Subgroups — C₄×AGL(1,ℤ/8)×C₂₃₃ #44448976

Order 29824.

548 conjugacy classes of subgroups.

The subgroup lattice has 306 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
2	C₄×#41×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#442×C₂₃₃	C₂	1	2	yes	maximal, complemented
5	#440×C₂₃₃	C₂	1	2	yes	maximal, complemented
6	C₄×SD₁₆×C₂₃₃	C₂	1	2	yes	maximal, complemented
7	C₄×D₈×C₂₃₃	C₂	1	2	yes	maximal, complemented
8	#428×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#418×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#417×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×M₁₆×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×C₂₃₃	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₂₃₃	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₂₃₃	—	2	1	no	—
15	AGL(1,ℤ/8)×C₂₃₃	C₄	1	8	yes	direct product factor
16	C₂×SD₁₆×C₂₃₃	C₂²	1	2	yes	—
17	C₂×D₈×C₂₃₃	C₂²	1	2	yes	—
18	C₂×M₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
21	C₄×Q₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
22	C₄×D₄×C₂₃₃	—	2	1	no	—
23	C₄×D₄×C₂₃₃	—	2	1	no	—
24	C₄×D₄×C₂₃₃	—	2	1	no	—
25	C₄×D₄×C₂₃₃	—	2	1	no	—
26	C₄×D₄×C₂₃₃	C₂²	1	2	yes	—
27	C₄×D₄×C₂₃₃	C₂²	1	2	yes	—
28	C₄×D₄×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
30	#117×C₂₃₃	—	2	1	no	—
31	#117×C₂₃₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₂₃₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₂₃₃	—	2	1	no	—
34	C₂×C₄²×C₂₃₃	—	2	1	no	—
35	C₂×C₄²×C₂₃₃	C₂²	1	1	yes	characteristic
36	#107×C₂₃₃	C₂²	1	2	yes	complemented
37	#106×C₂₃₃	C₂²	1	2	yes	complemented
38	#103×C₂₃₃	C₂²	1	2	yes	complemented
39	#102×C₂₃₃	C₂²	1	2	yes	—
40	#102×C₂₃₃	C₂²	1	2	yes	—
41	#102×C₂₃₃	C₂²	1	2	yes	complemented
42	#97×C₂₃₃	C₂²	1	2	yes	complemented
43	C₄×C₈×C₂₃₃	C₂²	1	2	yes	complemented
44	C₂⁴×C₂₃₃	—	2	1	no	—
45	#41×C₂₃₃	—	2	2	no	—
46	#41×C₂₃₃	C₂×C₄	1	4	yes	complemented
47	C₂×Q₈×C₂₃₃	C₂³	1	1	yes	characteristic
48	C₂×D₄×C₂₃₃	—	2	1	no	—
49	C₂×D₄×C₂₃₃	—	2	1	no	—
50	C₂×D₄×C₂₃₃	—	2	2	no	—
51	C₂×D₄×C₂₃₃	C₂×C₄	1	4	yes	complemented
52	C₂×D₄×C₂₃₃	C₂³	1	2	yes	—
53	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₂₃₃	—	2	1	no	—
55	C₂²×C₄×C₂₃₃	—	2	1	no	—
56	C₂²×C₄×C₂₃₃	—	2	1	no	—
57	C₂²×C₄×C₂₃₃	—	2	2	no	—
58	C₂²×C₄×C₂₃₃	—	2	1	no	—
59	C₂²×C₄×C₂₃₃	—	2	2	no	—
60	C₂²×C₄×C₂₃₃	—	4	4	no	—
61	C₂²×C₄×C₂₃₃	D₄	1	1	yes	characteristic
62	C₂²×C₄×C₂₃₃	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
64	SD₁₆×C₂₃₃	C₂×C₄	1	8	yes	complemented
65	D₈×C₂₃₃	C₂×C₄	1	8	yes	complemented
66	M₁₆×C₂₃₃	—	2	2	no	—
