Subgroups — C₂²×C₃×#577 #10681692

Order 768.

11118 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#577	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₃×#137	C₂	1	3	yes	maximal, complemented
5	C₂²×C₃×AGL(1,ℤ/8)	C₂	1	3	yes	maximal, complemented
6	C₂²×C₃×#135	C₂	1	3	yes	maximal, complemented
7	C₂³×C₃×SD₁₆	C₂	1	3	yes	maximal, complemented
8	C₂²×C₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#577	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃×2₋¹⁺⁴	—	2	12	no	—
11	C₂×C₃×2₋¹⁺⁴	C₂²	1	24	yes	complemented
12	C₂×C₃×H(5,𝔽₂)	—	2	12	no	—
13	C₂×C₃×H(5,𝔽₂)	C₂²	1	24	yes	complemented
14	C₂²×C₃×#41	—	2	1	no	—
15	C₂²×C₃×#41	—	2	3	no	—
16	C₂²×C₃×#41	C₂²	1	3	yes	—
17	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#41	C₂²	1	3	yes	complemented
19	C₂³×C₃×Q₈	—	2	1	no	—
20	C₂³×C₃×Q₈	C₂²	1	3	yes	complemented
21	C₂³×C₃×D₄	—	2	3	no	—
22	C₂³×C₃×D₄	C₂²	1	3	yes	—
23	C₃×#577	C₂²	1	256	yes	direct product factor
24	C₂×C₃×#137	C₂²	1	72	yes	complemented
25	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	72	yes	complemented
26	C₂×C₃×#135	C₂²	1	72	yes	complemented
27	C₂²×C₃×Q₁₆	C₂²	1	3	yes	complemented
28	C₂²×C₃×SD₁₆	C₂²	1	3	yes	complemented
29	C₂²×C₃×SD₁₆	C₂²	1	6	yes	complemented
30	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×SD₁₆	C₂²	1	72	yes	complemented
32	C₂²×C₃×D₈	C₂²	1	3	yes	complemented
33	C₂×C₃×#131	C₂²	1	24	yes	complemented
34	C₂²×C₃×M₁₆	C₂²	1	3	yes	complemented
35	C₂³×C₃×C₈	C₂²	1	3	yes	complemented
36	C₂²×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂²×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#577	C₂×C₃	1	48	yes	direct product factor
39	C₂²×#137	C₂×C₃	1	3	yes	complemented
40	C₂²×AGL(1,ℤ/8)	C₂×C₃	1	3	yes	complemented
41	C₂²×#135	C₂×C₃	1	3	yes	complemented
42	C₂³×SD₁₆	C₂×C₃	1	3	yes	complemented
43	C₂²×#131	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁵×C₃	—	2	3	no	—
45	C₃×2₋¹⁺⁴	—	2	96	no	—
46	C₃×2₋¹⁺⁴	C₂³	1	64	yes	complemented
47	C₃×H(5,𝔽₂)	—	2	96	no	—
48	C₃×H(5,𝔽₂)	C₂³	1	64	yes	complemented
49	C₂×C₃×#41	—	2	24	no	—
50	C₂×C₃×#41	—	2	72	no	—
51	C₂×C₃×#41	—	2	18	no	—
52	C₂×C₃×#41	—	2	18	no	—
53	C₂×C₃×#41	D₄	1	12	yes	—
54	C₂×C₃×#41	C₂³	1	36	yes	—
55	C₂×C₃×#41	C₂³	1	12	yes	—
56	C₂×C₃×#41	C₂³	1	36	yes	complemented
