Subgroups — C₂₃×#61936 #19209562

Order 5888.

1634 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	C₂₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3398	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3395	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3374	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3364	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3223	C₂	1	4	yes	maximal
8	C₂₃×#3209	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3127	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3107	C₂	1	2	yes	maximal
11	C₂₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#564	—	2	2	no	—
13	C₂₃×#557	—	2	2	no	—
14	C₂₃×#557	C₂²	1	4	yes	—
15	C₂₃×#557	C₂²	1	4	yes	—
16	C₂₃×#557	C₂²	1	4	yes	—
17	C₂₃×#556	C₂²	1	4	yes	—
18	C₂₃×#552	—	2	4	no	—
19	C₂₃×#541	—	2	2	no	—
20	C₂₃×#541	—	2	4	no	—
21	C₂₃×#541	C₂²	1	4	yes	—
22	C₂₃×#536	C₂²	1	2	yes	—
23	C₂₃×#533	—	2	2	no	—
24	C₂₃×#533	C₂²	1	2	yes	—
25	C₂₃×#533	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂₃×#519	C₂²	1	2	yes	—
28	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#497	C₂²	1	4	yes	—
30	C₂₃×#494	C₂²	1	4	yes	—
31	C₂₃×#494	C₂²	1	4	yes	—
32	C₂₃×#491	C₂²	1	4	yes	—
33	C₂₃×#488	C₂²	1	4	yes	—
34	C₂₃×#487	C₂²	1	4	yes	—
35	C₂₃×#485	C₂²	1	4	yes	—
36	C₂₃×#479	C₂²	1	8	yes	—
37	C₂₃×#475	C₂²	1	2	yes	—
38	C₂₃×#474	C₂²	1	2	yes	—
39	C₂₃×#464	C₂²	1	8	yes	—
40	C₂₃×#462	C₂²	1	4	yes	—
41	C₂₃×#462	C₂²	1	4	yes	—
42	C₂₃×#462	C₂²	1	8	yes	—
43	C₂₃×#462	C₂²	1	2	yes	—
44	C₂₃×#462	C₂²	1	8	yes	—
45	C₂₃×#461	C₂²	1	2	yes	—
46	C₂₃×#452	C₂²	1	4	yes	—
47	C₂₃×#451	C₂²	1	8	yes	—
48	C₂₃×#446	C₂²	1	4	yes	—
49	C₈×Q₈×C₂₃	C₂²	1	4	yes	—
50	C₂₃×#441	C₂²	1	8	yes	—
51	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
52	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	—
53	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
54	C₂₃×#433	C₂²	1	4	yes	—
55	C₂₃×#431	C₂²	1	2	yes	—
56	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
58	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
59	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
60	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
61	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
62	C₂₃×C₄⋊Q₈	—	2	4	no	—
63	C₂₃×C₄⋊Q₈	—	2	1	no	—
64	C₂₃×C₄⋊Q₈	—	2	1	no	—
65	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
66	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
69	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
70	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₂₃×#126	—	2	8	no	—
72	C₂₃×#126	—	2	8	no	—
73	C₂₃×#125	—	2	4	no	—
74	C₂₃×#125	—	2	8	no	—
75	C₂₃×#125	—	2	4	no	—
76	C₂₃×#125	—	2	8	no	—
77	C₂₃×#125	—	2	8	no	—
78	C₂₃×#125	—	2	8	no	—
79	C₂₃×#125	—	2	2	no	—
80	C₂₃×#125	D₄	1	2	yes	—
81	C₂₃×#125	C₂³	1	4	yes	—
82	C₂₃×#124	C₂³	1	4	yes	—
83	C₂₃×#123	—	2	4	no	—
84	C₂₃×C₂²⋊Q₈	—	2	4	no	—
85	C₂₃×C₂²⋊Q₈	—	2	2	no	—
86	C₂₃×C₂²⋊Q₈	—	2	4	no	—
87	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	—
88	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₄×Q₈×C₂₃	—	2	4	no	—
90	C₄×Q₈×C₂₃	—	2	4	no	—
91	C₄×Q₈×C₂₃	—	2	4	no	—
92	C₄×Q₈×C₂₃	—	2	4	no	—
93	C₄×Q₈×C₂₃	—	2	2	no	—
94	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
95	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
96	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
97	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
98	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
