Subgroups — C₂×C₂₃×#1632 #19166103

Order 5888.

1054 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1632	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₂₃	—	2	2	no	—
10	C₂₃×#554	—	2	2	no	—
11	C₂₃×#554	—	2	2	no	—
12	C₂₃×#554	—	2	2	no	—
13	C₂₃×#554	C₂²	1	4	yes	—
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#125	—	2	1	no	—
17	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₃	—	2	1	no	—
21	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
23	C₂₃×#494	—	2	2	no	—
24	C₂₃×#494	C₂²	1	4	yes	complemented
25	C₂₃×#477	—	2	2	no	—
26	C₂₃×#477	C₂²	1	4	yes	complemented
27	C₂₃×#476	—	2	2	no	—
28	C₂₃×#476	C₂²	1	4	yes	—
29	C₂×C₂₃×#107	—	2	1	no	—
30	C₂×C₂₃×#106	—	2	1	no	—
31	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#103	—	2	1	no	—
34	C₂×C₂₃×#102	—	2	1	no	—
35	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#333	C₂²	1	4	yes	complemented
37	C₂₃×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₂₃×D₄⋊C₈	C₂²	1	4	yes	—
39	C₂²×Q₈×C₂₃	—	2	1	no	—
40	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₂₃	D₄	1	2	yes	—
42	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	—	2	2	no	—
44	C₂³×C₄×C₂₃	—	2	1	no	—
45	C₂×Q₁₆×C₂₃	—	2	8	no	—
46	C₂×Q₁₆×C₂₃	—	4	8	no	—
47	C₂²×C₈×C₂₃	—	2	1	no	—
48	C₂²×C₈×C₂₃	—	2	1	no	—
49	C₂²×C₈×C₂₃	—	2	1	no	—
50	C₂₃×C₄⋊Q₈	—	2	1	no	—
51	C₂₃×C₄⋊Q₈	—	2	1	no	—
52	C₂₃×C₄⋊Q₈	—	2	1	no	—
53	C₂₃×C₄⋊Q₈	—	2	1	no	—
54	C₂₃×C₄⋊Q₈	—	2	1	no	—
55	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
56	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₂₃×#125	—	2	4	no	—
59	C₂₃×#125	—	2	4	no	—
60	C₂₃×C₂²⋊Q₈	—	2	4	no	—
61	C₂₃×C₂²⋊Q₈	—	2	8	no	—
62	C₂₃×C₂²⋊Q₈	—	2	4	no	—
63	C₂₃×C₂²⋊Q₈	—	2	8	no	—
64	C₄×Q₈×C₂₃	—	2	1	no	—
65	C₄×Q₈×C₂₃	—	2	1	no	—
66	C₄×Q₈×C₂₃	D₄	1	2	yes	—
67	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
68	C₄×D₄×C₂₃	—	2	4	no	—
69	C₄×D₄×C₂₃	—	2	4	no	—
70	C₄×D₄×C₂₃	—	2	1	no	—
71	C₄×D₄×C₂₃	—	2	1	no	—
72	C₄×D₄×C₂₃	D₄	1	2	yes	—
73	C₄×D₄×C₂₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
75	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
77	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
87	C₂×C₄²×C₂₃	—	2	1	no	—
88	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×#107	—	2	4	no	—
90	C₂₃×#106	—	2	4	no	—
91	C₂₃×C₄⋊C₈	—	2	1	no	—
92	C₂₃×C₄⋊C₈	—	2	1	no	—
93	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
94	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
95	C₂₃×#103	—	2	4	no	—
96	C₂₃×#102	—	2	4	no	—
97	C₄×C₈×C₂₃	—	2	1	no	—
98	C₄×C₈×C₂₃	C₂³	1	2	yes	—
99	C₂⁴×C₂₃	—	2	1	no	—
100	C₂×Q₈×C₂₃	—	2	1	no	—
101	C₂×Q₈×C₂₃	—	2	2	no	—
102	C₂×Q₈×C₂₃	—	2	2	no	—
103	C₂×Q₈×C₂₃	—	2	2	no	—
104	C₂×Q₈×C₂₃	—	2	2	no	—
105	C₂×Q₈×C₂₃	—	4	4	no	—
106	C₂×Q₈×C₂₃	—	4	4	no	—
107	C₂×Q₈×C₂₃	—	4	1	no	—
108	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
110	C₂×D₄×C₂₃	—	2	1	no	—
111	C₂×D₄×C₂₃	—	2	2	no	—
112	C₂×D₄×C₂₃	Q₁₆	1	4	yes	complemented
113	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₂₃	—	2	1	no	—
