Subgroups — D₂₃×#482 #15683277

Order 2944.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#121×D₂₃	C₂	1	1	yes	maximal, characteristic
2	#117×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092744	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092743	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092742	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092741	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092740	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092739	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092738	C₂	1	1	yes	maximal, characteristic, complemented
10	#107×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#102×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₂₃	—	2	1	no	—
17	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#121	C₂²	1	1	yes	characteristic
20	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
21	#10625110	—	2	1	no	—
22	#10625109	C₂²	1	1	yes	characteristic
23	#10625101	C₂²	1	1	yes	characteristic
24	#10625097	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
27	#10625066	C₂²	1	1	yes	characteristic
28	#10625063	C₂²	1	1	yes	characteristic, complemented
29	#10625063	C₂²	1	1	yes	characteristic, complemented
30	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
31	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
32	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
33	#10625055	—	2	1	no	—
34	C₂²⋊C₄×D₂₃	—	2	1	no	—
35	C₂²⋊C₄×D₂₃	—	2	1	no	—
36	#10625048	—	2	1	no	—
37	#10625043	—	2	1	no	—
38	C₄²×D₂₃	—	2	1	no	—
39	C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#10625014	C₂²	1	1	yes	characteristic, complemented
45	#10625014	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	#10625003	C₂²	1	1	yes	characteristic, complemented
48	#10625003	C₂²	1	1	yes	characteristic, complemented
49	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#10625000	C₂²	1	1	yes	characteristic, complemented
52	#10624999	C₂²	1	1	yes	characteristic, complemented
53	#10624991	C₂²	1	1	yes	characteristic, complemented
54	#10624991	C₂²	1	1	yes	characteristic, complemented
55	#10624990	C₂²	1	1	yes	characteristic, complemented
56	#10624990	C₂²	1	1	yes	characteristic, complemented
57	#10624989	C₂²	1	1	yes	characteristic, complemented
58	#10624989	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₂₃	—	2	1	no	—
60	C₂³×D₂₃	D₄	1	1	yes	characteristic
61	C₂×D₄×C₂₃	—	2	1	no	—
62	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₂₃	—	2	1	no	—
65	C₂×C₂²⋊D₂₃	—	2	1	no	—
66	C₂×C₂²⋊D₂₃	—	2	1	no	—
67	C₂²×Dic₂₃	D₄	1	1	yes	characteristic
68	D₄×D₂₃	—	2	2	no	—
69	D₄×D₂₃	—	2	2	no	—
70	D₄×D₂₃	—	4	4	no	—
71	C₂×D₉₂	—	2	1	no	—
72	C₂×D₉₂	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₂₃	—	2	2	no	—
74	C₂×C₄×D₂₃	—	2	2	no	—
75	C₂×C₄×D₂₃	—	2	1	no	—
76	C₂×C₄×D₂₃	—	2	1	no	—
77	C₂×C₄×D₂₃	—	2	1	no	—
78	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
79	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
80	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²⋊C₄×C₂₃	—	2	1	no	—
88	C₂²⋊C₄×C₂₃	—	2	1	no	—
89	C₄²×C₂₃	—	2	1	no	—
90	C₂²⋊Dic₂₃	—	2	1	no	—
91	C₂²⋊Dic₂₃	—	2	1	no	—
92	(C₂×D₂₃)⋊C₄	—	2	1	no	—
93	(C₂×D₂₃)⋊C₄	—	2	1	no	—
94	(C₂×D₂₃)⋊C₄	—	2	1	no	—
95	(C₂×D₂₃)⋊C₄	—	2	1	no	—
96	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
99	Dic₂₃⋊C₄	—	2	1	no	—
100	Dic₂₃⋊C₄	—	2	1	no	—
101	Dic₂₃⋊C₄	—	2	1	no	—
102	C₄×Dic₂₃	—	2	1	no	—
103	C₄×Dic₂₃	—	2	1	no	—
104	C₄×Dic₂₃	—	2	1	no	—
105	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
107	C₈×D₂₃	—	2	2	no	—