57	C₂²×C₃×Q₈	—	2	24	no	—
58	C₂²×C₃×Q₈	—	2	3	no	—
59	C₂²×C₃×Q₈	—	2	18	no	—
60	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
61	C₂²×C₃×Q₈	C₂³	1	3	yes	—
62	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₃×Q₈	C₂³	1	36	yes	complemented
64	C₂²×C₃×D₄	—	2	3	no	—
65	C₂²×C₃×D₄	—	2	3	no	—
66	C₂²×C₃×D₄	—	2	72	no	—
67	C₂²×C₃×D₄	—	2	3	no	—
68	C₂²×C₃×D₄	—	2	18	no	—
69	C₂²×C₃×D₄	D₄	1	3	yes	—
70	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₃×D₄	C₂³	1	3	yes	—
72	C₂²×C₃×D₄	C₂³	1	36	yes	—
73	C₂³×C₃×C₄	—	2	3	no	—
74	C₂³×C₃×C₄	—	2	3	no	—
75	C₂³×C₃×C₄	—	2	3	no	—
76	C₂³×C₃×C₄	C₂³	1	3	yes	—
77	C₃×#137	C₂³	1	192	yes	complemented
78	C₃×AGL(1,ℤ/8)	C₂³	1	192	yes	complemented
79	C₃×#135	C₂³	1	192	yes	complemented
80	C₂×C₃×Q₁₆	C₂³	1	36	yes	complemented
81	C₂×C₃×SD₁₆	C₂³	1	36	yes	complemented
82	C₂×C₃×SD₁₆	C₂³	1	72	yes	complemented
83	C₂×C₃×SD₁₆	C₂³	1	12	yes	complemented
84	C₂×C₃×SD₁₆	C₂³	1	192	yes	complemented
85	C₂×C₃×D₈	C₂³	1	36	yes	complemented
86	C₃×#131	C₂³	1	64	yes	complemented
87	C₂×C₃×M₁₆	C₂³	1	36	yes	complemented
88	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₈	C₂³	1	3	yes	—
90	C₂²×C₃×C₈	C₂³	1	36	yes	complemented
91	C₂×2₋¹⁺⁴	—	2	12	no	—
92	C₂×2₋¹⁺⁴	C₂²×C₃	1	24	yes	complemented
93	C₂×H(5,𝔽₂)	—	2	12	no	—
94	C₂×H(5,𝔽₂)	C₂²×C₃	1	24	yes	complemented
95	C₂²×#41	—	2	1	no	—
96	C₂²×#41	—	2	3	no	—
97	C₂²×#41	C₂²×C₃	1	3	yes	—
98	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂²×#41	C₂²×C₃	1	3	yes	complemented
100	C₂³×Q₈	—	2	1	no	—
101	C₂³×Q₈	C₂²×C₃	1	3	yes	complemented
102	C₂³×D₄	—	2	3	no	—
103	C₂³×D₄	C₂²×C₃	1	3	yes	—
104	#577	C₂²×C₃	1	256	yes	direct product factor
105	C₂×#137	C₂²×C₃	1	72	yes	complemented
106	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	72	yes	complemented
107	C₂×#135	C₂²×C₃	1	72	yes	complemented
108	C₂²×Q₁₆	C₂²×C₃	1	3	yes	complemented
109	C₂²×SD₁₆	C₂²×C₃	1	3	yes	complemented
110	C₂²×SD₁₆	C₂²×C₃	1	6	yes	complemented
111	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂²×SD₁₆	C₂²×C₃	1	72	yes	complemented
113	C₂²×D₈	C₂²×C₃	1	3	yes	complemented
114	C₂×#131	C₂²×C₃	1	24	yes	complemented
115	C₂²×M₁₆	C₂²×C₃	1	3	yes	complemented
116	C₂³×C₈	C₂²×C₃	1	3	yes	complemented
117	C₂⁴×C₃	—	2	3	no	—
118	C₂⁴×C₃	—	2	1	no	—
