Subgroups — #3264×C₂₃₃ #44449296

Order 29824.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,ℤ/8)×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₈×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#546×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄²×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#496×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#469×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#465×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#463×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#459×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#450×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#449×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#447×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#447×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#442×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄×C₂₃₃	—	2	1	no	—
18	C₂²×D₄×C₂₃₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
21	AGL(1,ℤ/8)×C₂₃₃	—	2	4	no	—
22	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₈×C₂₃₃	—	2	4	no	—
26	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic
27	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic
28	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×M₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
34	#127×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
35	#124×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
36	#123×C₂₃₃	—	2	1	no	—
37	C₂²⋊Q₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
38	#121×C₂₃₃	—	2	1	no	—
39	#121×C₂₃₃	—	2	1	no	—
40	#121×C₂₃₃	C₂²	1	1	yes	characteristic
41	#121×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
42	#121×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
43	#120×C₂₃₃	—	2	1	no	—
44	#120×C₂₃₃	—	2	1	no	—
45	#120×C₂₃₃	—	2	1	no	—
46	C₄×D₄×C₂₃₃	C₂²	1	1	yes	characteristic
47	C₄×D₄×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₄×C₂₃₃	—	2	1	no	—
50	#106×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
51	C₄⋊C₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
52	#103×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
53	#102×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
54	#102×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
55	#102×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
56	#102×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
57	#102×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
60	#97×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₂₃₃	—	2	1	no	—
62	C₂⁴×C₂₃₃	—	2	1	no	—
63	C₂⁴×C₂₃₃	—	2	1	no	—
64	#41×C₂₃₃	—	2	2	no	—
65	#41×C₂₃₃	—	4	1	no	—
66	C₂×Q₈×C₂₃₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₂₃₃	—	2	2	no	—
68	C₂×D₄×C₂₃₃	—	2	2	no	—
69	C₂×D₄×C₂₃₃	—	2	2	no	—
70	C₂×D₄×C₂₃₃	—	2	1	no	—
71	C₂×D₄×C₂₃₃	—	2	1	no	—
72	C₂×D₄×C₂₃₃	—	2	1	no	—
73	C₂×D₄×C₂₃₃	—	2	1	no	—
74	C₂×D₄×C₂₃₃	—	2	1	no	—
75	C₂×D₄×C₂₃₃	—	2	1	no	—
76	C₂×D₄×C₂₃₃	—	2	1	no	—
77	C₂×D₄×C₂₃₃	—	2	1	no	—
78	C₂×D₄×C₂₃₃	—	2	1	no	—
79	C₂×D₄×C₂₃₃	—	4	1	no	—
80	C₂×D₄×C₂₃₃	—	4	1	no	—
81	C₂×D₄×C₂₃₃	—	4	1	no	—
82	C₂×D₄×C₂₃₃	—	4	4	no	—
83	C₂×D₄×C₂₃₃	D₄	1	1	yes	characteristic
84	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₂₃₃	—	2	1	no	—
90	C₂²×C₄×C₂₃₃	—	2	1	no	—