99	C₄×D₄×C₂₃	—	2	2	no	—
100	C₄×D₄×C₂₃	C₂³	1	2	yes	—
101	C₂₃×#117	—	2	2	no	—
102	C₂₃×#117	—	2	4	no	—
103	C₂₃×#117	—	2	4	no	—
104	C₂₃×#117	—	2	1	no	—
105	C₂₃×#117	C₂³	1	1	yes	characteristic
106	C₂₃×#117	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
108	C₂×C₄²×C₂₃	—	2	1	no	—
109	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₂₃×#107	C₂³	1	4	yes	—
111	C₂₃×#106	C₂³	1	4	yes	—
112	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
115	C₂₃×#103	C₂³	1	4	yes	—
116	C₂₃×#103	C₂³	1	4	yes	—
117	C₂₃×#103	C₂³	1	8	yes	—
118	C₂₃×#103	C₂³	1	4	yes	—
119	C₂₃×#103	C₂³	1	8	yes	—
120	C₂₃×#102	C₂³	1	4	yes	—
121	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
122	C₂₃×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₂₃	C₂³	1	4	yes	—
124	C₄×C₈×C₂₃	C₂³	1	4	yes	—
125	#41×C₂₃	—	4	2	no	—
126	C₂×Q₈×C₂₃	—	2	2	no	—
127	C₂×Q₈×C₂₃	—	2	2	no	—
128	C₂×Q₈×C₂₃	—	4	4	no	—
129	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
131	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
133	C₂×D₄×C₂₃	—	2	1	no	—
134	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	—	2	2	no	—
136	C₂²×C₄×C₂₃	—	2	2	no	—
137	C₂²×C₄×C₂₃	—	2	1	no	—
138	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₂₃	—	4	8	no	—
141	Q₁₆×C₂₃	—	4	8	no	—
142	Q₁₆×C₂₃	—	4	4	no	—
143	SD₁₆×C₂₃	—	4	4	no	—
144	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
145	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
146	C₄⋊C₄×C₂₃	—	2	4	no	—
147	C₄⋊C₄×C₂₃	—	2	4	no	—
148	C₄⋊C₄×C₂₃	—	2	2	no	—
149	C₄⋊C₄×C₂₃	—	2	8	no	—
150	C₄⋊C₄×C₂₃	—	2	2	no	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	2	8	no	—
154	C₄⋊C₄×C₂₃	—	2	4	no	—
155	C₄⋊C₄×C₂₃	—	2	8	no	—
156	C₄⋊C₄×C₂₃	—	2	8	no	—
157	C₄⋊C₄×C₂₃	—	2	4	no	—
158	C₄⋊C₄×C₂₃	—	2	8	no	—
159	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
160	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
161	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
162	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
163	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
164	C₂²⋊C₄×C₂₃	—	2	1	no	—
165	C₂²⋊C₄×C₂₃	—	2	4	no	—
166	C₂²⋊C₄×C₂₃	—	2	2	no	—
167	C₂²⋊C₄×C₂₃	—	2	8	no	—
168	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
169	C₄²×C₂₃	—	2	1	no	—
170	C₄²×C₂₃	—	2	2	no	—
171	C₄²×C₂₃	—	2	8	no	—
172	C₄²×C₂₃	—	2	4	no	—
173	C₄²×C₂₃	—	2	8	no	—
174	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₂₃	C₂⁴	1	2	yes	—
177	C₄²×C₂₃	C₂⁴	1	4	yes	—
178	#61936	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₂₃	—	2	1	no	—
180	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₂₃	—	2	8	no	—
182	Q₈×C₂₃	—	2	4	no	—
183	Q₈×C₂₃	—	2	4	no	—
184	Q₈×C₂₃	—	2	8	no	—
185	Q₈×C₂₃	—	2	2	no	—
186	Q₈×C₂₃	—	4	4	no	—
187	Q₈×C₂₃	—	4	4	no	—
188	D₄×C₂₃	—	2	2	no	—
189	D₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	2	4	no	—
191	C₂×C₄×C₂₃	—	2	2	no	—
192	C₂×C₄×C₂₃	—	2	2	no	—
193	C₂×C₄×C₂₃	—	2	4	no	—
194	C₂×C₄×C₂₃	—	2	4	no	—
195	C₂×C₄×C₂₃	—	2	4	no	—
196	C₂×C₄×C₂₃	—	2	1	no	—
197	C₂×C₄×C₂₃	—	4	2	no	—
198	C₂×C₄×C₂₃	—	4	4	no	—
199	C₂×C₄×C₂₃	—	4	4	no	—
200	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
201	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
205	C₈×C₂₃	—	2	4	no	—
206	C₈×C₂₃	—	2	4	no	—
207	#3556	C₂×C₂₃	1	1	yes	characteristic, complemented
208	#3509	C₂×C₂₃	1	1	yes	characteristic
209	#3398	C₂×C₂₃	1	4	yes	complemented
210	#3395	C₂×C₂₃	1	4	yes	complemented
211	#3374	C₂×C₂₃	1	4	yes	complemented