119	C₂⁴×C₃	—	2	36	no	—
120	C₂⁴×C₃	—	8	12	no	—
121	C₂⁴×C₃	C₂×D₄	1	3	yes	—
122	C₃×#41	—	2	64	no	—
123	C₃×#41	—	2	192	no	—
124	C₃×#41	—	2	72	no	—
125	C₃×#41	—	2	72	no	—
126	C₃×#41	C₂×D₄	1	48	yes	—
127	C₃×#41	C₂⁴	1	48	yes	—
128	C₃×#41	C₂⁴	1	16	yes	—
129	C₃×#41	C₂⁴	1	48	yes	complemented
130	C₂×C₃×Q₈	—	2	64	no	—
131	C₂×C₃×Q₈	—	2	9	no	—
132	C₂×C₃×Q₈	—	2	36	no	—
133	C₂×C₃×Q₈	—	2	72	no	—
134	C₂×C₃×Q₈	—	2	3	no	—
135	C₂×C₃×Q₈	C₂×D₄	1	12	yes	—
136	C₂×C₃×Q₈	C₂⁴	1	18	yes	—
137	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
138	C₂×C₃×Q₈	C₂⁴	1	48	yes	complemented
139	C₂×C₃×D₄	—	2	36	no	—
140	C₂×C₃×D₄	—	2	36	no	—
141	C₂×C₃×D₄	—	2	192	no	—
142	C₂×C₃×D₄	—	2	36	no	—
143	C₂×C₃×D₄	—	2	9	no	—
144	C₂×C₃×D₄	—	2	72	no	—
145	C₂×C₃×D₄	—	2	3	no	—
146	C₂×C₃×D₄	C₂×D₄	1	36	yes	—
147	C₂×C₃×D₄	C₂⁴	1	6	yes	—
148	C₂×C₃×D₄	C₂⁴	1	18	yes	—
149	C₂×C₃×D₄	C₂⁴	1	48	yes	—
150	C₂²×C₃×C₄	—	2	36	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	2	3	no	—
153	C₂²×C₃×C₄	—	2	36	no	—
154	C₂²×C₃×C₄	—	2	36	no	—
155	C₂²×C₃×C₄	C₂×D₄	1	18	yes	—
156	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
157	C₂²×C₃×C₄	C₂⁴	1	18	yes	—
158	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
159	C₃×Q₁₆	C₂⁴	1	48	yes	complemented
160	C₃×SD₁₆	C₂⁴	1	48	yes	complemented
161	C₃×SD₁₆	C₂⁴	1	96	yes	complemented
162	C₃×SD₁₆	C₂⁴	1	16	yes	complemented
163	C₃×D₈	C₂⁴	1	48	yes	complemented
164	C₃×M₁₆	C₂⁴	1	48	yes	complemented
165	C₂×C₃×C₈	C₂⁴	1	6	yes	—
166	C₂×C₃×C₈	C₂⁴	1	18	yes	—
167	C₂×C₃×C₈	C₂⁴	1	48	yes	complemented
168	C₂⁵	—	2	3	no	—
169	2₋¹⁺⁴	—	2	96	no	—
170	2₋¹⁺⁴	C₂³×C₃	1	64	yes	complemented
171	H(5,𝔽₂)	—	2	96	no	—
172	H(5,𝔽₂)	C₂³×C₃	1	64	yes	complemented
173	C₂×#41	—	2	24	no	—
174	C₂×#41	—	2	72	no	—
175	C₂×#41	—	2	18	no	—
176	C₂×#41	—	2	18	no	—
177	C₂×#41	C₃×D₄	1	12	yes	—
178	C₂×#41	C₂³×C₃	1	36	yes	—
179	C₂×#41	C₂³×C₃	1	12	yes	—
180	C₂×#41	C₂³×C₃	1	36	yes	complemented
181	C₂²×Q₈	—	2	24	no	—
182	C₂²×Q₈	—	2	3	no	—
183	C₂²×Q₈	—	2	18	no	—
184	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
185	C₂²×Q₈	C₂³×C₃	1	3	yes	—
186	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
187	C₂²×Q₈	C₂³×C₃	1	36	yes	complemented
188	C₂²×D₄	—	2	3	no	—
189	C₂²×D₄	—	2	3	no	—
190	C₂²×D₄	—	2	72	no	—
