Subgroups — C₂₃×#33612 #19181238

Order 5888.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2218	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2217	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2215	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
15	C₂₃×#537	—	2	1	no	—
16	C₂₃×#535	—	2	1	no	—
17	C₂₃×#509	—	2	4	no	—
18	C₂×C₂₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₂₃×D₁₆	C₂²	1	2	yes	—
20	C₂₃×#504	—	2	4	no	—
21	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×M₃₂	C₂²	1	2	yes	complemented
23	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₂₃	C₂²	1	2	yes	complemented
25	C₂₃×#469	—	2	2	no	—
26	C₂₃×#468	—	2	2	no	—
27	C₂₃×#467	C₂²	1	2	yes	complemented
28	C₂₃×#466	C₂²	1	2	yes	—
29	C₂₃×#466	C₂²	1	2	yes	—
30	C₂₃×#466	C₂²	1	2	yes	complemented
31	C₂₃×#427	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
33	C₂₃×#418	—	2	1	no	—
34	C₂₃×#417	—	2	1	no	—
35	C₂₃×#367	C₂²	1	2	yes	complemented
36	C₂₃×#366	C₂²	1	2	yes	complemented
37	C₂₃×#358	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#358	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#357	C₂²	1	2	yes	—
40	C₂₃×#357	C₂²	1	2	yes	—
41	C₂₃×#357	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#357	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₂₃	—	2	1	no	—
44	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₂₃	—	2	1	no	—
46	C₂₃×#135	—	2	2	no	—
47	C₂₃×#135	—	2	2	no	—
48	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₂₃	—	2	1	no	—
50	C₂×D₈×C₂₃	—	2	2	no	—
51	C₂×D₈×C₂₃	—	2	1	no	—
52	C₂×D₈×C₂₃	—	2	2	no	—
53	C₂×D₈×C₂₃	C₂³	1	2	yes	—
54	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
55	C₂₃×#131	—	2	2	no	—
56	C₂₃×#131	—	2	2	no	—
57	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
59	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
61	C₂₃×#127	—	4	1	no	—
62	C₂₃×#124	—	4	1	no	—
63	C₂₃×C₂²⋊Q₈	—	2	2	no	—
64	C₂₃×C₂²⋊Q₈	—	4	1	no	—
65	C₂₃×#121	—	2	2	no	—
66	C₂₃×#121	—	2	2	no	—
67	C₂₃×#121	—	2	2	no	—
68	C₂₃×#121	—	4	1	no	—
69	C₂₃×#121	—	4	2	no	—
70	C₂₃×#120	—	4	2	no	—
71	C₂₃×#117	—	2	1	no	—
72	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
73	C₂₃×SD₃₂	—	2	4	no	—
74	C₂₃×D₁₆	—	2	4	no	—
75	C₂₃×M₃₂	—	2	4	no	—
76	C₂₃×M₃₂	D₄	1	4	yes	complemented
77	C₂×C₁₆×C₂₃	—	2	2	no	—
78	C₂×C₁₆×C₂₃	—	2	4	no	—
79	C₂×C₁₆×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×C₁₆×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
82	C₂₃×#107	—	2	1	no	—
83	C₂₃×#107	C₂³	1	2	yes	—
84	C₂₃×#107	C₂³	1	1	yes	characteristic
85	C₂₃×#107	C₂³	1	1	yes	characteristic
86	C₂₃×#106	—	2	1	no	—
87	C₂₃×#103	—	2	2	no	—
88	C₂₃×#102	—	2	2	no	—
89	C₂₃×#102	—	2	2	no	—
90	C₂₃×#102	—	2	2	no	—
91	C₂⁴×C₂₃	—	4	1	no	—
92	#41×C₂₃	—	2	2	no	—
93	#41×C₂₃	—	2	2	no	—
94	#41×C₂₃	—	4	2	no	—
95	#41×C₂₃	—	4	2	no	—
96	C₂×Q₈×C₂₃	—	2	1	no	—
97	C₂×Q₈×C₂₃	D₈	1	1	yes	characteristic
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	1	no	—
100	C₂×D₄×C₂₃	—	4	1	no	—
101	C₂×D₄×C₂₃	—	4	2	no	—
102	C₂×D₄×C₂₃	—	4	2	no	—
103	C₂×D₄×C₂₃	—	4	2	no	—
104	C₂×D₄×C₂₃	—	4	2	no	—
105	C₂×D₄×C₂₃	—	4	1	no	—
106	C₂×D₄×C₂₃	—	4	2	no	—
107	C₂×D₄×C₂₃	D₈	1	2	yes	—
108	C₂×D₄×C₂₃	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	—	4	1	no	—