212	#3364	C₂×C₂₃	1	4	yes	complemented
213	#3223	C₂×C₂₃	1	4	yes	—
214	#3209	C₂×C₂₃	1	2	yes	complemented
215	#3127	C₂×C₂₃	1	4	yes	complemented
216	#3107	C₂×C₂₃	1	2	yes	—
217	#2986	C₂×C₂₃	1	1	yes	characteristic, complemented
218	C₂²×C₂₃	—	2	1	no	—
219	C₂²×C₂₃	—	2	2	no	—
220	C₂²×C₂₃	—	4	1	no	—
221	C₂²×C₂₃	—	4	2	no	—
222	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
223	C₄×C₂₃	—	2	1	no	—
224	C₄×C₂₃	—	2	2	no	—
225	C₄×C₂₃	—	2	8	no	—
226	C₄×C₂₃	—	4	1	no	—
227	C₄×C₂₃	—	4	4	no	—
228	C₄×C₂₃	—	4	4	no	—
229	C₄×C₂₃	—	4	2	no	—
230	C₄×C₂₃	—	4	4	no	—
231	C₄×C₂₃	#578	1	4	yes	—
232	C₄×C₂₃	#585	1	2	yes	—
233	#564	—	2	2	no	—
234	#557	—	2	2	no	—
235	#557	C₂²×C₂₃	1	4	yes	—
236	#557	C₂²×C₂₃	1	4	yes	—
237	#557	C₂²×C₂₃	1	4	yes	—
238	#556	C₂²×C₂₃	1	4	yes	—
239	#552	—	2	4	no	—
240	#541	—	2	2	no	—
241	#541	—	2	4	no	—
242	#541	C₂²×C₂₃	1	4	yes	—
243	#536	C₂²×C₂₃	1	2	yes	—
244	#533	—	2	2	no	—
245	#533	C₂²×C₂₃	1	2	yes	—
246	#533	C₂²×C₂₃	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
248	#519	C₂²×C₂₃	1	2	yes	—
249	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
250	#497	C₂²×C₂₃	1	4	yes	—
251	#494	C₂²×C₂₃	1	4	yes	—
252	#494	C₂²×C₂₃	1	4	yes	—
253	#491	C₂²×C₂₃	1	4	yes	—
254	#488	C₂²×C₂₃	1	4	yes	—
255	#487	C₂²×C₂₃	1	4	yes	—
256	#485	C₂²×C₂₃	1	4	yes	—
257	#479	C₂²×C₂₃	1	8	yes	—
258	#475	C₂²×C₂₃	1	2	yes	—
259	#474	C₂²×C₂₃	1	2	yes	—
260	#464	C₂²×C₂₃	1	8	yes	—
261	#462	C₂²×C₂₃	1	2	yes	—
262	#462	C₂²×C₂₃	1	4	yes	—
263	#462	C₂²×C₂₃	1	8	yes	—
264	#462	C₂²×C₂₃	1	4	yes	—
265	#462	C₂²×C₂₃	1	8	yes	—
266	#461	C₂²×C₂₃	1	2	yes	—
267	#452	C₂²×C₂₃	1	4	yes	—
268	#451	C₂²×C₂₃	1	8	yes	—
269	#446	C₂²×C₂₃	1	4	yes	—
270	C₈×Q₈	C₂²×C₂₃	1	4	yes	—
271	#441	C₂²×C₂₃	1	8	yes	—
272	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
273	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	—
274	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
275	#433	C₂²×C₂₃	1	4	yes	—
276	#431	C₂²×C₂₃	1	2	yes	—
277	C₂×C₂₃	—	4	1	no	—
278	C₂×C₂₃	—	8	1	no	—
279	C₂×C₂₃	#3487	1	1	yes	characteristic
280	C₂×C₂₃	C₂×#578	1	2	yes	—
281	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
282	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
283	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
284	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
285	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
286	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
287	C₄⋊Q₈	—	2	4	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
291	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
292	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
293	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
294	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
295	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
296	#126	—	2	8	no	—
297	#126	—	2	8	no	—
298	#125	—	2	4	no	—
299	#125	—	2	8	no	—
300	#125	—	2	4	no	—
301	#125	—	2	8	no	—
302	#125	—	2	8	no	—
303	#125	—	2	8	no	—
304	#125	—	2	2	no	—
305	#125	D₄×C₂₃	1	2	yes	—
306	#125	C₂³×C₂₃	1	4	yes	—
307	#124	C₂³×C₂₃	1	4	yes	—
308	#123	—	2	4	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	—
313	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
314	C₄×Q₈	—	2	4	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	2	4	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
320	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
321	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