108	C₈×D₂₃	—	2	2	no	—
109	C₂³×C₂₃	—	2	1	no	—
110	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×D₂₃	—	2	2	no	—
112	C₂²×D₂₃	—	2	2	no	—
113	C₂²×D₂₃	—	2	2	no	—
114	C₂²×D₂₃	—	2	1	no	—
115	C₂²×D₂₃	—	4	2	no	—
116	C₂²×D₂₃	—	4	2	no	—
117	C₂²×D₂₃	—	4	2	no	—
118	C₂²×D₂₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×D₂₃	C₂×D₄	1	1	yes	characteristic
120	D₄×C₂₃	—	2	1	no	—
121	D₄×C₂₃	—	2	1	no	—
122	D₄×C₂₃	—	4	2	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	—	2	1	no	—
125	C₂×C₄×C₂₃	—	2	1	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
130	C₂²⋊D₂₃	—	4	2	no	—
131	C₂²⋊D₂₃	—	4	2	no	—
132	C₂²⋊D₂₃	—	4	2	no	—
133	C₂×Dic₂₃	—	2	2	no	—
134	C₂×Dic₂₃	—	2	1	no	—
135	C₂×Dic₂₃	—	2	1	no	—
136	C₂×Dic₂₃	—	2	1	no	—
137	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
139	D₉₂	—	2	1	no	—
140	D₉₂	—	2	1	no	—
141	D₉₂	—	4	2	no	—
142	C₄×D₂₃	—	2	2	no	—
143	C₄×D₂₃	—	2	1	no	—
144	C₄×D₂₃	—	2	1	no	—
145	C₄×D₂₃	—	2	2	no	—
146	C₄×D₂₃	—	4	2	no	—
147	C₄×D₂₃	—	4	2	no	—
148	C₄×D₂₃	—	4	2	no	—
149	C₄×D₂₃	#41	1	2	yes	—
150	C₄×D₂₃	#41	1	2	yes	—
151	C₈×C₂₃	—	2	1	no	—
152	C₈×C₂₃	—	2	1	no	—
153	C₂₃⋊C₈	—	2	1	no	—
154	C₂₃⋊C₈	—	2	1	no	—
155	C₂×#482	—	23	1	no	maximal, Sylow
156	C₂²×C₂₃	—	2	1	no	—
157	C₂²×C₂₃	—	2	1	no	—
158	C₂²×C₂₃	—	2	1	no	—
159	C₂²×C₂₃	—	4	1	no	—
160	C₂²×C₂₃	—	4	1	no	—
161	C₂²×C₂₃	—	4	1	no	—
162	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×D₂₃	—	2	1	no	—
164	C₂×D₂₃	—	2	1	no	—
165	C₂×D₂₃	—	2	1	no	—
166	C₂×D₂₃	—	4	4	no	—
167	C₂×D₂₃	—	4	1	no	—
168	C₂×D₂₃	—	4	1	no	—
169	C₂×D₂₃	—	4	1	no	—
170	C₂×D₂₃	—	8	4	no	—
171	C₂×D₂₃	#123	1	2	yes	—
172	C₂×D₂₃	#135	1	2	yes	—
173	C₂×D₂₃	AGL(1,ℤ/8)	1	2	yes	—
174	C₄×C₂₃	—	2	1	no	—
175	C₄×C₂₃	—	4	1	no	—
176	C₄×C₂₃	—	4	1	no	—
177	C₄×C₂₃	—	4	1	no	—
178	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
179	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
180	Dic₂₃	—	2	1	no	—
181	Dic₂₃	—	4	1	no	—
182	Dic₂₃	—	4	1	no	—
183	Dic₂₃	—	4	1	no	—
184	Dic₂₃	#123	1	2	yes	—
185	C₂×#121	—	23	1	no	—
186	C₂×#117	—	23	1	no	—
187	#482	—	23	1	no	—
188	#482	—	23	1	no	—
189	#482	—	23	1	no	—
190	#482	—	23	1	no	—
191	#482	—	23	1	no	—
192	#482	—	23	1	no	—
193	#482	—	23	1	no	—
194	#482	D₂₃	1	1	yes	characteristic, direct product factor
195	C₂×#107	—	23	1	no	—
196	C₂×#106	—	23	1	no	—
197	C₂×#102	—	23	1	no	—
198	C₂×#102	—	23	1	no	—
199	C₂×C₂²⋊C₈	—	23	1	no	—
200	C₂×C₂₃	—	4	1	no	—
201	C₂×C₂₃	—	8	1	no	—
202	C₂×C₂₃	C₂×#123	1	1	yes	characteristic
203	C₂×C₂₃	C₂×#135	1	1	yes	characteristic
204	C₂×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	D₂₃	—	4	1	no	—
206	D₂₃	—	8	1	no	—
207	D₂₃	#482	1	4	yes	direct product factor
208	C₂²×D₄	—	23	1	no	—
209	C₂²×D₄	—	46	1	no	—
210	C₂³×C₄	—	23	1	no	—
211	C₂²×C₈	—	23	1	no	—
212	C₂²×C₈	—	23	1	no	—
213	#121	—	23	1	no	—
214	#121	—	23	1	no	—
215	#121	—	23	1	no	—
216	#121	—	46	1	no	—
217	#121	—	46	1	no	—
218	#121	C₂×D₂₃	1	1	yes	characteristic
219	#117	—	23	1	no	—
220	#117	—	23	1	no	—
221	#117	—	23	1	no	—
222	#117	—	46	1	no	—
223	#117	—	46	1	no	—
224	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
225	C₂×C₄⋊C₄	—	23	1	no	—
226	C₂×C₄⋊C₄	—	23	1	no	—
227	C₂×C₄⋊C₄	—	23	1	no	—
228	C₂×C₂²⋊C₄	—	46	1	no	—
229	C₂×C₂²⋊C₄	—	46	1	no	—
230	C₂×C₄²	—	46	1	no	—
231	#107	—	23	1	no	—
232	#107	—	23	1	no	—
233	#107	—	23	1	no	—
234	#107	C₂×D₂₃	1	1	yes	characteristic, complemented
235	#106	—	23	1	no	—
236	#106	—	23	1	no	—
237	#106	—	23	1	no	—
238	#106	C₂×D₂₃	1	1	yes	characteristic, complemented
239	#102	—	23	1	no	—
240	#102	—	23	1	no	—
241	#102	—	23	1	no	—
242	#102	—	23	1	no	—
243	#102	—	23	1	no	—