191	C₂²×D₄	—	2	3	no	—
192	C₂²×D₄	—	2	18	no	—
193	C₂²×D₄	C₃×D₄	1	3	yes	—
194	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×D₄	C₂³×C₃	1	3	yes	—
196	C₂²×D₄	C₂³×C₃	1	36	yes	—
197	C₂³×C₄	—	2	3	no	—
198	C₂³×C₄	—	2	3	no	—
199	C₂³×C₄	—	2	3	no	—
200	C₂³×C₄	C₂³×C₃	1	3	yes	—
201	#137	C₂³×C₃	1	192	yes	complemented
202	AGL(1,ℤ/8)	C₂³×C₃	1	192	yes	complemented
203	#135	C₂³×C₃	1	192	yes	complemented
204	C₂×Q₁₆	C₂³×C₃	1	36	yes	complemented
205	C₂×SD₁₆	C₂³×C₃	1	36	yes	complemented
206	C₂×SD₁₆	C₂³×C₃	1	72	yes	complemented
207	C₂×SD₁₆	C₂³×C₃	1	12	yes	complemented
208	C₂×SD₁₆	C₂³×C₃	1	192	yes	complemented
209	C₂×D₈	C₂³×C₃	1	36	yes	complemented
210	#131	C₂³×C₃	1	64	yes	complemented
211	C₂×M₁₆	C₂³×C₃	1	36	yes	complemented
212	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₃	1	3	yes	—
214	C₂²×C₈	C₂³×C₃	1	36	yes	complemented
215	C₂³×C₃	—	2	12	no	—
216	C₂³×C₃	—	2	6	no	—
217	C₂³×C₃	—	2	18	no	—
218	C₂³×C₃	—	2	48	no	—
219	C₂³×C₃	—	4	4	no	—
220	C₂³×C₃	—	4	12	no	—
221	C₂³×C₃	—	8	72	no	—
222	C₂³×C₃	C₂²×D₄	1	18	yes	—
223	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
224	C₃×Q₈	—	2	18	no	—
225	C₃×Q₈	—	2	48	no	—
226	C₃×Q₈	—	2	6	no	—
227	C₃×Q₈	C₂²×D₄	1	16	yes	—
228	C₃×Q₈	C₂⁵	1	12	yes	—
229	C₃×Q₈	C₂⁵	1	4	yes	—
230	C₃×D₄	—	2	48	no	—
231	C₃×D₄	—	2	48	no	—
232	C₃×D₄	—	2	48	no	—
233	C₃×D₄	—	2	18	no	—
234	C₃×D₄	—	2	6	no	—
235	C₃×D₄	C₂²×D₄	1	48	yes	—
236	C₃×D₄	C₂⁵	1	4	yes	—
237	C₃×D₄	C₂⁵	1	12	yes	—
238	C₂×C₃×C₄	—	2	6	no	—
239	C₂×C₃×C₄	—	2	18	no	—
240	C₂×C₃×C₄	—	2	48	no	—
241	C₂×C₃×C₄	—	2	48	no	—
242	C₂×C₃×C₄	—	2	48	no	—
243	C₂×C₃×C₄	C₂²×D₄	1	18	yes	—
244	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
245	C₂×C₃×C₄	C₂²×D₄	1	36	yes	—
246	C₂×C₃×C₄	C₂⁵	1	3	yes	—
247	C₂×C₃×C₄	C₂⁵	1	12	yes	—
248	C₃×C₈	C₂⁵	1	4	yes	—
249	C₃×C₈	C₂⁵	1	12	yes	—
250	C₂⁴	—	2	1	no	—
251	C₂⁴	—	2	3	no	—
252	C₂⁴	—	2	36	no	—
253	C₂⁴	—	8	12	no	—
254	C₂⁴	C₂×C₃×D₄	1	3	yes	—
255	#41	—	2	64	no	—
256	#41	—	2	192	no	—
257	#41	—	2	72	no	—
258	#41	—	2	72	no	—
259	#41	C₂×C₃×D₄	1	48	yes	—
260	#41	C₂⁴×C₃	1	48	yes	—
261	#41	C₂⁴×C₃	1	16	yes	—
262	#41	C₂⁴×C₃	1	48	yes	complemented
263	C₂×Q₈	—	2	64	no	—
264	C₂×Q₈	—	2	9	no	—
265	C₂×Q₈	—	2	36	no	—
266	C₂×Q₈	—	2	72	no	—
267	C₂×Q₈	—	2	3	no	—
268	C₂×Q₈	C₂×C₃×D₄	1	12	yes	—