110	C₂²×C₄×C₂₃	—	4	1	no	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
113	Q₁₆×C₂₃	—	2	1	no	—
114	Q₁₆×C₂₃	—	2	1	no	—
115	SD₁₆×C₂₃	—	4	2	no	—
116	D₈×C₂₃	—	2	1	no	—
117	D₈×C₂₃	—	2	2	no	—
118	D₈×C₂₃	—	2	2	no	—
119	D₈×C₂₃	—	2	1	no	—
120	D₈×C₂₃	—	4	2	no	—
121	M₁₆×C₂₃	—	2	2	no	—
122	M₁₆×C₂₃	—	2	4	no	—
123	C₂×C₈×C₂₃	—	2	2	no	—
124	C₂×C₈×C₂₃	—	2	2	no	—
125	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₂₃	#41	1	2	yes	—
129	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
130	C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₄⋊C₄×C₂₃	—	2	1	no	—
132	C₄⋊C₄×C₂₃	—	2	2	no	—
133	C₄⋊C₄×C₂₃	—	4	1	no	—
134	C₄⋊C₄×C₂₃	—	4	2	no	—
135	C₂²⋊C₄×C₂₃	—	4	1	no	—
136	C₂²⋊C₄×C₂₃	—	4	2	no	—
137	C₂²⋊C₄×C₂₃	—	4	2	no	—
138	C₂²⋊C₄×C₂₃	—	4	2	no	—
139	C₂²⋊C₄×C₂₃	—	4	2	no	—
140	C₄²×C₂₃	—	4	1	no	—
141	C₁₆×C₂₃	—	2	1	no	—
142	C₁₆×C₂₃	—	2	1	no	—
143	C₁₆×C₂₃	C₂×D₄	1	4	yes	—
144	#33612	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₂₃	—	4	1	no	—
146	C₂³×C₂₃	—	4	2	no	—
147	C₂³×C₂₃	—	8	2	no	—
148	C₂³×C₂₃	—	16	1	no	—
149	C₂³×C₂₃	—	16	1	no	—
150	C₂³×C₂₃	C₂×D₈	1	2	yes	—
151	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
152	Q₈×C₂₃	—	2	2	no	—
153	Q₈×C₂₃	—	4	1	no	—
154	Q₈×C₂₃	—	4	1	no	—
155	D₄×C₂₃	—	2	4	no	—
156	D₄×C₂₃	—	2	2	no	—
157	D₄×C₂₃	—	4	2	no	—
158	D₄×C₂₃	—	4	1	no	—
159	D₄×C₂₃	—	4	2	no	—
160	D₄×C₂₃	—	4	1	no	—
161	D₄×C₂₃	—	8	2	no	—
162	D₄×C₂₃	—	8	2	no	—
163	D₄×C₂₃	—	16	2	no	—
164	D₄×C₂₃	—	16	2	no	—
165	D₄×C₂₃	—	16	2	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	4	1	no	—
169	C₂×C₄×C₂₃	—	4	1	no	—
170	C₂×C₄×C₂₃	—	4	2	no	—
171	C₂×C₄×C₂₃	—	4	1	no	—
172	C₂×C₄×C₂₃	—	8	2	no	—
173	C₂×C₄×C₂₃	—	16	1	no	—
174	C₂×C₄×C₂₃	#121	1	2	yes	—
175	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₂₃	#135	1	2	yes	—
178	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₂₃	—	2	2	no	—
180	C₈×C₂₃	#121	1	2	yes	—
181	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₂₃	C₂×#41	1	1	yes	characteristic
183	C₂×#509	C₂×C₂₃	1	1	yes	characteristic, complemented
184	C₂×#504	C₂×C₂₃	1	1	yes	characteristic, complemented
185	#3061	C₂×C₂₃	1	1	yes	characteristic, complemented
186	#3058	C₂×C₂₃	1	1	yes	characteristic, complemented
187	#2220	C₂×C₂₃	1	2	yes	complemented
188	#2218	C₂×C₂₃	1	2	yes	complemented
189	#2217	C₂×C₂₃	1	2	yes	complemented
190	#2215	C₂×C₂₃	1	2	yes	complemented
191	#2159	C₂×C₂₃	1	1	yes	characteristic, complemented
192	#2138	C₂×C₂₃	1	1	yes	characteristic, complemented
193	C₂×#357	C₂×C₂₃	1	1	yes	characteristic, complemented
194	C₂²×C₂₃	—	2	1	no	—
195	C₂²×C₂₃	—	2	1	no	—
196	C₂²×C₂₃	—	2	2	no	—
197	C₂²×C₂₃	—	2	2	no	—
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	8	1	no	—
200	C₂²×C₂₃	—	8	2	no	—
201	C₂²×C₂₃	—	8	2	no	—
202	C₂²×C₂₃	—	8	1	no	—
203	C₂²×C₂₃	—	8	1	no	—
204	C₂²×C₂₃	—	8	2	no	—
205	C₂²×C₂₃	—	16	4	no	—
206	C₂²×C₂₃	#466	1	2	yes	—
207	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
208	C₄×C₂₃	—	2	2	no	—
209	C₄×C₂₃	—	8	2	no	—
210	C₄×C₂₃	—	8	1	no	—
211	C₄×C₂₃	—	8	1	no	—
212	C₄×C₂₃	—	8	1	no	—
213	C₄×C₂₃	#466	1	2	yes	—
214	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
215	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
