Subgroups — #3275×C₂₃₃ #44449307

Order 29824.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#137×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×AGL(1,ℤ/8)×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#548×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#546×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#495×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#470×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#469×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#464×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#463×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#452×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#450×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#449×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#448×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×SD₁₆×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#436×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₃₃	C₂²	1	1	yes	characteristic
17	C₂×#41×C₂₃₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₂₃₃	C₂²	1	1	yes	characteristic
20	#137×C₂₃₃	—	2	4	no	—
21	AGL(1,ℤ/8)×C₂₃₃	—	2	4	no	—
22	C₂×Q₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×Q₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
26	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
27	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
28	C₂×SD₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic
30	C₂×D₈×C₂₃₃	C₂²	1	1	yes	characteristic
31	C₂×M₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
32	C₂×M₁₆×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
33	#124×C₂₃₃	—	2	1	no	—
34	#124×C₂₃₃	C₂²	1	1	yes	characteristic
35	#124×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
36	#123×C₂₃₃	—	2	1	no	—
37	C₂²⋊Q₈×C₂₃₃	—	2	1	no	—
38	C₂²⋊Q₈×C₂₃₃	C₂²	1	1	yes	characteristic
39	C₂²⋊Q₈×C₂₃₃	C₂²	1	1	yes	characteristic
40	#121×C₂₃₃	—	2	1	no	—
41	#121×C₂₃₃	—	2	1	no	—
42	#121×C₂₃₃	C₂²	1	1	yes	characteristic
43	#121×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
44	#120×C₂₃₃	—	2	1	no	—
45	C₄×Q₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
46	C₄×D₄×C₂₃₃	—	2	1	no	—
47	C₄×D₄×C₂₃₃	C₂²	1	1	yes	characteristic
48	C₄×D₄×C₂₃₃	C₂²	1	1	yes	characteristic
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	#103×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
54	#103×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
55	#102×C₂₃₃	C₂²	1	1	yes	characteristic
56	#102×C₂₃₃	C₂²	1	1	yes	characteristic
57	#102×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₂₃₃	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₈×C₂₃₃	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₂₃₃	—	2	1	no	—
62	#41×C₂₃₃	—	2	2	no	—
63	#41×C₂₃₃	—	2	2	no	—
64	#41×C₂₃₃	—	4	1	no	—
65	#41×C₂₃₃	—	4	1	no	—
66	C₂×Q₈×C₂₃₃	—	2	1	no	—
67	C₂×Q₈×C₂₃₃	—	2	2	no	—
68	C₂×Q₈×C₂₃₃	—	4	1	no	—
69	C₂×Q₈×C₂₃₃	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₂₃₃	C₂³	1	1	yes	characteristic