244	#102	—	23	1	no	—
245	#102	C₂×D₂₃	1	1	yes	characteristic, complemented
246	#102	C₂×D₂₃	1	1	yes	characteristic, complemented
247	C₂²⋊C₈	—	23	1	no	—
248	C₂²⋊C₈	—	23	1	no	—
249	C₂²⋊C₈	—	23	1	no	—
250	C₂²⋊C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
251	C₂₃	C₂×#482	1	1	yes	characteristic, complemented, Sylow
252	C₂⁴	—	23	1	no	—
253	C₂⁴	—	46	1	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	—	23	1	no	—
256	C₂×D₄	—	46	1	no	—
257	C₂×D₄	—	46	2	no	—
258	C₂×D₄	—	46	2	no	—
259	C₂×D₄	—	46	1	no	—
260	C₂×D₄	—	46	1	no	—
261	C₂×D₄	—	46	1	no	—
262	C₂×D₄	—	92	4	no	—
263	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
264	C₂²×C₄	—	23	1	no	—
265	C₂²×C₄	—	23	1	no	—
266	C₂²×C₄	—	23	1	no	—
267	C₂²×C₄	—	23	1	no	—
268	C₂²×C₄	—	23	1	no	—
269	C₂²×C₄	—	46	2	no	—
270	C₂²×C₄	—	46	2	no	—
271	C₂²×C₄	—	46	1	no	—
272	C₂²×C₄	—	46	1	no	—
273	C₂²×C₄	—	46	1	no	—
274	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
275	C₂×C₈	—	23	1	no	—
276	C₂×C₈	—	23	1	no	—
277	C₂×C₈	—	46	2	no	—
278	C₂×C₈	—	46	2	no	—
279	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
280	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
281	C₄⋊C₄	—	23	1	no	—
282	C₄⋊C₄	—	23	1	no	—
283	C₄⋊C₄	—	23	1	no	—
284	C₄⋊C₄	—	46	1	no	—
285	C₄⋊C₄	—	46	1	no	—
286	C₄⋊C₄	—	46	1	no	—
287	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
288	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
289	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	46	1	no	—
293	C₂²⋊C₄	—	46	1	no	—
294	C₂²⋊C₄	—	46	1	no	—
295	C₂²⋊C₄	—	46	1	no	—
296	C₂²⋊C₄	—	46	1	no	—
297	C₂²⋊C₄	—	46	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	46	1	no	—
300	C₄²	—	46	1	no	—
301	C₄²	—	46	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	23	1	no	—
304	C₂³	—	23	1	no	—
305	C₂³	—	46	2	no	—
306	C₂³	—	46	2	no	—
307	C₂³	—	46	2	no	—
308	C₂³	—	46	1	no	—
309	C₂³	—	92	2	no	—
310	C₂³	—	92	2	no	—
311	C₂³	—	92	2	no	—
312	C₂³	D₄×D₂₃	1	1	yes	characteristic
313	D₄	—	2	1	no	—
314	D₄	—	2	1	no	—
315	D₄	—	4	2	no	—
316	D₄	—	46	1	no	—
317	D₄	—	46	1	no	—
318	D₄	—	92	2	no	—
319	D₄	—	92	2	no	—
320	D₄	—	92	2	no	—
321	D₄	—	92	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	23	1	no	—
328	C₂×C₄	—	23	2	no	—
329	C₂×C₄	—	23	2	no	—
330	C₂×C₄	—	23	1	no	—
331	C₂×C₄	—	46	2	no	—
332	C₂×C₄	—	46	2	no	—
333	C₂×C₄	—	46	2	no	—
334	C₂×C₄	—	46	1	no	—
335	C₂×C₄	—	46	1	no	—
336	C₂×C₄	—	46	1	no	—
337	C₂×C₄	—	46	1	no	—
338	C₂×C₄	—	46	1	no	—
339	C₂×C₄	—	92	2	no	—
340	C₂×C₄	—	92	2	no	—
341	C₂×C₄	—	92	2	no	—
342	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
344	C₈	—	2	1	no	—
345	C₈	—	2	1	no	—
346	C₈	—	46	1	no	—
347	C₈	—	46	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	23	2	no	—
355	C₂²	—	23	2	no	—
356	C₂²	—	23	2	no	—
357	C₂²	—	46	1	no	—
358	C₂²	—	46	1	no	—
359	C₂²	—	46	1	no	—
360	C₂²	—	92	4	no	—
361	C₂²	—	92	1	no	—
362	C₂²	—	92	1	no	—
363	C₂²	—	92	1	no	—
364	C₂²	—	184	4	no	—
365	C₂²	C₂×D₄×D₂₃	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	23	2	no	—
371	C₄	—	46	1	no	—
372	C₄	—	92	1	no	—
373	C₄	—	92	1	no	—
374	C₄	—	92	1	no	—
375	C₄	#41×D₂₃	1	1	yes	characteristic
376	C₄	#41×D₂₃	1	1	yes	characteristic
377	C₂	—	4	1	no	—
378	C₂	—	8	1	no	—
379	C₂	—	23	4	no	—
380	C₂	—	92	1	no	—
381	C₂	—	184	1	no	—
382	C₂	#123×D₂₃	1	1	yes	characteristic
383	C₂	#135×D₂₃	1	1	yes	characteristic
384	C₂	AGL(1,ℤ/8)×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂₃×#482	C₂
socle	C₂²×C₂₃	C₂²×D₄
prime radical	#121×D₂₃	C₂
hypercenter	#482	D₂₃
hypocenter	C₂₃	C₂×#482
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #482