216	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
217	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
218	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
219	#537	—	2	1	no	—
220	#535	—	2	1	no	—
221	#509	—	2	4	no	—
222	C₂×SD₃₂	C₂²×C₂₃	1	2	yes	—
223	C₂×D₁₆	C₂²×C₂₃	1	2	yes	—
224	#504	—	2	4	no	—
225	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×M₃₂	C₂²×C₂₃	1	2	yes	complemented
227	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
228	C₂²×C₁₆	C₂²×C₂₃	1	2	yes	complemented
229	#469	—	2	2	no	—
230	#468	—	2	2	no	—
231	#467	C₂²×C₂₃	1	2	yes	complemented
232	#466	C₂²×C₂₃	1	2	yes	—
233	#466	C₂²×C₂₃	1	2	yes	—
234	#466	C₂²×C₂₃	1	2	yes	complemented
235	#427	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
237	#418	—	2	1	no	—
238	#417	—	2	1	no	—
239	#367	C₂²×C₂₃	1	2	yes	complemented
240	#366	C₂²×C₂₃	1	2	yes	complemented
241	#358	C₂²×C₂₃	1	1	yes	characteristic, complemented
242	#358	C₂²×C₂₃	1	1	yes	characteristic, complemented
243	#357	C₂²×C₂₃	1	2	yes	—
244	#357	C₂²×C₂₃	1	2	yes	—
245	#357	C₂²×C₂₃	1	1	yes	characteristic, complemented
246	#357	C₂²×C₂₃	1	1	yes	characteristic, complemented
247	C₂×C₂₃	—	2	2	no	—
248	C₂×C₂₃	—	4	2	no	—
249	C₂×C₂₃	—	16	1	no	—
250	C₂×C₂₃	—	16	2	no	—
251	C₂×C₂₃	C₂×#466	1	1	yes	characteristic
252	C₂×C₂₃	#3415	1	1	yes	characteristic
253	C₂×C₂₃	#3416	1	1	yes	characteristic
254	C₂×#41	—	2	1	no	—
255	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
256	C₂²×D₄	—	2	1	no	—
257	#135	—	2	2	no	—
258	#135	—	2	2	no	—
259	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
260	C₂×SD₁₆	—	2	1	no	—
261	C₂×D₈	—	2	2	no	—
262	C₂×D₈	—	2	1	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	C₂³×C₂₃	1	2	yes	—
265	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
266	#131	—	2	2	no	—
267	#131	—	2	2	no	—
268	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
269	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
271	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
272	#127	—	4	1	no	—
273	#124	—	4	1	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	4	1	no	—
276	#121	—	2	2	no	—
277	#121	—	2	2	no	—
278	#121	—	2	2	no	—
279	#121	—	4	1	no	—
280	#121	—	4	2	no	—
281	#120	—	4	2	no	—
282	#117	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	SD₃₂	—	2	4	no	—
285	D₁₆	—	2	4	no	—
286	M₃₂	—	2	4	no	—
287	M₃₂	D₄×C₂₃	1	4	yes	complemented
288	C₂×C₁₆	—	2	2	no	—
289	C₂×C₁₆	—	2	4	no	—
290	C₂×C₁₆	C₂³×C₂₃	1	1	yes	characteristic
291	C₂×C₁₆	C₂³×C₂₃	1	1	yes	characteristic
292	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
293	#107	—	2	1	no	—
294	#107	C₂³×C₂₃	1	2	yes	—
295	#107	C₂³×C₂₃	1	1	yes	characteristic
296	#107	C₂³×C₂₃	1	1	yes	characteristic
297	#106	—	2	1	no	—
298	#103	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	C₂₃	#33612	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	—	4	1	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	D₈×C₂₃	1	1	yes	characteristic
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	D₈×C₂₃	1	2	yes	—
320	C₂×D₄	D₈×C₂₃	1	1	yes	characteristic
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
325	Q₁₆	—	2	1	no	—
326	Q₁₆	—	2	1	no	—
327	SD₁₆	—	4	2	no	—
328	D₈	—	2	1	no	—
329	D₈	—	2	2	no	—
330	D₈	—	2	2	no	—