71	C₂×Q₈×C₂₃₃	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₂₃₃	—	2	2	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	—	4	1	no	—
79	C₂×D₄×C₂₃₃	D₄	1	1	yes	characteristic
80	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
81	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₂₃₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₂₃₃	—	2	1	no	—
84	C₂²×C₄×C₂₃₃	—	2	1	no	—
85	C₂²×C₄×C₂₃₃	—	2	1	no	—
86	C₂²×C₄×C₂₃₃	—	2	1	no	—
87	C₂²×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
89	Q₁₆×C₂₃₃	—	2	2	no	—
90	Q₁₆×C₂₃₃	—	2	2	no	—
91	SD₁₆×C₂₃₃	—	2	2	no	—
92	SD₁₆×C₂₃₃	—	2	2	no	—
93	SD₁₆×C₂₃₃	—	4	1	no	—
94	SD₁₆×C₂₃₃	—	4	1	no	—
95	SD₁₆×C₂₃₃	D₄	1	4	yes	complemented
96	D₈×C₂₃₃	—	2	2	no	—
97	D₈×C₂₃₃	—	2	2	no	—
98	M₁₆×C₂₃₃	—	2	2	no	—
99	M₁₆×C₂₃₃	—	2	2	no	—
100	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
101	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
103	C₂×C₈×C₂₃₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₄×C₂₃₃	—	2	1	no	—
105	C₄⋊C₄×C₂₃₃	—	2	1	no	—
106	C₄⋊C₄×C₂₃₃	—	2	1	no	—
107	C₄⋊C₄×C₂₃₃	D₄	1	1	yes	characteristic
108	C₄⋊C₄×C₂₃₃	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₂₃₃	C₂³	1	1	yes	characteristic
110	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
111	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
112	C₂²⋊C₄×C₂₃₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
120	C₂²⋊C₄×C₂₃₃	D₄	1	1	yes	characteristic
121	C₄²×C₂₃₃	—	2	1	no	—
122	C₄²×C₂₃₃	C₂³	1	1	yes	characteristic
123	C₂³×C₂₃₃	—	2	1	no	—
124	C₂³×C₂₃₃	—	2	1	no	—
125	C₂³×C₂₃₃	—	2	1	no	—
126	C₂³×C₂₃₃	—	4	2	no	—
127	C₂³×C₂₃₃	—	4	2	no	—
128	C₂³×C₂₃₃	—	8	1	no	—
129	C₂³×C₂₃₃	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₂₃₃	C₂×D₄	1	1	yes	characteristic
131	Q₈×C₂₃₃	—	2	1	no	—
132	Q₈×C₂₃₃	—	2	1	no	—
133	Q₈×C₂₃₃	—	2	1	no	—
134	Q₈×C₂₃₃	—	2	1	no	—
135	Q₈×C₂₃₃	—	2	1	no	—
136	Q₈×C₂₃₃	—	4	2	no	—
137	Q₈×C₂₃₃	C₂×D₄	1	2	yes	—
138	D₄×C₂₃₃	—	2	1	no	—
139	D₄×C₂₃₃	—	2	1	no	—
140	D₄×C₂₃₃	—	2	1	no	—
141	D₄×C₂₃₃	—	2	1	no	—
142	D₄×C₂₃₃	—	2	1	no	—
143	D₄×C₂₃₃	—	4	1	no	—
144	D₄×C₂₃₃	—	4	2	no	—
145	D₄×C₂₃₃	—	4	2	no	—
146	D₄×C₂₃₃	—	4	2	no	—
147	D₄×C₂₃₃	—	4	2	no	—
148	D₄×C₂₃₃	—	8	1	no	—
149	D₄×C₂₃₃	C₂×D₄	1	2	yes	—
150	C₂×C₄×C₂₃₃	—	2	1	no	—
151	C₂×C₄×C₂₃₃	—	2	1	no	—
152	C₂×C₄×C₂₃₃	—	2	1	no	—
153	C₂×C₄×C₂₃₃	—	2	1	no	—
154	C₂×C₄×C₂₃₃	—	2	1	no	—
155	C₂×C₄×C₂₃₃	—	2	1	no	—
156	C₂×C₄×C₂₃₃	—	2	1	no	—
157	C₂×C₄×C₂₃₃	—	2	1	no	—
158	C₂×C₄×C₂₃₃	—	2	1	no	—
159	C₂×C₄×C₂₃₃	—	4	2	no	—
160	C₂×C₄×C₂₃₃	—	4	2	no	—
161	C₂×C₄×C₂₃₃	—	4	2	no	—
162	C₂×C₄×C₂₃₃	—	8	1	no	—
163	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×C₂₃₃	C₂⁴	1	1	yes	characteristic
168	C₈×C₂₃₃	—	2	1	no	—
169	C₈×C₂₃₃	—	2	1	no	—
170	C₈×C₂₃₃	—	2	1	no	—
171	C₈×C₂₃₃	C₂×D₄	1	2	yes	—
172	C₂²×C₂₃₃	—	2	1	no	—
173	C₂²×C₂₃₃	—	2	1	no	—
174	C₂²×C₂₃₃	—	2	2	no	—
175	C₂²×C₂₃₃	—	2	1	no	—
176	C₂²×C₂₃₃	—	2	1	no	—
177	C₂²×C₂₃₃	—	2	1	no	—
178	C₂²×C₂₃₃	—	2	1	no	—