67	M₁₆×C₂₃₃	C₂×C₄	1	4	yes	complemented
68	C₂×C₈×C₂₃₃	C₂³	1	2	yes	—
69	C₂×C₈×C₂₃₃	C₂³	1	2	yes	—
70	C₄⋊C₄×C₂₃₃	—	2	1	no	—
71	C₄⋊C₄×C₂₃₃	—	2	1	no	—
72	C₄⋊C₄×C₂₃₃	—	2	1	no	—
73	C₄⋊C₄×C₂₃₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₄×C₂₃₃	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₂₃₃	C₂³	1	2	yes	—
76	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
77	C₂²⋊C₄×C₂₃₃	—	2	2	no	—
78	C₂²⋊C₄×C₂₃₃	—	2	2	no	—
79	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
80	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
81	C₄²×C₂₃₃	—	2	1	no	—
82	C₄²×C₂₃₃	—	2	1	no	—
83	C₄²×C₂₃₃	—	2	1	no	—
84	C₄²×C₂₃₃	D₄	1	1	yes	characteristic
85	C₄²×C₂₃₃	D₄	1	1	yes	characteristic
86	C₄²×C₂₃₃	C₂³	1	1	yes	characteristic
87	C₄²×C₂₃₃	C₂³	1	1	yes	characteristic
88	C₂³×C₂₃₃	—	2	4	no	—
89	C₂³×C₂₃₃	—	2	1	no	—
90	C₂³×C₂₃₃	—	2	2	no	—
91	C₂³×C₂₃₃	—	4	2	no	—
92	C₂³×C₂₃₃	—	4	2	no	—
93	C₂³×C₂₃₃	C₂×D₄	1	1	yes	characteristic
94	Q₈×C₂₃₃	—	2	1	no	—
95	Q₈×C₂₃₃	C₂²×C₄	1	2	yes	complemented
96	D₄×C₂₃₃	—	2	4	no	—
97	D₄×C₂₃₃	—	2	4	no	—
98	D₄×C₂₃₃	—	2	2	no	—
99	D₄×C₂₃₃	—	2	1	no	—
100	D₄×C₂₃₃	C₂²×C₄	1	4	yes	—
101	D₄×C₂₃₃	C₂²×C₄	1	2	yes	complemented
102	C₂×C₄×C₂₃₃	—	2	1	no	—
103	C₂×C₄×C₂₃₃	—	2	4	no	—
104	C₂×C₄×C₂₃₃	—	2	2	no	—
105	C₂×C₄×C₂₃₃	—	2	1	no	—
106	C₂×C₄×C₂₃₃	—	2	1	no	—
107	C₂×C₄×C₂₃₃	—	2	2	no	—
108	C₂×C₄×C₂₃₃	—	4	1	no	—
109	C₂×C₄×C₂₃₃	—	4	2	no	—
110	C₂×C₄×C₂₃₃	—	4	4	no	—
111	C₂×C₄×C₂₃₃	—	4	2	no	—
112	C₂×C₄×C₂₃₃	—	4	2	no	—
113	C₂×C₄×C₂₃₃	—	4	4	no	—
114	C₂×C₄×C₂₃₃	C₂²×C₄	1	2	yes	—
115	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×C₂₃₃	#41	1	2	yes	—
121	C₂×C₄×C₂₃₃	C₂⁴	1	1	yes	characteristic
122	C₈×C₂₃₃	—	2	2	no	—
123	C₈×C₂₃₃	C₂²×C₄	1	4	yes	complemented
124	C₂²×C₂₃₃	—	2	1	no	—
125	C₂²×C₂₃₃	—	2	1	no	—
126	C₂²×C₂₃₃	—	2	2	no	—
127	C₂²×C₂₃₃	—	2	4	no	—
128	C₂²×C₂₃₃	—	4	8	no	—
129	C₂²×C₂₃₃	—	4	2	no	—
130	C₂²×C₂₃₃	—	4	1	no	—
131	C₂²×C₂₃₃	—	4	1	no	—
132	C₂²×C₂₃₃	—	4	2	no	—
133	C₂²×C₂₃₃	C₄×D₄	1	2	yes	—
134	C₂²×C₂₃₃	C₂²×D₄	1	1	yes	characteristic
135	C₄×C₂₃₃	—	2	2	no	—
136	C₄×C₂₃₃	—	2	1	no	—
137	C₄×C₂₃₃	—	2	1	no	—
138	C₄×C₂₃₃	—	2	1	no	—
139	C₄×C₂₃₃	—	4	1	no	—
140	C₄×C₂₃₃	—	4	2	no	—
141	C₄×C₂₃₃	—	4	1	no	—
142	C₄×C₂₃₃	C₄×D₄	1	2	yes	—
143	C₄×C₂₃₃	AGL(1,ℤ/8)	1	2	yes	direct product factor
144	C₄×C₂₃₃	C₂³×C₄	1	1	yes	characteristic
145	C₄×C₂₃₃	C₂×#41	1	1	yes	characteristic
146	C₂×C₂₃₃	—	2	2	no	—
147	C₂×C₂₃₃	—	4	2	no	—
148	C₂×C₂₃₃	—	4	4	no	—
149	C₂×C₂₃₃	C₂×C₄×D₄	1	1	yes	characteristic
150	C₂×C₂₃₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₂₃₃	#575	1	1	yes	characteristic