331	D₈	—	2	1	no	—
332	D₈	—	4	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	4	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
340	C₂×C₈	#41×C₂₃	1	2	yes	—
341	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₄²	—	4	1	no	—
353	C₁₆	—	2	1	no	—
354	C₁₆	—	2	1	no	—
355	C₁₆	C₂×D₄×C₂₃	1	4	yes	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	16	1	no	—
360	C₂³	—	16	1	no	—
361	C₂³	C₂×D₈×C₂₃	1	2	yes	—
362	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	1	no	—
366	D₄	—	2	4	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	16	2	no	—
375	D₄	—	16	2	no	—
376	D₄	—	16	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	16	1	no	—
385	C₂×C₄	C₂₃×#121	1	2	yes	—
386	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
387	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
388	C₂×C₄	C₂₃×#135	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	C₂₃×#121	1	2	yes	—
392	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
393	C₈	C₂×#41×C₂₃	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	16	4	no	—
406	C₂²	C₂₃×#466	1	2	yes	—
407	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	C₂₃×#466	1	2	yes	—
414	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
415	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	16	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₂₃×#466	1	1	yes	characteristic
421	C₂	C₂₃×#3415	1	1	yes	characteristic
422	C₂	C₂₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×#41×C₂₃ ◁ C₂×C₂₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#509	C₂	semidirect
2. C₂×C₂₃×#504	C₂	semidirect
3. C₂₃×#3061	C₂	semidirect
4. C₂₃×#3058	C₂	semidirect
5. C₂₃×#2220	C₂	semidirect
6. C₂₃×#2218	C₂	semidirect
7. C₂₃×#2217	C₂	semidirect
8. C₂₃×#2215	C₂	semidirect
9. C₂₃×#2159	C₂	semidirect
10. C₂₃×#2138	C₂	semidirect
11. C₂×C₂₃×#357	C₂	semidirect
22. C₂×C₂₃×M₃₂	C₂²	semidirect
24. C₂²×C₁₆×C₂₃	C₂²	semidirect
27. C₂₃×#467	C₂²	semidirect
30. C₂₃×#466	C₂²	semidirect
35. C₂₃×#367	C₂²	semidirect
36. C₂₃×#366	C₂²	semidirect
37. C₂₃×#358	C₂²	semidirect
38. C₂₃×#358	C₂²	semidirect
41. C₂₃×#357	C₂²	semidirect
42. C₂₃×#357	C₂²	semidirect
76. C₂₃×M₃₂	D₄	semidirect
144. #33612	C₂₃	direct (N × H)
183. C₂×#509	C₂×C₂₃	semidirect
184. C₂×#504	C₂×C₂₃	semidirect
185. #3061	C₂×C₂₃	semidirect
186. #3058	C₂×C₂₃	semidirect
187. #2220	C₂×C₂₃	semidirect
188. #2218	C₂×C₂₃	semidirect
189. #2217	C₂×C₂₃	semidirect
190. #2215	C₂×C₂₃	semidirect
191. #2159	C₂×C₂₃	semidirect
192. #2138	C₂×C₂₃	semidirect
193. C₂×#357	C₂×C₂₃	semidirect
226. C₂×M₃₂	C₂²×C₂₃	semidirect
228. C₂²×C₁₆	C₂²×C₂₃	semidirect
231. #467	C₂²×C₂₃	semidirect
234. #466	C₂²×C₂₃	semidirect
239. #367	C₂²×C₂₃	semidirect
240. #366	C₂²×C₂₃	semidirect
241. #358	C₂²×C₂₃	semidirect
242. #358	C₂²×C₂₃	semidirect
245. #357	C₂²×C₂₃	semidirect
246. #357	C₂²×C₂₃	semidirect
287. M₃₂	D₄×C₂₃	semidirect
302. C₂₃	#33612	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×#509	2
C₂×C₂₃×#504	2
C₂₃×#3061	2
C₂₃×#3058	2
C₂₃×#2220	2
C₂₃×#2218	2
C₂₃×#2217	2
C₂₃×#2215	2
C₂₃×#2159	2
C₂₃×#2138	2
C₂×C₂₃×#357	2
#33612	23

Subgroups — C23×#33612 #19181238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33612 #19181238