269	C₂×Q₈	C₂⁴×C₃	1	18	yes	—
270	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
271	C₂×Q₈	C₂⁴×C₃	1	48	yes	complemented
272	C₂×D₄	—	2	36	no	—
273	C₂×D₄	—	2	36	no	—
274	C₂×D₄	—	2	192	no	—
275	C₂×D₄	—	2	36	no	—
276	C₂×D₄	—	2	9	no	—
277	C₂×D₄	—	2	72	no	—
278	C₂×D₄	—	2	3	no	—
279	C₂×D₄	C₂×C₃×D₄	1	36	yes	—
280	C₂×D₄	C₂⁴×C₃	1	6	yes	—
281	C₂×D₄	C₂⁴×C₃	1	18	yes	—
282	C₂×D₄	C₂⁴×C₃	1	48	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	3	no	—
285	C₂²×C₄	—	2	36	no	—
286	C₂²×C₄	—	2	36	no	—
287	C₂²×C₄	—	2	36	no	—
288	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
289	C₂²×C₄	C₂×C₃×D₄	1	18	yes	—
290	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴×C₃	1	18	yes	—
292	Q₁₆	C₂⁴×C₃	1	48	yes	complemented
293	SD₁₆	C₂⁴×C₃	1	48	yes	complemented
294	SD₁₆	C₂⁴×C₃	1	96	yes	complemented
295	SD₁₆	C₂⁴×C₃	1	16	yes	complemented
296	D₈	C₂⁴×C₃	1	48	yes	complemented
297	M₁₆	C₂⁴×C₃	1	48	yes	complemented
298	C₂×C₈	C₂⁴×C₃	1	6	yes	—
299	C₂×C₈	C₂⁴×C₃	1	18	yes	—
300	C₂×C₈	C₂⁴×C₃	1	48	yes	complemented
301	C₂²×C₃	—	2	36	no	—
302	C₂²×C₃	—	2	4	no	—
303	C₂²×C₃	—	2	12	no	—
304	C₂²×C₃	—	4	12	no	—
305	C₂²×C₃	—	4	36	no	—
306	C₂²×C₃	—	8	48	no	—
307	C₂²×C₃	#577	1	4	yes	direct product factor
308	C₂²×C₃	C₂³×D₄	1	12	yes	—
309	C₂²×C₃	C₂³×D₄	1	3	yes	—
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	—	2	12	no	—
312	C₃×C₄	C₂³×D₄	1	12	yes	—
313	C₃×C₄	C₂³×D₄	1	3	yes	—
314	C₃×C₄	C₂⁶	1	1	yes	characteristic
315	C₂³	—	2	12	no	—
316	C₂³	—	2	6	no	—
317	C₂³	—	2	18	no	—
318	C₂³	—	2	48	no	—
319	C₂³	—	4	12	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	8	72	no	—
322	C₂³	C₂²×C₃×D₄	1	18	yes	—
323	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
324	Q₈	—	2	18	no	—
325	Q₈	—	2	48	no	—
326	Q₈	—	2	6	no	—
327	Q₈	C₂²×C₃×D₄	1	16	yes	—
328	Q₈	C₂⁵×C₃	1	12	yes	—
329	Q₈	C₂⁵×C₃	1	4	yes	—
330	D₄	—	2	48	no	—
331	D₄	—	2	48	no	—
332	D₄	—	2	48	no	—
333	D₄	—	2	18	no	—
334	D₄	—	2	6	no	—
335	D₄	C₂²×C₃×D₄	1	48	yes	—
336	D₄	C₂⁵×C₃	1	4	yes	—
337	D₄	C₂⁵×C₃	1	12	yes	—
338	C₂×C₄	—	2	6	no	—
339	C₂×C₄	—	2	18	no	—
340	C₂×C₄	—	2	48	no	—
341	C₂×C₄	—	2	48	no	—
342	C₂×C₄	—	2	48	no	—
343	C₂×C₄	C₂²×C₃×D₄	1	18	yes	—
344	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
345	C₂×C₄	C₂²×C₃×D₄	1	36	yes	—