91	C₂²×C₄×C₂₃₃	—	2	1	no	—
92	C₂²×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
94	SD₁₆×C₂₃₃	—	2	2	no	—
95	SD₁₆×C₂₃₃	—	2	2	no	—
96	SD₁₆×C₂₃₃	—	4	1	no	—
97	D₈×C₂₃₃	—	2	2	no	—
98	D₈×C₂₃₃	—	2	2	no	—
99	D₈×C₂₃₃	—	2	2	no	—
100	D₈×C₂₃₃	—	2	2	no	—
101	D₈×C₂₃₃	—	4	1	no	—
102	D₈×C₂₃₃	D₄	1	4	yes	complemented
103	M₁₆×C₂₃₃	—	2	2	no	—
104	C₂×C₈×C₂₃₃	—	2	2	no	—
105	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₂₃₃	—	2	1	no	—
110	C₄⋊C₄×C₂₃₃	D₄	1	1	yes	characteristic
111	C₄⋊C₄×C₂₃₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₂₃₃	C₂³	1	1	yes	characteristic
113	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
114	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
115	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
116	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
117	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
118	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
119	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
120	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
121	C₂²⋊C₄×C₂₃₃	D₄	1	1	yes	characteristic
122	C₂²⋊C₄×C₂₃₃	D₄	1	1	yes	characteristic
123	C₄²×C₂₃₃	C₂³	1	1	yes	characteristic
124	C₂³×C₂₃₃	—	2	1	no	—
125	C₂³×C₂₃₃	—	2	1	no	—
126	C₂³×C₂₃₃	—	2	1	no	—
127	C₂³×C₂₃₃	—	2	1	no	—
128	C₂³×C₂₃₃	—	2	1	no	—
129	C₂³×C₂₃₃	—	4	2	no	—
130	C₂³×C₂₃₃	—	4	2	no	—
131	C₂³×C₂₃₃	—	4	2	no	—
132	C₂³×C₂₃₃	—	4	2	no	—
133	C₂³×C₂₃₃	—	4	2	no	—
134	C₂³×C₂₃₃	—	4	2	no	—
135	C₂³×C₂₃₃	—	8	1	no	—
136	C₂³×C₂₃₃	—	8	1	no	—
137	C₂³×C₂₃₃	—	8	1	no	—
138	C₂³×C₂₃₃	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₂₃₃	C₂×D₄	1	1	yes	characteristic
140	Q₈×C₂₃₃	—	2	1	no	—
141	Q₈×C₂₃₃	—	2	1	no	—
142	D₄×C₂₃₃	—	2	2	no	—
143	D₄×C₂₃₃	—	2	1	no	—
144	D₄×C₂₃₃	—	2	1	no	—
145	D₄×C₂₃₃	—	2	1	no	—
146	D₄×C₂₃₃	—	2	1	no	—
147	D₄×C₂₃₃	—	2	1	no	—
148	D₄×C₂₃₃	—	2	1	no	—
149	D₄×C₂₃₃	—	2	1	no	—
150	D₄×C₂₃₃	—	2	1	no	—
151	D₄×C₂₃₃	—	4	2	no	—
152	D₄×C₂₃₃	—	4	2	no	—
153	D₄×C₂₃₃	—	4	2	no	—
154	D₄×C₂₃₃	—	4	2	no	—
155	D₄×C₂₃₃	—	4	2	no	—
156	D₄×C₂₃₃	—	4	2	no	—
157	D₄×C₂₃₃	—	4	2	no	—
158	D₄×C₂₃₃	—	8	1	no	—
159	D₄×C₂₃₃	—	8	1	no	—
160	D₄×C₂₃₃	C₂×D₄	1	2	yes	—
161	D₄×C₂₃₃	C₂×D₄	1	2	yes	complemented
162	C₂×C₄×C₂₃₃	—	2	1	no	—
163	C₂×C₄×C₂₃₃	—	2	1	no	—
164	C₂×C₄×C₂₃₃	—	2	1	no	—
165	C₂×C₄×C₂₃₃	—	2	1	no	—
166	C₂×C₄×C₂₃₃	—	2	1	no	—
167	C₂×C₄×C₂₃₃	—	2	1	no	—
168	C₂×C₄×C₂₃₃	—	2	1	no	—
169	C₂×C₄×C₂₃₃	—	4	2	no	—
170	C₂×C₄×C₂₃₃	—	4	2	no	—
171	C₂×C₄×C₂₃₃	—	8	1	no	—
172	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×C₂₃₃	C₂⁴	1	1	yes	characteristic
177	C₈×C₂₃₃	—	2	1	no	—
178	C₈×C₂₃₃	—	2	1	no	—
179	C₈×C₂₃₃	—	2	1	no	—
180	C₈×C₂₃₃	C₂×D₄	1	2	yes	complemented
181	C₂²×C₂₃₃	—	2	1	no	—
182	C₂²×C₂₃₃	—	2	1	no	—
183	C₂²×C₂₃₃	—	2	1	no	—
184	C₂²×C₂₃₃	—	2	2	no	—
185	C₂²×C₂₃₃	—	2	2	no	—
186	C₂²×C₂₃₃	—	2	1	no	—
187	C₂²×C₂₃₃	—	2	1	no	—
188	C₂²×C₂₃₃	—	4	1	no	—
189	C₂²×C₂₃₃	—	4	1	no	—
190	C₂²×C₂₃₃	—	4	1	no	—
191	C₂²×C₂₃₃	—	4	1	no	—
192	C₂²×C₂₃₃	—	4	1	no	—
193	C₂²×C₂₃₃	—	4	1	no	—
194	C₂²×C₂₃₃	—	4	1	no	—
195	C₂²×C₂₃₃	—	4	1	no	—
196	C₂²×C₂₃₃	—	4	1	no	—
197	C₂²×C₂₃₃	—	4	1	no	—
198	C₂²×C₂₃₃	—	4	1	no	—
199	C₂²×C₂₃₃	—	4	1	no	—
200	C₂²×C₂₃₃	—	4	1	no	—
201	C₂²×C₂₃₃	—	8	4	no	—
202	C₂²×C₂₃₃	—	8	4	no	—
203	C₂²×C₂₃₃	—	8	4	no	—
204	C₂²×C₂₃₃	AGL(1,ℤ/8)	1	2	yes	complemented
205	C₂²×C₂₃₃	C₂²×D₄	1	1	yes	characteristic
