Subgroups — D₂₃×#534 #15686695

Order 2944.

1984 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
2	#13092979	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092978	C₂	1	4	yes	maximal, complemented
4	#13092977	C₂	1	4	yes	maximal, complemented
5	#13092976	C₂	1	2	yes	maximal, complemented
6	#13092975	C₂	1	4	yes	maximal, complemented
7	#123×D₂₃	C₂	1	4	yes	maximal, complemented
8	#121×D₂₃	C₂	1	4	yes	maximal, complemented
9	#120×D₂₃	C₂	1	4	yes	maximal, complemented
10	C₂×C₂²⋊C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic
13	C₂⁴×D₂₃	C₂²	1	2	yes	complemented
14	C₂²×D₄×C₂₃	C₂²	1	2	yes	complemented
15	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
16	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
17	C₂×D₄×D₂₃	—	2	16	no	—
18	C₂×D₄×D₂₃	C₂²	1	4	yes	—
19	C₂×D₄×D₂₃	C₂²	1	4	yes	complemented
20	C₂×D₄×D₂₃	C₂²	1	4	yes	complemented
21	C₂×D₄×D₂₃	C₂²	1	4	yes	complemented
22	C₂×D₄×D₂₃	C₂²	1	4	yes	complemented
23	C₂²×D₉₂	C₂²	1	2	yes	complemented
24	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
26	C₂₃×#123	C₂²	1	4	yes	complemented
27	C₂₃×#121	C₂²	1	4	yes	complemented
28	C₂₃×#120	C₂²	1	4	yes	complemented
29	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
30	#10625124	C₂²	1	4	yes	complemented
31	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
32	#10625110	C₂²	1	8	yes	complemented
33	#10625109	C₂²	1	4	yes	complemented
34	#10625108	C₂²	1	8	yes	complemented
35	#10625108	C₂²	1	4	yes	complemented
36	#10625106	C₂²	1	4	yes	complemented
37	#10625101	C₂²	1	4	yes	complemented
38	#10625100	C₂²	1	4	yes	complemented
39	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
40	#10625066	C₂²	1	4	yes	complemented
41	#10625065	C₂²	1	8	yes	complemented
42	C₄⋊C₄×D₂₃	C₂²	1	4	yes	complemented
43	#10625057	C₂²	1	4	yes	complemented
44	#10625055	C₂²	1	8	yes	complemented
45	#10625054	C₂²	1	8	yes	complemented
46	#10625053	C₂²	1	8	yes	complemented
47	#10625053	C₂²	1	4	yes	complemented
48	C₂²⋊C₄×D₂₃	C₂²	1	8	yes	complemented
49	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	complemented
50	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	complemented
51	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
52	C₂⁴×C₂₃	C₂³	1	2	yes	complemented
53	C₂³×D₂₃	—	2	8	no	—
54	C₂³×D₂₃	—	4	4	no	—
55	C₂³×D₂₃	—	4	8	no	—
56	C₂³×D₂₃	D₄	1	8	yes	complemented
57	C₂³×D₂₃	C₂³	1	4	yes	—
58	C₂³×D₂₃	C₂³	1	2	yes	—
59	C₂³×D₂₃	C₂³	1	1	yes	characteristic