Complements

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

N	H ≅ G/N	type
2. #117×D₂₃	C₂	semidirect
3. #13092744	C₂	semidirect
4. #13092743	C₂	semidirect
5. #13092742	C₂	semidirect
6. #13092741	C₂	semidirect
7. #13092740	C₂	semidirect
8. #13092739	C₂	semidirect
9. #13092738	C₂	semidirect
10. #107×D₂₃	C₂	semidirect
11. #106×D₂₃	C₂	semidirect
12. #102×D₂₃	C₂	semidirect
13. #102×D₂₃	C₂	semidirect
14. C₂²⋊C₈×D₂₃	C₂	semidirect
15. C₂₃×#482	C₂	semidirect
20. C₂₃×#117	C₂²	semidirect
24. #10625097	C₂²	semidirect
28. #10625063	C₂²	semidirect
29. #10625063	C₂²	semidirect
39. C₂₃×#107	C₂²	semidirect
40. C₂₃×#106	C₂²	semidirect
41. C₂₃×#102	C₂²	semidirect
42. C₂₃×#102	C₂²	semidirect
43. C₂₃×C₂²⋊C₈	C₂²	semidirect
44. #10625014	C₂²	semidirect
45. #10625014	C₂²	semidirect
46. C₂²⋊(C₂₃⋊C₈)	C₂²	semidirect
47. #10625003	C₂²	semidirect
48. #10625003	C₂²	semidirect
49. (C₂×D₂₃)⋊C₈	C₂²	semidirect
50. (C₂×D₂₃)⋊C₈	C₂²	semidirect
51. #10625000	C₂²	semidirect
52. #10624999	C₂²	semidirect
53. #10624991	C₂²	semidirect
54. #10624991	C₂²	semidirect
55. #10624990	C₂²	semidirect
56. #10624990	C₂²	semidirect
57. #10624989	C₂²	semidirect
58. #10624989	C₂²	semidirect
194. #482	D₂₃	direct (N × H)
207. D₂₃	#482	direct (N × H)
224. #117	C₂×D₂₃	semidirect
234. #107	C₂×D₂₃	semidirect
238. #106	C₂×D₂₃	semidirect
245. #102	C₂×D₂₃	semidirect
246. #102	C₂×D₂₃	semidirect
250. C₂²⋊C₈	C₂×D₂₃	semidirect
251. C₂₃	C₂×#482	semidirect

Maximal subgroups

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

subgroup	index
#121×D₂₃	2
#117×D₂₃	2
#13092744	2
#13092743	2
#13092742	2
#13092741	2
#13092740	2
#13092739	2
#13092738	2
#107×D₂₃	2
#106×D₂₃	2
#102×D₂₃	2
C₂²⋊C₈×D₂₃	2
C₂₃×#482	2
C₂×#482	23

Subgroups — D23×#482 #15683277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#482 #15683277