346	C₂×C₄	C₂⁵×C₃	1	3	yes	—
347	C₂×C₄	C₂⁵×C₃	1	12	yes	—
348	C₈	C₂⁵×C₃	1	4	yes	—
349	C₈	C₂⁵×C₃	1	12	yes	—
350	C₂×C₃	—	2	12	no	—
351	C₂×C₃	—	4	4	no	—
352	C₂×C₃	—	4	12	no	—
353	C₂×C₃	C₂×#577	1	6	yes	direct product factor
354	C₂×C₃	C₂⁴×D₄	1	1	yes	characteristic
355	C₂²	—	2	36	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	12	no	—
358	C₂²	—	4	36	no	—
359	C₂²	—	4	12	no	—
360	C₂²	—	8	48	no	—
361	C₂²	C₃×#577	1	4	yes	direct product factor
362	C₂²	C₂³×C₃×D₄	1	12	yes	—
363	C₂²	C₂³×C₃×D₄	1	3	yes	—
364	C₄	—	2	4	no	—
365	C₄	—	2	12	no	—
366	C₄	C₂³×C₃×D₄	1	12	yes	—
367	C₄	C₂³×C₃×D₄	1	3	yes	—
368	C₄	C₂⁶×C₃	1	1	yes	characteristic
369	C₃	C₂²×#577	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	12	no	—
371	C₂	—	4	12	no	—
372	C₂	—	4	4	no	—
373	C₂	C₂×C₃×#577	1	6	yes	direct product factor
374	C₂	C₂⁴×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×2₋¹⁺⁴	C₂	semidirect
2. C₂²×C₃×H(5,𝔽₂)	C₂	semidirect
3. C₂×C₃×#577	C₂	direct (N × H)
4. C₂²×C₃×#137	C₂	semidirect
5. C₂²×C₃×AGL(1,ℤ/8)	C₂	semidirect
6. C₂²×C₃×#135	C₂	semidirect
7. C₂³×C₃×SD₁₆	C₂	semidirect
8. C₂²×C₃×#131	C₂	semidirect
9. C₂²×#577	C₃	direct (N × H)
11. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₃×#41	C₂²	semidirect
20. C₂³×C₃×Q₈	C₂²	semidirect
23. C₃×#577	C₂²	direct (N × H)
24. C₂×C₃×#137	C₂²	semidirect
25. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₃×#135	C₂²	semidirect
27. C₂²×C₃×Q₁₆	C₂²	semidirect
28. C₂²×C₃×SD₁₆	C₂²	semidirect
29. C₂²×C₃×SD₁₆	C₂²	semidirect
30. C₂²×C₃×SD₁₆	C₂²	semidirect
31. C₂²×C₃×SD₁₆	C₂²	semidirect
32. C₂²×C₃×D₈	C₂²	semidirect
33. C₂×C₃×#131	C₂²	semidirect
34. C₂²×C₃×M₁₆	C₂²	semidirect
35. C₂³×C₃×C₈	C₂²	semidirect
36. C₂²×2₋¹⁺⁴	C₂×C₃	semidirect
37. C₂²×H(5,𝔽₂)	C₂×C₃	semidirect
38. C₂×#577	C₂×C₃	direct (N × H)
39. C₂²×#137	C₂×C₃	semidirect
40. C₂²×AGL(1,ℤ/8)	C₂×C₃	semidirect
41. C₂²×#135	C₂×C₃	semidirect
42. C₂³×SD₁₆	C₂×C₃	semidirect
43. C₂²×#131	C₂×C₃	semidirect
46. C₃×2₋¹⁺⁴	C₂³	semidirect
48. C₃×H(5,𝔽₂)	C₂³	semidirect
56. C₂×C₃×#41	C₂³	semidirect
63. C₂²×C₃×Q₈	C₂³	semidirect
77. C₃×#137	C₂³	semidirect
78. C₃×AGL(1,ℤ/8)	C₂³	semidirect
79. C₃×#135	C₂³	semidirect
80. C₂×C₃×Q₁₆	C₂³	semidirect
81. C₂×C₃×SD₁₆	C₂³	semidirect
82. C₂×C₃×SD₁₆	C₂³	semidirect