115	C₂²×C₄×C₂₃	—	2	1	no	—
116	C₂²×C₄×C₂₃	—	2	1	no	—
117	C₂²×C₄×C₂₃	—	2	2	no	—
118	C₂²×C₄×C₂₃	—	2	8	no	—
119	C₂²×C₄×C₂₃	—	2	2	no	—
120	C₂²×C₄×C₂₃	—	2	2	no	—
121	C₂²×C₄×C₂₃	—	4	2	no	—
122	C₂²×C₄×C₂₃	—	4	2	no	—
123	C₂²×C₄×C₂₃	—	4	1	no	—
124	C₂²×C₄×C₂₃	—	8	4	no	—
125	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₂₃	—	4	16	no	—
129	C₂×C₈×C₂₃	—	2	4	no	—
130	C₂×C₈×C₂₃	—	2	2	no	—
131	C₂×C₈×C₂₃	—	2	2	no	—
132	C₂×C₈×C₂₃	—	2	2	no	—
133	C₂×C₈×C₂₃	—	4	2	no	—
134	C₂×C₈×C₂₃	—	4	2	no	—
135	C₄⋊C₄×C₂₃	—	2	8	no	—
136	C₄⋊C₄×C₂₃	—	2	8	no	—
137	C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₄⋊C₄×C₂₃	—	2	2	no	—
139	C₄⋊C₄×C₂₃	—	2	2	no	—
140	C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₄⋊C₄×C₂₃	—	2	1	no	—
142	C₄⋊C₄×C₂₃	—	2	2	no	—
143	C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₄⋊C₄×C₂₃	—	2	2	no	—
145	C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₄⋊C₄×C₂₃	—	2	2	no	—
147	C₄⋊C₄×C₂₃	—	4	1	no	—
148	C₄⋊C₄×C₂₃	—	4	1	no	—
149	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₂₃	—	2	8	no	—
152	C₂²⋊C₄×C₂₃	—	2	2	no	—
153	C₂²⋊C₄×C₂₃	—	2	2	no	—
154	C₄²×C₂₃	—	2	2	no	—
155	C₄²×C₂₃	—	2	2	no	—
156	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
160	C₂×#1632	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂³×C₂₃	—	2	2	no	—
162	C₂³×C₂₃	—	2	4	no	—
163	C₂³×C₂₃	—	4	2	no	—
164	C₂³×C₂₃	—	4	2	no	—
165	C₂³×C₂₃	#120	1	1	yes	characteristic
166	Q₈×C₂₃	—	2	2	no	—
167	Q₈×C₂₃	—	2	2	no	—
168	Q₈×C₂₃	—	4	4	no	—
169	Q₈×C₂₃	—	4	4	no	—
170	Q₈×C₂₃	—	4	2	no	—
171	Q₈×C₂₃	—	8	2	no	—
172	Q₈×C₂₃	—	8	2	no	—
173	D₄×C₂₃	—	2	2	no	—
174	D₄×C₂₃	—	2	4	no	—
175	D₄×C₂₃	C₂×Q₁₆	1	4	yes	complemented
176	C₂×C₄×C₂₃	—	2	2	no	—
177	C₂×C₄×C₂₃	—	2	2	no	—
178	C₂×C₄×C₂₃	—	2	2	no	—
179	C₂×C₄×C₂₃	—	2	2	no	—
180	C₂×C₄×C₂₃	—	2	4	no	—
181	C₂×C₄×C₂₃	—	4	2	no	—
182	C₂×C₄×C₂₃	—	4	2	no	—
183	C₂×C₄×C₂₃	—	4	2	no	—
184	C₂×C₄×C₂₃	—	4	4	no	—
185	C₂×C₄×C₂₃	—	4	2	no	—
186	C₂×C₄×C₂₃	—	4	2	no	—
187	C₂×C₄×C₂₃	—	4	4	no	—
188	C₂×C₄×C₂₃	—	4	2	no	—
189	C₂×C₄×C₂₃	—	8	8	no	—
190	C₂×C₄×C₂₃	—	8	2	no	—
191	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
192	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
193	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
194	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
195	C₂×C₄×C₂₃	#135	1	2	yes	—
196	C₂×C₄×C₂₃	#137	1	2	yes	—
197	C₂×C₄×C₂₃	#137	1	2	yes	—
198	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
201	C₈×C₂₃	—	2	4	no	—
202	C₈×C₂₃	—	4	2	no	—
203	C₈×C₂₃	—	4	2	no	—
204	C₂×#554	C₂×C₂₃	1	1	yes	characteristic
205	C₂×#494	C₂×C₂₃	1	1	yes	characteristic, complemented
206	C₂×#477	C₂×C₂₃	1	1	yes	characteristic, complemented
207	C₂×#476	C₂×C₂₃	1	1	yes	characteristic
208	#1632	C₂×C₂₃	1	8	yes	direct product factor
209	C₂×#333	C₂×C₂₃	1	1	yes	characteristic, complemented
210	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
211	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