152	C₂₃₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
153	C₄×AGL(1,ℤ/8)	C₂₃₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂×AGL(1,ℤ/8)	C₂×C₂₃₃	1	1	yes	characteristic
155	C₄×#41	C₂×C₂₃₃	1	1	yes	characteristic, complemented
156	C₂×C₄×D₄	C₂×C₂₃₃	1	1	yes	characteristic, complemented
157	#442	C₂×C₂₃₃	1	2	yes	complemented
158	#440	C₂×C₂₃₃	1	2	yes	complemented
159	C₄×SD₁₆	C₂×C₂₃₃	1	2	yes	complemented
160	C₄×D₈	C₂×C₂₃₃	1	2	yes	complemented
161	#428	C₂×C₂₃₃	1	1	yes	characteristic, complemented
162	#418	C₂×C₂₃₃	1	1	yes	characteristic, complemented
163	#417	C₂×C₂₃₃	1	1	yes	characteristic, complemented
164	C₄×M₁₆	C₂×C₂₃₃	1	1	yes	characteristic, complemented
165	C₂×#41	C₂²×C₂₃₃	1	1	yes	characteristic
166	C₂²×D₄	C₂²×C₂₃₃	1	1	yes	characteristic
167	C₂³×C₄	—	2	1	no	—
168	AGL(1,ℤ/8)	C₄×C₂₃₃	1	8	yes	direct product factor
169	C₂×SD₁₆	C₂²×C₂₃₃	1	2	yes	—
170	C₂×D₈	C₂²×C₂₃₃	1	2	yes	—
171	C₂×M₁₆	C₂²×C₂₃₃	1	1	yes	characteristic
172	C₂×M₁₆	C₂²×C₂₃₃	1	1	yes	characteristic
173	C₄×Q₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
174	C₄×Q₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
175	C₄×D₄	—	2	1	no	—
176	C₄×D₄	—	2	1	no	—
177	C₄×D₄	—	2	1	no	—
178	C₄×D₄	—	2	1	no	—
179	C₄×D₄	C₂²×C₂₃₃	1	2	yes	—
180	C₄×D₄	C₂²×C₂₃₃	1	2	yes	—
181	C₄×D₄	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
182	C₄×D₄	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
183	#117	—	2	1	no	—
184	#117	C₂²×C₂₃₃	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₂²×C₂₃₃	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₄²	—	2	1	no	—
188	C₂×C₄²	C₂²×C₂₃₃	1	1	yes	characteristic
189	#107	C₂²×C₂₃₃	1	2	yes	complemented
190	#106	C₂²×C₂₃₃	1	2	yes	complemented
191	#103	C₂²×C₂₃₃	1	2	yes	complemented
192	#102	C₂²×C₂₃₃	1	2	yes	—
193	#102	C₂²×C₂₃₃	1	2	yes	—
194	#102	C₂²×C₂₃₃	1	2	yes	complemented
195	#97	C₂²×C₂₃₃	1	2	yes	complemented
196	C₄×C₈	C₂²×C₂₃₃	1	2	yes	complemented
197	C₂⁴	—	2	1	no	—
198	#41	—	2	2	no	—
199	#41	C₂×C₄×C₂₃₃	1	4	yes	complemented
200	C₂×Q₈	C₂³×C₂₃₃	1	1	yes	characteristic
201	C₂×D₄	—	2	1	no	—
202	C₂×D₄	—	2	1	no	—
203	C₂×D₄	—	2	2	no	—
204	C₂×D₄	C₂×C₄×C₂₃₃	1	4	yes	complemented
205	C₂×D₄	C₂³×C₂₃₃	1	2	yes	—
206	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
207	C₂²×C₄	—	2	1	no	—
208	C₂²×C₄	—	2	1	no	—
209	C₂²×C₄	—	2	1	no	—
210	C₂²×C₄	—	2	1	no	—
211	C₂²×C₄	—	2	2	no	—
212	C₂²×C₄	—	2	2	no	—
213	C₂²×C₄	—	4	4	no	—
214	C₂²×C₄	D₄×C₂₃₃	1	1	yes	characteristic
215	C₂²×C₄	D₄×C₂₃₃	1	1	yes	characteristic