206	C₄×C₂₃₃	—	2	1	no	—
207	C₄×C₂₃₃	—	2	1	no	—
208	C₄×C₂₃₃	—	2	1	no	—
209	C₄×C₂₃₃	—	2	1	no	—
210	C₄×C₂₃₃	—	4	1	no	—
211	C₄×C₂₃₃	—	4	1	no	—
212	C₄×C₂₃₃	—	4	1	no	—
213	C₄×C₂₃₃	C₂²×D₄	1	1	yes	characteristic
214	C₄×C₂₃₃	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₂₃₃	—	2	2	no	—
216	C₂×C₂₃₃	—	4	1	no	—
217	C₂×C₂₃₃	—	4	2	no	—
218	C₂×C₂₃₃	—	4	2	no	—
219	C₂×C₂₃₃	—	8	1	no	—
220	C₂×C₂₃₃	—	8	1	no	—
221	C₂×C₂₃₃	—	8	1	no	—
222	C₂×C₂₃₃	D₄²	1	1	yes	characteristic
223	C₂×C₂₃₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂×C₂₃₃	#576	1	1	yes	characteristic
225	C₂₃₃	#3264	1	1	yes	characteristic, direct product factor, Sylow
226	#3264	C₂₃₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×AGL(1,ℤ/8)	C₂×C₂₃₃	1	1	yes	characteristic, complemented
228	C₂²×D₈	C₂×C₂₃₃	1	1	yes	characteristic, complemented
229	#546	C₂×C₂₃₃	1	1	yes	characteristic, complemented
230	D₄²	C₂×C₂₃₃	1	1	yes	characteristic, complemented
231	#496	C₂×C₂₃₃	1	1	yes	characteristic, complemented
232	#469	C₂×C₂₃₃	1	1	yes	characteristic, complemented
233	#465	C₂×C₂₃₃	1	1	yes	characteristic, complemented
234	#463	C₂×C₂₃₃	1	1	yes	characteristic, complemented
235	#459	C₂×C₂₃₃	1	1	yes	characteristic, complemented
236	#450	C₂×C₂₃₃	1	1	yes	characteristic, complemented
237	#449	C₂×C₂₃₃	1	1	yes	characteristic, complemented
238	#447	C₂×C₂₃₃	1	1	yes	characteristic, complemented
239	#447	C₂×C₂₃₃	1	1	yes	characteristic, complemented
240	#442	C₂×C₂₃₃	1	1	yes	characteristic, complemented
241	#435	C₂×C₂₃₃	1	1	yes	characteristic, complemented
242	C₂×#41	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂²×C₂₃₃	1	1	yes	characteristic
245	C₂²×D₄	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
246	C₂²×D₄	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
247	AGL(1,ℤ/8)	—	2	4	no	—
248	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
249	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
250	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
251	C₂×D₈	—	2	4	no	—
252	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic
253	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic
254	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
255	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
256	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
257	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
258	C₂×M₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
259	C₂²×C₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
260	#127	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
261	#124	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
262	#123	—	2	1	no	—
263	C₂²⋊Q₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	#121	C₂²×C₂₃₃	1	1	yes	characteristic
267	#121	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
268	#121	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
269	#120	—	2	1	no	—
270	#120	—	2	1	no	—
271	#120	—	2	1	no	—
272	C₄×D₄	C₂²×C₂₃₃	1	1	yes	characteristic
273	C₄×D₄	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
274	C₄×D₄	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	#106	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
277	C₄⋊C₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
278	#103	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