322	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
323	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	C₂³×C₂₃	1	2	yes	—
326	#117	—	2	2	no	—
327	#117	—	2	4	no	—
328	#117	—	2	4	no	—
329	#117	—	2	1	no	—
330	#117	C₂³×C₂₃	1	1	yes	characteristic
331	#117	C₂³×C₂₃	1	2	yes	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
335	#107	C₂³×C₂₃	1	4	yes	—
336	#106	C₂³×C₂₃	1	4	yes	—
337	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
338	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
339	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
340	#103	C₂³×C₂₃	1	4	yes	—
341	#103	C₂³×C₂₃	1	4	yes	—
342	#103	C₂³×C₂₃	1	8	yes	—
343	#103	C₂³×C₂₃	1	4	yes	—
344	#103	C₂³×C₂₃	1	8	yes	—
345	#102	C₂³×C₂₃	1	4	yes	—
346	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
347	#97	C₂³×C₂₃	1	4	yes	—
348	C₄×C₈	C₂³×C₂₃	1	4	yes	—
349	C₄×C₈	C₂³×C₂₃	1	4	yes	—
350	C₂₃	#61936	1	1	yes	characteristic, direct product factor, Sylow
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
356	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
357	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
358	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
366	Q₁₆	—	4	8	no	—
367	Q₁₆	—	4	8	no	—
368	Q₁₆	—	4	4	no	—
369	SD₁₆	—	4	4	no	—
370	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
371	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
386	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
387	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
388	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
389	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	8	no	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	8	no	—
400	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
401	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
402	C₄²	C₂⁴×C₂₃	1	2	yes	—
403	C₄²	C₂⁴×C₂₃	1	4	yes	—
404	C₂³	—	2	1	no	—
405	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	2	4	no	—
409	Q₈	—	2	8	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	4	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
426	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
429	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
430	C₈	—	2	4	no	—
431	C₈	—	2	4	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	8	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	4	no	—
445	C₄	C₂₃×#578	1	4	yes	—
446	C₄	C₂₃×#585	1	2	yes	—
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	C₂₃×#3487	1	1	yes	characteristic
450	C₂	C₂×C₂₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×#41×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3556	C₂	semidirect
3. C₂₃×#3398	C₂	semidirect
4. C₂₃×#3395	C₂	semidirect
5. C₂₃×#3374	C₂	semidirect
6. C₂₃×#3364	C₂	semidirect
8. C₂₃×#3209	C₂	semidirect
9. C₂₃×#3127	C₂	semidirect
11. C₂₃×#2986	C₂	semidirect
178. #61936	C₂₃	direct (N × H)
207. #3556	C₂×C₂₃	semidirect
209. #3398	C₂×C₂₃	semidirect
210. #3395	C₂×C₂₃	semidirect
211. #3374	C₂×C₂₃	semidirect
212. #3364	C₂×C₂₃	semidirect
214. #3209	C₂×C₂₃	semidirect
215. #3127	C₂×C₂₃	semidirect
217. #2986	C₂×C₂₃	semidirect
350. C₂₃	#61936	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3556	2
C₂₃×#3509	2
C₂₃×#3398	2
C₂₃×#3395	2
C₂₃×#3374	2
C₂₃×#3364	2
C₂₃×#3223	2
C₂₃×#3209	2
C₂₃×#3127	2
C₂₃×#3107	2
C₂₃×#2986	2
#61936	23

Subgroups — C23×#61936 #19209562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61936 #19209562