83. C₂×C₃×SD₁₆	C₂³	semidirect
84. C₂×C₃×SD₁₆	C₂³	semidirect
85. C₂×C₃×D₈	C₂³	semidirect
86. C₃×#131	C₂³	semidirect
87. C₂×C₃×M₁₆	C₂³	semidirect
90. C₂²×C₃×C₈	C₂³	semidirect
92. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
94. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
99. C₂²×#41	C₂²×C₃	semidirect
101. C₂³×Q₈	C₂²×C₃	semidirect
104. #577	C₂²×C₃	direct (N × H)
105. C₂×#137	C₂²×C₃	semidirect
106. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
107. C₂×#135	C₂²×C₃	semidirect
108. C₂²×Q₁₆	C₂²×C₃	semidirect
109. C₂²×SD₁₆	C₂²×C₃	semidirect
110. C₂²×SD₁₆	C₂²×C₃	semidirect
111. C₂²×SD₁₆	C₂²×C₃	semidirect
112. C₂²×SD₁₆	C₂²×C₃	semidirect
113. C₂²×D₈	C₂²×C₃	semidirect
114. C₂×#131	C₂²×C₃	semidirect
115. C₂²×M₁₆	C₂²×C₃	semidirect
116. C₂³×C₈	C₂²×C₃	semidirect
129. C₃×#41	C₂⁴	semidirect
138. C₂×C₃×Q₈	C₂⁴	semidirect
159. C₃×Q₁₆	C₂⁴	semidirect
160. C₃×SD₁₆	C₂⁴	semidirect
161. C₃×SD₁₆	C₂⁴	semidirect
162. C₃×SD₁₆	C₂⁴	semidirect
163. C₃×D₈	C₂⁴	semidirect
164. C₃×M₁₆	C₂⁴	semidirect
167. C₂×C₃×C₈	C₂⁴	semidirect
170. 2₋¹⁺⁴	C₂³×C₃	semidirect
172. H(5,𝔽₂)	C₂³×C₃	semidirect
180. C₂×#41	C₂³×C₃	semidirect
187. C₂²×Q₈	C₂³×C₃	semidirect
201. #137	C₂³×C₃	semidirect
202. AGL(1,ℤ/8)	C₂³×C₃	semidirect
203. #135	C₂³×C₃	semidirect
204. C₂×Q₁₆	C₂³×C₃	semidirect
205. C₂×SD₁₆	C₂³×C₃	semidirect
206. C₂×SD₁₆	C₂³×C₃	semidirect
207. C₂×SD₁₆	C₂³×C₃	semidirect
208. C₂×SD₁₆	C₂³×C₃	semidirect
209. C₂×D₈	C₂³×C₃	semidirect
210. #131	C₂³×C₃	semidirect
211. C₂×M₁₆	C₂³×C₃	semidirect
214. C₂²×C₈	C₂³×C₃	semidirect
262. #41	C₂⁴×C₃	semidirect
271. C₂×Q₈	C₂⁴×C₃	semidirect
292. Q₁₆	C₂⁴×C₃	semidirect
293. SD₁₆	C₂⁴×C₃	semidirect
294. SD₁₆	C₂⁴×C₃	semidirect
295. SD₁₆	C₂⁴×C₃	semidirect
296. D₈	C₂⁴×C₃	semidirect
297. M₁₆	C₂⁴×C₃	semidirect
300. C₂×C₈	C₂⁴×C₃	semidirect
307. C₂²×C₃	#577	direct (N × H)
353. C₂×C₃	C₂×#577	direct (N × H)
361. C₂²	C₃×#577	direct (N × H)
369. C₃	C₂²×#577	direct (N × H)
373. C₂	C₂×C₃×#577	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×C₃×2₋¹⁺⁴	2
C₂²×C₃×H(5,𝔽₂)	2
C₂×C₃×#577	2
C₂²×C₃×#137	2
C₂²×C₃×AGL(1,ℤ/8)	2
C₂²×C₃×#135	2
C₂³×C₃×SD₁₆	2
C₂²×C₃×#131	2
C₂²×#577	3

Subgroups — C22×C3×#577 #10681692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#577 #10681692