60	C₂³×D₂₃	C₂³	1	2	yes	—
61	C₂³×D₂₃	C₂³	1	1	yes	characteristic
62	C₂³×D₂₃	C₂³	1	2	yes	complemented
63	C₂³×D₂₃	C₂³	1	4	yes	complemented
64	C₂×D₄×C₂₃	—	2	8	no	—
65	C₂×D₄×C₂₃	C₂³	1	4	yes	—
66	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
67	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
68	C₂²×C₄×C₂₃	C₂³	1	2	yes	complemented
69	C₂²×C₄×C₂₃	C₂³	1	2	yes	complemented
70	C₂×C₂²⋊D₂₃	—	2	8	no	—
71	C₂×C₂²⋊D₂₃	—	2	8	no	—
72	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
73	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	complemented
75	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	complemented
76	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
77	C₂²×Dic₂₃	C₂³	1	2	yes	complemented
78	C₂²×Dic₂₃	C₂³	1	2	yes	complemented
79	D₄×D₂₃	—	2	16	no	—
80	D₄×D₂₃	—	2	16	no	—
81	D₄×D₂₃	—	2	16	no	—
82	D₄×D₂₃	—	2	16	no	—
83	D₄×D₂₃	—	4	8	no	—
84	C₂×D₉₂	—	2	8	no	—
85	C₂×D₉₂	C₂³	1	4	yes	—
86	C₂×D₉₂	C₂³	1	4	yes	complemented
87	C₂×D₉₂	C₂³	1	4	yes	complemented
88	C₂×C₄×D₂₃	—	2	8	no	—
89	C₂×C₄×D₂₃	—	4	4	no	—
90	C₂×C₄×D₂₃	C₂³	1	4	yes	—
91	C₂×C₄×D₂₃	C₂³	1	4	yes	—
92	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
93	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
94	C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
95	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
96	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
97	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
98	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
99	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
100	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
101	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
102	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
103	Dic₂₃⋊C₄	C₂³	1	8	yes	complemented
104	C₂³×C₂₃	—	2	4	no	—
105	C₂³×C₂₃	—	4	2	no	—
106	C₂³×C₂₃	—	4	4	no	—
107	C₂³×C₂₃	C₂×D₄	1	4	yes	complemented
108	C₂³×C₂₃	C₂⁴	1	4	yes	—
109	C₂³×C₂₃	C₂⁴	1	2	yes	—
110	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
111	C₂²×D₂₃	—	2	4	no	—
112	C₂²×D₂₃	—	2	8	no	—
113	C₂²×D₂₃	—	2	4	no	—
114	C₂²×D₂₃	—	2	8	no	—
115	C₂²×D₂₃	—	2	8	no	—
116	C₂²×D₂₃	—	2	16	no	—
117	C₂²×D₂₃	—	4	16	no	—
118	C₂²×D₂₃	—	4	4	no	—
119	C₂²×D₂₃	—	4	2	no	—
120	C₂²×D₂₃	—	4	8	no	—
121	C₂²×D₂₃	—	4	4	no	—
122	C₂²×D₂₃	—	4	32	no	—
123	C₂²×D₂₃	C₂×D₄	1	8	yes	—
124	C₂²×D₂₃	C₂×D₄	1	4	yes	—
125	C₂²×D₂₃	C₂×D₄	1	8	yes	complemented
