×#67	C₂²×C₃	semidirect
87. C₂²×#67	C₂²×C₃	semidirect
88. C₂²×#67	C₂²×C₃	semidirect
89. C₂³×Dic₃	C₂²×C₃	semidirect
90. #1004	C₂²×C₃	direct (N × H)
91. C₂×#237	C₂²×C₃	semidirect
92. C₂×D₃×D₄	C₂²×C₃	semidirect
93. C₂×#235	C₂²×C₃	semidirect
94. C₂²×D₁₂	C₂²×C₃	semidirect
95. C₂²×C₄×D₃	C₂²×C₃	semidirect
96. C₂²×Dic₆	C₂²×C₃	semidirect
103. C₂³×C₃²	C₂⁴	semidirect
107. C₂²×C₃×D₃	C₂⁴	semidirect
108. C₃²×D₄	C₂⁴	semidirect
110. C₂×C₃²×C₄	C₂⁴	semidirect
111. C₃×#67	C₂⁴	semidirect
112. C₃×#67	C₂⁴	semidirect
114. C₂×C₃×Dic₃	C₂⁴	semidirect
115. C₃×D₁₂	C₂⁴	semidirect
116. C₃×C₄×D₃	C₂⁴	semidirect
117. C₃×Dic₆	C₂⁴	semidirect
123. C₂³×D₄	C₃×D₃	semidirect
135. C₂⁴×C₃	C₂²×D₃	semidirect
138. C₂⁴×C₃	C₂³×C₃	semidirect
141. C₂³×D₃	C₂³×C₃	semidirect
152. C₂×C₃×D₄	C₂²×D₃	semidirect
153. C₂×C₃×D₄	C₂²×D₃	semidirect
154. C₂×C₃×D₄	C₂³×C₃	semidirect
155. C₂×C₃×D₄	C₂³×C₃	semidirect
162. C₂²×C₃×C₄	C₂²×D₃	semidirect
164. C₂²×C₃×C₄	C₂³×C₃	semidirect
165. C₂×#67	C₂³×C₃	semidirect
166. C₂×#67	C₂³×C₃	semidirect
167. C₂×#67	C₂³×C₃	semidirect
169. C₂²×Dic₃	C₂³×C₃	semidirect
170. #237	C₂³×C₃	semidirect
171. D₃×D₄	C₂³×C₃	semidirect
172. #235	C₂³×C₃	semidirect
173. C₂×D₁₂	C₂³×C₃	semidirect
174. C₂×C₄×D₃	C₂³×C₃	semidirect
175. C₂×Dic₆	C₂³×C₃	semidirect
179. C₂²×C₃²	H(5,𝔽₂)	semidirect
189. C₂⁵	C₂×C₃×D₃	semidirect
199. C₂²×D₄	C₂×C₃×D₃	semidirect
200. C₂²×D₄	C₂×C₃×D₃	semidirect
203. C₂³×C₄	C₂×C₃×D₃	semidirect
224. C₂³×C₃	C₂³×D₃	semidirect
228. C₂³×C₃	C₂⁴×C₃	semidirect
232. C₂²×D₃	C₂⁴×C₃	semidirect
238. C₃×D₄	C₂³×D₃	semidirect
239. C₃×D₄	C₂⁴×C₃	semidirect
246. C₂×C₃×C₄	C₂³×D₃	semidirect
248. C₂×C₃×C₄	C₂⁴×C₃	semidirect
249. #67	C₂⁴×C₃	semidirect
250. #67	C₂⁴×C₃	semidirect
252. C₂×Dic₃	C₂⁴×C₃	semidirect
253. D₁₂	C₂⁴×C₃	semidirect
254. C₄×D₃	C₂⁴×C₃	semidirect
255. Dic₆	C₂⁴×C₃	semidirect
258. C₂×C₃²	C₂×H(5,𝔽₂)	semidirect
267. C₂⁴	C₂²×C₃×D₃	semidirect
276. C₂×D₄	C₂²×C₃×D₃	semidirect
277. C₂×D₄	C₂²×C₃×D₃	semidirect
282. C₂²×C₄	C₂²×C₃×D₃	semidirect
299. C₂²×C₃	#1004	direct (N × H)
300. C₂²×C₃	C₃×H(5,𝔽₂)	semidirect
315. C₃²	C₂²×H(5,𝔽₂)	semidirect
326. C₂³	C₂³×C₃×D₃	semidirect
331. D₄	C₂³×C₃×D₃	semidirect
336. C₂×C₄	C₂³×C₃×D₃	semidirect
346. C₂×C₃	C₂×#1004	direct (N × H)
347. C₂×C₃	C₂×C₃×H(5,𝔽₂)	semidirect
357. C₂²	C₃×#1004	direct (N × H)
364. C₃	C₂²×#1004	direct (N × H)
365. C₃	C₂²×C₃×H(5,𝔽₂)	semidirect
369. C₂	C₂×C₃×#1004	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃²×D₄	2
C₂³×C₃×#67	2
C₂×C₃×#1004	2
C₂²×C₃×#237	2
C₂²×C₃×D₃×D₄	2
C₂²×C₃×#235	2
C₂²×C₃×H(5,𝔽₂)	3
C₂²×#1004	3

Subgroups — C22×C3×#1004 #11919213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#1004 #11919213