179	C₂²×C₂₃₃	—	4	1	no	—
180	C₂²×C₂₃₃	—	4	1	no	—
181	C₂²×C₂₃₃	—	4	1	no	—
182	C₂²×C₂₃₃	—	4	1	no	—
183	C₂²×C₂₃₃	—	4	1	no	—
184	C₂²×C₂₃₃	—	4	1	no	—
185	C₂²×C₂₃₃	—	4	1	no	—
186	C₂²×C₂₃₃	—	4	1	no	—
187	C₂²×C₂₃₃	—	8	4	no	—
188	C₂²×C₂₃₃	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₂₃₃	—	2	1	no	—
190	C₄×C₂₃₃	—	2	1	no	—
191	C₄×C₂₃₃	—	2	2	no	—
192	C₄×C₂₃₃	—	2	1	no	—
193	C₄×C₂₃₃	—	2	1	no	—
194	C₄×C₂₃₃	—	4	1	no	—
195	C₄×C₂₃₃	—	4	1	no	—
196	C₄×C₂₃₃	—	4	1	no	—
197	C₄×C₂₃₃	—	4	1	no	—
198	C₄×C₂₃₃	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₂₃₃	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₂₃₃	—	4	1	no	—
201	C₂×C₂₃₃	—	4	1	no	—
202	C₂×C₂₃₃	—	4	2	no	—
203	C₂×C₂₃₃	—	8	1	no	—
204	C₂×C₂₃₃	—	8	1	no	—
205	C₂×C₂₃₃	D₄²	1	1	yes	characteristic
206	C₂×C₂₃₃	#575	1	1	yes	characteristic
207	C₂×C₂₃₃	#577	1	1	yes	characteristic
208	C₂₃₃	#3275	1	1	yes	characteristic, direct product factor, Sylow
209	#3275	C₂₃₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂×#137	C₂×C₂₃₃	1	1	yes	characteristic, complemented
211	C₂×AGL(1,ℤ/8)	C₂×C₂₃₃	1	1	yes	characteristic, complemented
212	#548	C₂×C₂₃₃	1	1	yes	characteristic, complemented
213	#546	C₂×C₂₃₃	1	1	yes	characteristic, complemented
214	#495	C₂×C₂₃₃	1	1	yes	characteristic, complemented
215	#470	C₂×C₂₃₃	1	1	yes	characteristic, complemented
216	#469	C₂×C₂₃₃	1	1	yes	characteristic, complemented
217	#464	C₂×C₂₃₃	1	1	yes	characteristic, complemented
218	#463	C₂×C₂₃₃	1	1	yes	characteristic, complemented
219	#452	C₂×C₂₃₃	1	1	yes	characteristic, complemented
220	#450	C₂×C₂₃₃	1	1	yes	characteristic, complemented
221	#449	C₂×C₂₃₃	1	1	yes	characteristic, complemented
222	#448	C₂×C₂₃₃	1	1	yes	characteristic, complemented
223	C₄×SD₁₆	C₂×C₂₃₃	1	1	yes	characteristic, complemented
224	#436	C₂×C₂₃₃	1	1	yes	characteristic, complemented
225	C₂×#41	C₂²×C₂₃₃	1	1	yes	characteristic
226	C₂×#41	C₂²×C₂₃₃	1	1	yes	characteristic
227	C₂²×Q₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
228	C₂²×D₄	C₂²×C₂₃₃	1	1	yes	characteristic
229	#137	—	2	4	no	—
230	AGL(1,ℤ/8)	—	2	4	no	—
231	C₂×Q₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
232	C₂×Q₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
233	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic
234	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic
235	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic
236	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic
237	C₂×SD₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
238	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic
239	C₂×D₈	C₂²×C₂₃₃	1	1	yes	characteristic
240	C₂×M₁₆	C₂²×C₂₃₃	1	1	yes	characteristic
241	C₂×M₁₆	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
242	#124	—	2	1	no	—
243	#124	C₂²×C₂₃₃	1	1	yes	characteristic
244	#124	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
245	#123	—	2	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₂²⋊Q₈	C₂²×C₂₃₃	1	1	yes	characteristic