126	C₂²×D₂₃	C₂×D₄	1	4	yes	complemented
127	C₂²×D₂₃	C₂⁴	1	4	yes	—
128	C₂²×D₂₃	C₂⁴	1	2	yes	—
129	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
130	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
131	D₄×C₂₃	—	2	8	no	—
132	D₄×C₂₃	—	2	8	no	—
133	D₄×C₂₃	—	4	4	no	—
134	C₂×C₄×C₂₃	—	2	4	no	—
135	C₂×C₄×C₂₃	—	4	2	no	—
136	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
137	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
138	C₂²⋊D₂₃	—	2	8	no	—
139	C₂²⋊D₂₃	—	2	8	no	—
140	C₂²⋊D₂₃	—	2	8	no	—
141	C₂²⋊D₂₃	—	2	8	no	—
142	C₂²⋊D₂₃	—	4	8	no	—
143	C₂×Dic₂₃	—	2	4	no	—
144	C₂×Dic₂₃	—	4	2	no	—
145	C₂×Dic₂₃	C₂⁴	1	4	yes	—
146	C₂×Dic₂₃	C₂⁴	1	4	yes	—
147	D₉₂	—	2	8	no	—
148	D₉₂	—	2	8	no	—
149	D₉₂	—	4	4	no	—
150	C₄×D₂₃	—	2	8	no	—
151	C₄×D₂₃	—	2	8	no	—
152	C₄×D₂₃	—	2	8	no	—
153	C₄×D₂₃	—	4	4	no	—
154	C₂×#534	—	23	1	no	maximal, Sylow
155	C₂²×C₂₃	—	2	2	no	—
156	C₂²×C₂₃	—	2	4	no	—
157	C₂²×C₂₃	—	2	4	no	—
158	C₂²×C₂₃	—	2	8	no	—
159	C₂²×C₂₃	—	4	4	no	—
160	C₂²×C₂₃	—	4	8	no	—
161	C₂²×C₂₃	C₂²×D₄	1	4	yes	—
162	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
163	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
164	C₂×D₂₃	—	2	2	no	—
165	C₂×D₂₃	—	2	4	no	—
166	C₂×D₂₃	—	2	16	no	—
167	C₂×D₂₃	—	2	8	no	—
168	C₂×D₂₃	—	2	4	no	—
169	C₂×D₂₃	—	2	8	no	—
170	C₂×D₂₃	—	4	4	no	—
171	C₂×D₂₃	—	4	8	no	—
172	C₂×D₂₃	—	4	16	no	—
173	C₂×D₂₃	—	4	8	no	—
174	C₂×D₂₃	—	4	16	no	—
175	C₂×D₂₃	C₂²×D₄	1	4	yes	—
176	C₂×D₂₃	C₂²×D₄	1	2	yes	—
177	C₂×D₂₃	C₂²×D₄	1	2	yes	—
178	C₂×D₂₃	H(5,𝔽₂)	1	4	yes	—
179	C₄×C₂₃	—	2	4	no	—
180	C₄×C₂₃	—	2	4	no	—
181	Dic₂₃	—	2	4	no	—
182	Dic₂₃	—	2	4	no	—
183	C₂³×D₄	—	23	2	no	—
184	#534	—	23	2	no	—
185	#534	—	23	4	no	—
186	#534	—	23	4	no	—
187	#534	—	23	4	no	—
188	#534	—	23	1	no	—
189	#534	D₂₃	1	1	yes	characteristic, direct product factor
190	C₂×#123	—	23	4	no	—
191	C₂×#121	—	23	4	no	—
192	C₂×#120	—	23	4	no	—
193	C₂²×C₂²⋊C₄	—	23	1	no	—
194	C₂×C₂₃	—	2	4	no	—
195	C₂×C₂₃	—	2	2	no	—
196	C₂×C₂₃	—	4	4	no	—
197	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
198	C₂×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
199	D₂₃	—	2	4	no	—
200	D₂₃	—	2	2	no	—
201	D₂₃	—	4	4	no	—
202	D₂₃	#534	1	4	yes	direct product factor
203	C₂⁵	—	23	1	no	—
204	C₂⁵	—	23	2	no	—
205	C₂²×D₄	—	23	2	no	—
206	C₂²×D₄	—	23	2	no	—
207	C₂²×D₄	—	23	4	no	—
208	C₂²×D₄	—	23	4	no	—
209	C₂²×D₄	—	23	4	no	—
210	C₂²×D₄	—	23	4	no	—
211	C₂²×D₄	—	23	4	no	—
212	C₂²×D₄	—	23	2	no	—
213	C₂²×D₄	—	46	16	no	—