279	#102	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
280	#102	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
281	#102	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
282	#102	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
283	#102	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
284	C₂²⋊C₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
285	C₂²⋊C₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
286	#97	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
287	C₂⁴	—	2	1	no	—
288	C₂⁴	—	2	1	no	—
289	C₂⁴	—	2	1	no	—
290	#41	—	2	2	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	C₂³×C₂₃₃	1	1	yes	characteristic
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	D₄×C₂₃₃	1	1	yes	characteristic
310	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
311	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
312	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
313	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
314	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	C₂³×C₂₃₃	1	1	yes	characteristic
319	C₂²×C₄	C₂³×C₂₃₃	1	1	yes	characteristic
320	SD₁₆	—	2	2	no	—
321	SD₁₆	—	2	2	no	—
322	SD₁₆	—	4	1	no	—
323	D₈	—	2	2	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	2	no	—
327	D₈	—	4	1	no	—
328	D₈	D₄×C₂₃₃	1	4	yes	complemented
329	M₁₆	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
332	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
333	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
334	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	D₄×C₂₃₃	1	1	yes	characteristic
337	C₄⋊C₄	C₂³×C₂₃₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂³×C₂₃₃	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	D₄×C₂₃₃	1	1	yes	characteristic
348	C₂²⋊C₄	D₄×C₂₃₃	1	1	yes	characteristic
349	C₄²	C₂³×C₂₃₃	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	1	no	—
363	C₂³	—	8	1	no	—
364	C₂³	C₂×D₄×C₂₃₃	1	1	yes	characteristic
365	C₂³	C₂×D₄×C₂₃₃	1	1	yes	characteristic
366	Q₈	—	2	1	no	—
367	Q₈	—	2	1	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	2	1	no	—
376	D₄	—	2	1	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	8	1	no	—
385	D₄	—	8	1	no	—
386	D₄	C₂×D₄×C₂₃₃	1	2	yes	—
387	D₄	C₂×D₄×C₂₃₃	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	1	no	—
398	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
399	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
402	C₂×C₄	C₂⁴×C₂₃₃	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	C₂×D₄×C₂₃₃	1	2	yes	complemented
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	AGL(1,ℤ/8)×C₂₃₃	1	2	yes	complemented
431	C₂²	C₂²×D₄×C₂₃₃	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	C₂²×D₄×C₂₃₃	1	1	yes	characteristic
440	C₄	H(5,𝔽₂)×C₂₃₃	1	1	yes	characteristic
441	C₂	—	2	2	no	—
442	C₂	—	4	1	no	—
443	C₂	—	4	2	no	—
444	C₂	—	4	2	no	—
445	C₂	—	8	1	no	—
446	C₂	—	8	1	no	—
447	C₂	—	8	1	no	—
448	C₂	D₄²×C₂₃₃	1	1	yes	characteristic
449	C₂	C₂×AGL(1,ℤ/8)×C₂₃₃	1	1	yes	characteristic
450	C₂	#576×C₂₃₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃₃ ◁ C₄×D₄×C₂₃₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×AGL(1,ℤ/8)×C₂₃₃	C₂	semidirect
2. C₂²×D₈×C₂₃₃	C₂	semidirect
3. #546×C₂₃₃	C₂	semidirect
4. D₄²×C₂₃₃	C₂	semidirect