248	C₂²⋊Q₈	C₂²×C₂₃₃	1	1	yes	characteristic
249	#121	—	2	1	no	—
250	#121	—	2	1	no	—
251	#121	C₂²×C₂₃₃	1	1	yes	characteristic
252	#121	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
253	#120	—	2	1	no	—
254	C₄×Q₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	C₂²×C₂₃₃	1	1	yes	characteristic
257	C₄×D₄	C₂²×C₂₃₃	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	#106	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
260	C₄⋊C₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
261	#103	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
262	#103	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
263	#103	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
264	#102	C₂²×C₂₃₃	1	1	yes	characteristic
265	#102	C₂²×C₂₃₃	1	1	yes	characteristic
266	#102	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
267	C₂²⋊C₈	C₂²×C₂₃₃	1	1	yes	characteristic
268	C₂²⋊C₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
269	C₄×C₈	C₂²×C₂₃₃	1	1	yes	characteristic, complemented
270	C₂⁴	—	2	1	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	4	1	no	—
274	#41	—	4	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	C₂³×C₂₃₃	1	1	yes	characteristic
279	C₂×Q₈	C₂³×C₂₃₃	1	1	yes	characteristic
280	C₂×Q₈	C₂³×C₂₃₃	1	1	yes	characteristic
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	D₄×C₂₃₃	1	1	yes	characteristic
289	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
290	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
291	C₂×D₄	C₂³×C₂₃₃	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	C₂³×C₂₃₃	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₂₃₃	1	1	yes	characteristic
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	2	2	no	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	4	1	no	—
303	SD₁₆	—	4	1	no	—
304	SD₁₆	D₄×C₂₃₃	1	4	yes	complemented
305	D₈	—	2	2	no	—
306	D₈	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
310	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
311	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
312	C₂×C₈	C₂³×C₂₃₃	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	D₄×C₂₃₃	1	1	yes	characteristic
317	C₄⋊C₄	C₂³×C₂₃₃	1	1	yes	characteristic
318	C₄⋊C₄	C₂³×C₂₃₃	1	1	yes	characteristic
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	1	no	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	D₄×C₂₃₃	1	1	yes	characteristic
329	C₂²⋊C₄	D₄×C₂₃₃	1	1	yes	characteristic
330	C₄²	—	2	1	no	—
331	C₄²	C₂³×C₂₃₃	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	1	no	—
338	C₂³	C₂×D₄×C₂₃₃	1	1	yes	characteristic
339	C₂³	C₂×D₄×C₂₃₃	1	1	yes	characteristic
340	Q₈	—	2	1	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	2	1	no	—
345	Q₈	—	4	2	no	—
346	Q₈	C₂×D₄×C₂₃₃	1	2	yes	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	2	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	1	no	—
358	D₄	C₂×D₄×C₂₃₃	1	2	yes	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
375	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