212	C₂²×C₂₃	—	2	4	no	—
213	C₂²×C₂₃	—	4	8	no	—
214	C₂²×C₂₃	—	4	2	no	—
215	C₂²×C₂₃	—	4	2	no	—
216	C₂²×C₂₃	#451	1	2	yes	—
217	C₂²×C₂₃	#452	1	2	yes	—
218	C₂²×C₂₃	#453	1	2	yes	—
219	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
220	C₄×C₂₃	—	2	1	no	—
221	C₄×C₂₃	—	2	1	no	—
222	C₄×C₂₃	—	4	2	no	—
223	C₄×C₂₃	—	4	2	no	—
224	C₄×C₂₃	—	4	2	no	—
225	C₄×C₂₃	—	4	4	no	—
226	C₄×C₂₃	—	8	2	no	—
227	C₄×C₂₃	#451	1	2	yes	—
228	C₄×C₂₃	#452	1	2	yes	—
229	C₄×C₂₃	C₂²×Q₁₆	1	1	yes	characteristic
230	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
231	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
232	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
233	C₂²×Q₁₆	—	2	2	no	—
234	#554	—	2	2	no	—
235	#554	—	2	2	no	—
236	#554	—	2	2	no	—
237	#554	C₂²×C₂₃	1	4	yes	—
238	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×#125	—	2	1	no	—
241	C₂×C₂²⋊Q₈	—	2	1	no	—
242	C₂×C₂²⋊Q₈	—	2	2	no	—
243	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×C₄×D₄	—	2	1	no	—
245	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	—	2	1	no	—
247	#494	—	2	2	no	—
248	#494	C₂²×C₂₃	1	4	yes	complemented
249	#477	—	2	2	no	—
250	#477	C₂²×C₂₃	1	4	yes	complemented
251	#476	—	2	2	no	—
252	#476	C₂²×C₂₃	1	4	yes	—
253	C₂×#107	—	2	1	no	—
254	C₂×#106	—	2	1	no	—
255	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
257	C₂×#103	—	2	1	no	—
258	C₂×#102	—	2	1	no	—
259	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
260	#333	C₂²×C₂₃	1	4	yes	complemented
261	Q₈⋊C₈	C₂²×C₂₃	1	4	yes	complemented
262	D₄⋊C₈	C₂²×C₂₃	1	4	yes	—
263	C₂×C₂₃	—	4	4	no	—
264	C₂×C₂₃	#1632	1	4	yes	direct product factor
265	C₂×C₂₃	C₂×#451	1	1	yes	characteristic
266	C₂×C₂₃	C₂×#452	1	1	yes	characteristic
267	C₂×C₂₃	C₂×#453	1	1	yes	characteristic
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
270	C₂²×Q₈	D₄×C₂₃	1	2	yes	—
271	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂×Q₁₆	—	2	8	no	—
275	C₂×Q₁₆	—	4	8	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
285	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
287	#125	—	2	4	no	—
288	#125	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	8	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	D₄×C₂₃	1	2	yes	—
296	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	D₄×C₂₃	1	2	yes	—
302	C₄×D₄	C₂³×C₂₃	1	2	yes	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
318	#107	—	2	4	no	—
319	#106	—	2	4	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
323	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
324	#103	—	2	4	no	—
325	#102	—	2	4	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	C₂³×C₂₃	1	2	yes	—
328	C₂₃	C₂×#1632	1	1	yes	characteristic, direct product factor, Sylow
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	4	no	—
336	C₂×Q₈	—	4	4	no	—
337	C₂×Q₈	—	4	1	no	—
338	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
339	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	Q₁₆×C₂₃	1	4	yes	complemented