216	C₂²×C₄	C₂³×C₂₃₃	1	1	yes	characteristic
217	SD₁₆	C₂×C₄×C₂₃₃	1	8	yes	complemented
218	D₈	C₂×C₄×C₂₃₃	1	8	yes	complemented
219	M₁₆	—	2	2	no	—
220	M₁₆	C₂×C₄×C₂₃₃	1	4	yes	complemented
221	C₂×C₈	C₂³×C₂₃₃	1	2	yes	—
222	C₂×C₈	C₂³×C₂₃₃	1	2	yes	—
223	C₄⋊C₄	—	2	1	no	—
224	C₄⋊C₄	—	2	1	no	—
225	C₄⋊C₄	—	2	1	no	—
226	C₄⋊C₄	C₂³×C₂₃₃	1	1	yes	characteristic
227	C₄⋊C₄	C₂³×C₂₃₃	1	1	yes	characteristic
228	C₄⋊C₄	C₂³×C₂₃₃	1	2	yes	—
229	C₂²⋊C₄	—	2	1	no	—
230	C₂²⋊C₄	—	2	2	no	—
231	C₂²⋊C₄	—	2	2	no	—
232	C₂²⋊C₄	—	2	1	no	—
233	C₂²⋊C₄	—	2	1	no	—
234	C₄²	—	2	1	no	—
235	C₄²	—	2	1	no	—
236	C₄²	—	2	1	no	—
237	C₄²	D₄×C₂₃₃	1	1	yes	characteristic
238	C₄²	D₄×C₂₃₃	1	1	yes	characteristic
239	C₄²	C₂³×C₂₃₃	1	1	yes	characteristic
240	C₄²	C₂³×C₂₃₃	1	1	yes	characteristic
241	C₂³	—	2	4	no	—
242	C₂³	—	2	1	no	—
243	C₂³	—	2	2	no	—
244	C₂³	—	4	2	no	—
245	C₂³	—	4	2	no	—
246	C₂³	C₂×D₄×C₂₃₃	1	1	yes	characteristic
247	Q₈	—	2	1	no	—
248	Q₈	C₂²×C₄×C₂₃₃	1	2	yes	complemented
249	D₄	—	2	4	no	—
250	D₄	—	2	4	no	—
251	D₄	—	2	2	no	—
252	D₄	—	2	1	no	—
253	D₄	C₂²×C₄×C₂₃₃	1	4	yes	—
254	D₄	C₂²×C₄×C₂₃₃	1	2	yes	complemented
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	4	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	C₂²×C₄×C₂₃₃	1	2	yes	—
268	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
269	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
270	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
271	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
272	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
273	C₂×C₄	#41×C₂₃₃	1	2	yes	—
274	C₂×C₄	C₂⁴×C₂₃₃	1	1	yes	characteristic
275	C₈	—	2	2	no	—
276	C₈	C₂²×C₄×C₂₃₃	1	4	yes	complemented
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	2	2	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	4	8	no	—
282	C₂²	—	4	2	no	—
283	C₂²	—	4	1	no	—
284	C₂²	—	4	1	no	—
285	C₂²	—	4	2	no	—
286	C₂²	C₄×D₄×C₂₃₃	1	2	yes	—
287	C₂²	C₂²×D₄×C₂₃₃	1	1	yes	characteristic
288	C₄	—	2	2	no	—
289	C₄	—	2	1	no	—
290	C₄	—	2	1	no	—
291	C₄	—	2	1	no	—
292	C₄	—	4	2	no	—
293	C₄	—	4	1	no	—
294	C₄	—	4	1	no	—
295	C₄	C₄×D₄×C₂₃₃	1	2	yes	—
296	C₄	AGL(1,ℤ/8)×C₂₃₃	1	2	yes	direct product factor
297	C₄	C₂³×C₄×C₂₃₃	1	1	yes	characteristic
298	C₄	C₂×#41×C₂₃₃	1	1	yes	characteristic
299	C₂	—	2	2	no	—
300	C₂	—	4	4	no	—
301	C₂	—	4	2	no	—
302	C₂	C₂×C₄×D₄×C₂₃₃	1	1	yes	characteristic
303	C₂	C₂×AGL(1,ℤ/8)×C₂₃₃	1	1	yes	characteristic
304	C₂	#575×C₂₃₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃₃	C₂×D₄
commutator	C₄	C₂³×C₄×C₂₃₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃₃
socle	C₂²×C₂₃₃	C₂²×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₂₃₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃₃ ◁ C₂×C₄²×C₂₃₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#41×C₂₃₃	C₂	semidirect
3. C₂×C₄×D₄×C₂₃₃	C₂	semidirect
4. #442×C₂₃₃	C₂	semidirect
5. #440×C₂₃₃	C₂	semidirect
6. C₄×SD₁₆×C₂₃₃	C₂	semidirect
7. C₄×D₈×C₂₃₃	C₂	semidirect
8. #428×C₂₃₃	C₂	semidirect
9. #418×C₂₃₃	C₂	semidirect
10. #417×C₂₃₃	C₂	semidirect
11. C₄×M₁₆×C₂₃₃	C₂	semidirect
15. AGL(1,ℤ/8)×C₂₃₃	C₄	direct (N × H)
20. C₄×Q₈×C₂₃₃	C₂²	semidirect
21. C₄×Q₈×C₂₃₃	C₂²	semidirect
28. C₄×D₄×C₂₃₃	C₂²	semidirect
29. C₄×D₄×C₂₃₃	C₂²	semidirect
36. #107×C₂₃₃	C₂²	semidirect
37. #106×C₂₃₃	C₂²	semidirect
38. #103×C₂₃₃	C₂²	semidirect
41. #102×C₂₃₃	C₂²	semidirect
42. #97×C₂₃₃	C₂²	semidirect
43. C₄×C₈×C₂₃₃	C₂²	semidirect
46. #41×C₂₃₃	C₂×C₄	semidirect
51. C₂×D₄×C₂₃₃	C₂×C₄	semidirect
64. SD₁₆×C₂₃₃	C₂×C₄	semidirect
65. D₈×C₂₃₃	C₂×C₄	semidirect
67. M₁₆×C₂₃₃	C₂×C₄	semidirect
95. Q₈×C₂₃₃	C₂²×C₄	semidirect
101. D₄×C₂₃₃	C₂²×C₄	semidirect
123. C₈×C₂₃₃	C₂²×C₄	semidirect
143. C₄×C₂₃₃	AGL(1,ℤ/8)	direct (N × H)
152. C₂₃₃	C₄×AGL(1,ℤ/8)	direct (N × H)
153. C₄×AGL(1,ℤ/8)	C₂₃₃	direct (N × H)
155. C₄×#41	C₂×C₂₃₃	semidirect
156. C₂×C₄×D₄	C₂×C₂₃₃	semidirect
157. #442	C₂×C₂₃₃	semidirect
158. #440	C₂×C₂₃₃	semidirect
159. C₄×SD₁₆	C₂×C₂₃₃	semidirect
160. C₄×D₈	C₂×C₂₃₃	semidirect
161. #428	C₂×C₂₃₃	semidirect
162. #418	C₂×C₂₃₃	semidirect
163. #417	C₂×C₂₃₃	semidirect
164. C₄×M₁₆	C₂×C₂₃₃	semidirect
168. AGL(1,ℤ/8)	C₄×C₂₃₃	direct (N × H)
173. C₄×Q₈	C₂²×C₂₃₃	semidirect
174. C₄×Q₈	C₂²×C₂₃₃	semidirect
181. C₄×D₄	C₂²×C₂₃₃	semidirect
182. C₄×D₄	C₂²×C₂₃₃	semidirect
189. #107	C₂²×C₂₃₃	semidirect
190. #106	C₂²×C₂₃₃	semidirect
191. #103	C₂²×C₂₃₃	semidirect
194. #102	C₂²×C₂₃₃	semidirect
195. #97	C₂²×C₂₃₃	semidirect
196. C₄×C₈	C₂²×C₂₃₃	semidirect
199. #41	C₂×C₄×C₂₃₃	semidirect
204. C₂×D₄	C₂×C₄×C₂₃₃	semidirect
217. SD₁₆	C₂×C₄×C₂₃₃	semidirect
218. D₈	C₂×C₄×C₂₃₃	semidirect
220. M₁₆	C₂×C₄×C₂₃₃	semidirect
248. Q₈	C₂²×C₄×C₂₃₃	semidirect
254. D₄	C₂²×C₄×C₂₃₃	semidirect
276. C₈	C₂²×C₄×C₂₃₃	semidirect
296. C₄	AGL(1,ℤ/8)×C₂₃₃	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×AGL(1,ℤ/8)×C₂₃₃	2
C₄×#41×C₂₃₃	2
C₂×C₄×D₄×C₂₃₃	2
#442×C₂₃₃	2
#440×C₂₃₃	2
C₄×SD₁₆×C₂₃₃	2
C₄×D₈×C₂₃₃	2
#428×C₂₃₃	2
#418×C₂₃₃	2
#417×C₂₃₃	2
C₄×M₁₆×C₂₃₃	2
C₄×AGL(1,ℤ/8)	233

Subgroups — C4×AGL(1,ℤ/8)×C233 #44448976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×AGL(1,ℤ/8)×C₂₃₃ #44448976