376	C₂×C₄	C₂⁴×C₂₃₃	1	1	yes	characteristic
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	C₂×D₄×C₂₃₃	1	2	yes	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	8	4	no	—
397	C₂²	C₂²×D₄×C₂₃₃	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	C₂²×D₄×C₂₃₃	1	1	yes	characteristic
408	C₄	H(5,𝔽₂)×C₂₃₃	1	1	yes	characteristic
409	C₂	—	4	1	no	—
410	C₂	—	4	1	no	—
411	C₂	—	4	2	no	—
412	C₂	—	8	1	no	—
413	C₂	—	8	1	no	—
414	C₂	D₄²×C₂₃₃	1	1	yes	characteristic
415	C₂	#575×C₂₃₃	1	1	yes	characteristic
416	C₂	#577×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×#137×C₂₃₃	C₂	semidirect
2. C₂×AGL(1,ℤ/8)×C₂₃₃	C₂	semidirect
3. #548×C₂₃₃	C₂	semidirect
4. #546×C₂₃₃	C₂	semidirect
5. #495×C₂₃₃	C₂	semidirect
6. #470×C₂₃₃	C₂	semidirect
7. #469×C₂₃₃	C₂	semidirect
8. #464×C₂₃₃	C₂	semidirect
9. #463×C₂₃₃	C₂	semidirect
10. #452×C₂₃₃	C₂	semidirect
11. #450×C₂₃₃	C₂	semidirect
12. #449×C₂₃₃	C₂	semidirect
13. #448×C₂₃₃	C₂	semidirect
14. C₄×SD₁₆×C₂₃₃	C₂	semidirect
15. #436×C₂₃₃	C₂	semidirect
18. C₂²×Q₈×C₂₃₃	C₂²	semidirect
22. C₂×Q₁₆×C₂₃₃	C₂²	semidirect
23. C₂×Q₁₆×C₂₃₃	C₂²	semidirect
28. C₂×SD₁₆×C₂₃₃	C₂²	semidirect
32. C₂×M₁₆×C₂₃₃	C₂²	semidirect
35. #124×C₂₃₃	C₂²	semidirect
43. #121×C₂₃₃	C₂²	semidirect
45. C₄×Q₈×C₂₃₃	C₂²	semidirect
50. #106×C₂₃₃	C₂²	semidirect
51. C₄⋊C₈×C₂₃₃	C₂²	semidirect
52. #103×C₂₃₃	C₂²	semidirect
53. #103×C₂₃₃	C₂²	semidirect
54. #103×C₂₃₃	C₂²	semidirect
57. #102×C₂₃₃	C₂²	semidirect
59. C₂²⋊C₈×C₂₃₃	C₂²	semidirect
60. C₄×C₈×C₂₃₃	C₂²	semidirect
95. SD₁₆×C₂₃₃	D₄	semidirect
208. C₂₃₃	#3275	direct (N × H)
209. #3275	C₂₃₃	direct (N × H)
210. C₂×#137	C₂×C₂₃₃	semidirect
211. C₂×AGL(1,ℤ/8)	C₂×C₂₃₃	semidirect
212. #548	C₂×C₂₃₃	semidirect
213. #546	C₂×C₂₃₃	semidirect
214. #495	C₂×C₂₃₃	semidirect
215. #470	C₂×C₂₃₃	semidirect
216. #469	C₂×C₂₃₃	semidirect
217. #464	C₂×C₂₃₃	semidirect
218. #463	C₂×C₂₃₃	semidirect
219. #452	C₂×C₂₃₃	semidirect
220. #450	C₂×C₂₃₃	semidirect
221. #449	C₂×C₂₃₃	semidirect
222. #448	C₂×C₂₃₃	semidirect
223. C₄×SD₁₆	C₂×C₂₃₃	semidirect
224. #436	C₂×C₂₃₃	semidirect
227. C₂²×Q₈	C₂²×C₂₃₃	semidirect
231. C₂×Q₁₆	C₂²×C₂₃₃	semidirect
232. C₂×Q₁₆	C₂²×C₂₃₃	semidirect
237. C₂×SD₁₆	C₂²×C₂₃₃	semidirect
241. C₂×M₁₆	C₂²×C₂₃₃	semidirect
244. #124	C₂²×C₂₃₃	semidirect
252. #121	C₂²×C₂₃₃	semidirect
254. C₄×Q₈	C₂²×C₂₃₃	semidirect
259. #106	C₂²×C₂₃₃	semidirect
260. C₄⋊C₈	C₂²×C₂₃₃	semidirect
261. #103	C₂²×C₂₃₃	semidirect
262. #103	C₂²×C₂₃₃	semidirect
263. #103	C₂²×C₂₃₃	semidirect
266. #102	C₂²×C₂₃₃	semidirect
268. C₂²⋊C₈	C₂²×C₂₃₃	semidirect
269. C₄×C₈	C₂²×C₂₃₃	semidirect
304. SD₁₆	D₄×C₂₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#137×C₂₃₃	2
C₂×AGL(1,ℤ/8)×C₂₃₃	2
#548×C₂₃₃	2
#546×C₂₃₃	2
#495×C₂₃₃	2
#470×C₂₃₃	2
#469×C₂₃₃	2
#464×C₂₃₃	2
#463×C₂₃₃	2
#452×C₂₃₃	2
#450×C₂₃₃	2
#449×C₂₃₃	2
#448×C₂₃₃	2
C₄×SD₁₆×C₂₃₃	2
#436×C₂₃₃	2
#3275	233

Subgroups — #3275×C233 #44449307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3275×C₂₃₃ #44449307