343	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	8	4	no	—
355	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
358	Q₁₆	—	4	16	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	4	2	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
380	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
389	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
390	C₂³	—	2	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₂₃×#120	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	4	no	—
398	Q₈	—	4	4	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	8	2	no	—
401	Q₈	—	8	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	4	no	—
404	D₄	C₂×Q₁₆×C₂₃	1	4	yes	complemented
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
421	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
422	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
423	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
424	C₂×C₄	C₂₃×#135	1	2	yes	—
425	C₂×C₄	C₂₃×#137	1	2	yes	—
426	C₂×C₄	C₂₃×#137	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
430	C₈	—	2	4	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	C₂₃×#451	1	2	yes	—
438	C₂²	C₂₃×#452	1	2	yes	—
439	C₂²	C₂₃×#453	1	2	yes	—
440	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	8	2	no	—
448	C₄	C₂₃×#451	1	2	yes	—
449	C₄	C₂₃×#452	1	2	yes	—
450	C₄	C₂²×Q₁₆×C₂₃	1	1	yes	characteristic
451	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
452	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
453	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
454	C₂	—	4	4	no	—
455	C₂	C₂₃×#1632	1	4	yes	direct product factor
456	C₂	C₂×C₂₃×#451	1	1	yes	characteristic
457	C₂	C₂×C₂₃×#452	1	1	yes	characteristic
458	C₂	C₂×C₂₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#494	C₂	semidirect
3. C₂×C₂₃×#477	C₂	semidirect
5. C₂₃×#1632	C₂	direct (N × H)
6. C₂×C₂₃×#333	C₂	semidirect
7. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
24. C₂₃×#494	C₂²	semidirect
26. C₂₃×#477	C₂²	semidirect
36. C₂₃×#333	C₂²	semidirect
37. C₂₃×Q₈⋊C₈	C₂²	semidirect
112. C₂×D₄×C₂₃	Q₁₆	semidirect
160. C₂×#1632	C₂₃	direct (N × H)
175. D₄×C₂₃	C₂×Q₁₆	semidirect
205. C₂×#494	C₂×C₂₃	semidirect
206. C₂×#477	C₂×C₂₃	semidirect
208. #1632	C₂×C₂₃	direct (N × H)
209. C₂×#333	C₂×C₂₃	semidirect
210. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
248. #494	C₂²×C₂₃	semidirect
250. #477	C₂²×C₂₃	semidirect
260. #333	C₂²×C₂₃	semidirect
261. Q₈⋊C₈	C₂²×C₂₃	semidirect
264. C₂×C₂₃	#1632	direct (N × H)
328. C₂₃	C₂×#1632	direct (N × H)
342. C₂×D₄	Q₁₆×C₂₃	semidirect
404. D₄	C₂×Q₁₆×C₂₃	semidirect
455. C₂	C₂₃×#1632	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×C₂₃×#554	2
C₂×C₂₃×#494	2
C₂×C₂₃×#477	2
C₂×C₂₃×#476	2
C₂₃×#1632	2
C₂×C₂₃×#333	2
C₂×C₂₃×Q₈⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
C₂×#1632	23

Subgroups — C2×C23×#1632 #19166103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1632 #19166103