5. #496×C₂₃₃	C₂	semidirect
6. #469×C₂₃₃	C₂	semidirect
7. #465×C₂₃₃	C₂	semidirect
8. #463×C₂₃₃	C₂	semidirect
9. #459×C₂₃₃	C₂	semidirect
10. #450×C₂₃₃	C₂	semidirect
11. #449×C₂₃₃	C₂	semidirect
12. #447×C₂₃₃	C₂	semidirect
13. #447×C₂₃₃	C₂	semidirect
14. #442×C₂₃₃	C₂	semidirect
15. #435×C₂₃₃	C₂	semidirect
16. C₂×#41×C₂₃₃	C₂²	semidirect
19. C₂²×D₄×C₂₃₃	C₂²	semidirect
20. C₂²×D₄×C₂₃₃	C₂²	semidirect
22. C₂×SD₁₆×C₂₃₃	C₂²	semidirect
23. C₂×SD₁₆×C₂₃₃	C₂²	semidirect
24. C₂×SD₁₆×C₂₃₃	C₂²	semidirect
28. C₂×D₈×C₂₃₃	C₂²	semidirect
29. C₂×D₈×C₂₃₃	C₂²	semidirect
30. C₂×D₈×C₂₃₃	C₂²	semidirect
31. C₂×D₈×C₂₃₃	C₂²	semidirect
32. C₂×M₁₆×C₂₃₃	C₂²	semidirect
33. C₂²×C₈×C₂₃₃	C₂²	semidirect
34. #127×C₂₃₃	C₂²	semidirect
35. #124×C₂₃₃	C₂²	semidirect
37. C₂²⋊Q₈×C₂₃₃	C₂²	semidirect
41. #121×C₂₃₃	C₂²	semidirect
42. #121×C₂₃₃	C₂²	semidirect
47. C₄×D₄×C₂₃₃	C₂²	semidirect
48. C₄×D₄×C₂₃₃	C₂²	semidirect
50. #106×C₂₃₃	C₂²	semidirect
51. C₄⋊C₈×C₂₃₃	C₂²	semidirect
52. #103×C₂₃₃	C₂²	semidirect
53. #102×C₂₃₃	C₂²	semidirect
54. #102×C₂₃₃	C₂²	semidirect
55. #102×C₂₃₃	C₂²	semidirect
56. #102×C₂₃₃	C₂²	semidirect
57. #102×C₂₃₃	C₂²	semidirect
58. C₂²⋊C₈×C₂₃₃	C₂²	semidirect
59. C₂²⋊C₈×C₂₃₃	C₂²	semidirect
60. #97×C₂₃₃	C₂²	semidirect
102. D₈×C₂₃₃	D₄	semidirect
161. D₄×C₂₃₃	C₂×D₄	semidirect
180. C₈×C₂₃₃	C₂×D₄	semidirect
204. C₂²×C₂₃₃	AGL(1,ℤ/8)	semidirect
225. C₂₃₃	#3264	direct (N × H)
226. #3264	C₂₃₃	direct (N × H)
227. C₂×AGL(1,ℤ/8)	C₂×C₂₃₃	semidirect
228. C₂²×D₈	C₂×C₂₃₃	semidirect
229. #546	C₂×C₂₃₃	semidirect
230. D₄²	C₂×C₂₃₃	semidirect
231. #496	C₂×C₂₃₃	semidirect
232. #469	C₂×C₂₃₃	semidirect
233. #465	C₂×C₂₃₃	semidirect
234. #463	C₂×C₂₃₃	semidirect
235. #459	C₂×C₂₃₃	semidirect
236. #450	C₂×C₂₃₃	semidirect
237. #449	C₂×C₂₃₃	semidirect
238. #447	C₂×C₂₃₃	semidirect
239. #447	C₂×C₂₃₃	semidirect
240. #442	C₂×C₂₃₃	semidirect
241. #435	C₂×C₂₃₃	semidirect
242. C₂×#41	C₂²×C₂₃₃	semidirect
245. C₂²×D₄	C₂²×C₂₃₃	semidirect
246. C₂²×D₄	C₂²×C₂₃₃	semidirect
248. C₂×SD₁₆	C₂²×C₂₃₃	semidirect
249. C₂×SD₁₆	C₂²×C₂₃₃	semidirect
250. C₂×SD₁₆	C₂²×C₂₃₃	semidirect
254. C₂×D₈	C₂²×C₂₃₃	semidirect
255. C₂×D₈	C₂²×C₂₃₃	semidirect
256. C₂×D₈	C₂²×C₂₃₃	semidirect
257. C₂×D₈	C₂²×C₂₃₃	semidirect
258. C₂×M₁₆	C₂²×C₂₃₃	semidirect
259. C₂²×C₈	C₂²×C₂₃₃	semidirect
260. #127	C₂²×C₂₃₃	semidirect
261. #124	C₂²×C₂₃₃	semidirect
263. C₂²⋊Q₈	C₂²×C₂₃₃	semidirect
267. #121	C₂²×C₂₃₃	semidirect
268. #121	C₂²×C₂₃₃	semidirect
273. C₄×D₄	C₂²×C₂₃₃	semidirect
274. C₄×D₄	C₂²×C₂₃₃	semidirect
276. #106	C₂²×C₂₃₃	semidirect
277. C₄⋊C₈	C₂²×C₂₃₃	semidirect
278. #103	C₂²×C₂₃₃	semidirect
279. #102	C₂²×C₂₃₃	semidirect
280. #102	C₂²×C₂₃₃	semidirect
281. #102	C₂²×C₂₃₃	semidirect
282. #102	C₂²×C₂₃₃	semidirect
283. #102	C₂²×C₂₃₃	semidirect
284. C₂²⋊C₈	C₂²×C₂₃₃	semidirect
285. C₂²⋊C₈	C₂²×C₂₃₃	semidirect
286. #97	C₂²×C₂₃₃	semidirect
328. D₈	D₄×C₂₃₃	semidirect
387. D₄	C₂×D₄×C₂₃₃	semidirect
406. C₈	C₂×D₄×C₂₃₃	semidirect
430. C₂²	AGL(1,ℤ/8)×C₂₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×AGL(1,ℤ/8)×C₂₃₃	2
C₂²×D₈×C₂₃₃	2
#546×C₂₃₃	2
D₄²×C₂₃₃	2
#496×C₂₃₃	2
#469×C₂₃₃	2
#465×C₂₃₃	2
#463×C₂₃₃	2
#459×C₂₃₃	2
#450×C₂₃₃	2
#449×C₂₃₃	2
#447×C₂₃₃	2
#442×C₂₃₃	2
#435×C₂₃₃	2
#3264	233

Subgroups — #3264×C233 #44449296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3264×C₂₃₃ #44449296