214	C₂²×D₄	C₂×D₂₃	1	2	yes	complemented
215	C₂³×C₄	—	23	2	no	—
216	C₂³×C₄	—	23	2	no	—
217	#123	—	23	4	no	—
218	#123	—	23	4	no	—
219	#123	—	23	8	no	—
220	#123	—	23	8	no	—
221	#123	—	23	4	no	—
222	#123	C₂×D₂₃	1	4	yes	complemented
223	#121	—	23	4	no	—
224	#121	—	23	8	no	—
225	#121	—	23	4	no	—
226	#121	—	23	4	no	—
227	#121	—	23	8	no	—
228	#121	C₂×D₂₃	1	4	yes	complemented
229	#120	—	23	4	no	—
230	#120	—	23	4	no	—
231	#120	—	23	8	no	—
232	#120	—	23	8	no	—
233	#120	—	23	4	no	—
234	#120	C₂×D₂₃	1	4	yes	complemented
235	C₂×C₄⋊C₄	—	23	4	no	—
236	C₂×C₂²⋊C₄	—	23	1	no	—
237	C₂×C₂²⋊C₄	—	23	2	no	—
238	C₂×C₂²⋊C₄	—	23	4	no	—
239	C₂×C₂²⋊C₄	—	23	4	no	—
240	C₂×C₂²⋊C₄	—	23	8	no	—
241	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
242	C₂₃	C₂×#534	1	1	yes	characteristic, complemented, Sylow
243	C₂⁴	—	23	2	no	—
244	C₂⁴	—	23	1	no	—
245	C₂⁴	—	23	8	no	—
246	C₂⁴	—	23	1	no	—
247	C₂⁴	—	23	2	no	—
248	C₂⁴	—	23	4	no	—
249	C₂⁴	—	23	4	no	—
250	C₂⁴	—	23	2	no	—
251	C₂⁴	—	46	8	no	—
252	C₂⁴	—	92	4	no	—
253	C₂⁴	—	92	8	no	—
254	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
255	C₂⁴	C₂²×D₂₃	1	2	yes	complemented
256	C₂×D₄	—	2	8	no	—
257	C₂×D₄	—	23	4	no	—
258	C₂×D₄	—	23	4	no	—
259	C₂×D₄	—	23	4	no	—
260	C₂×D₄	—	23	4	no	—
261	C₂×D₄	—	23	8	no	—
262	C₂×D₄	—	23	4	no	—
263	C₂×D₄	—	23	4	no	—
264	C₂×D₄	—	23	4	no	—
265	C₂×D₄	—	46	8	no	—
266	C₂×D₄	—	46	16	no	—
267	C₂×D₄	—	46	16	no	—
268	C₂×D₄	—	46	16	no	—
269	C₂×D₄	—	46	16	no	—
270	C₂×D₄	—	46	8	no	—
271	C₂×D₄	—	46	8	no	—
272	C₂×D₄	—	92	8	no	—
273	C₂×D₄	C₂²×D₂₃	1	4	yes	—
274	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
275	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
276	C₂²×C₄	—	23	2	no	—
277	C₂²×C₄	—	23	2	no	—
278	C₂²×C₄	—	23	4	no	—
279	C₂²×C₄	—	23	4	no	—
280	C₂²×C₄	—	23	4	no	—
281	C₂²×C₄	—	23	4	no	—
282	C₂²×C₄	—	46	8	no	—
283	C₂²×C₄	—	92	4	no	—
284	C₂²×C₄	C₂²×D₂₃	1	2	yes	complemented
285	C₂²×C₄	C₂²×D₂₃	1	2	yes	complemented
286	C₄⋊C₄	—	23	8	no	—
287	C₄⋊C₄	—	23	4	no	—
288	C₄⋊C₄	C₂²×D₂₃	1	4	yes	complemented
289	C₂²⋊C₄	—	23	4	no	—
290	C₂²⋊C₄	—	23	8	no	—
291	C₂²⋊C₄	—	23	8	no	—
292	C₂²⋊C₄	—	23	8	no	—
293	C₂²⋊C₄	—	23	8	no	—
294	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
295	C₂²⋊C₄	C₂²×D₂₃	1	8	yes	complemented
296	C₂³	—	2	4	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	4	no	—
299	C₂³	—	23	1	no	—
300	C₂³	—	23	8	no	—
301	C₂³	—	23	4	no	—
302	C₂³	—	23	2	no	—
303	C₂³	—	23	1	no	—
304	C₂³	—	23	4	no	—
305	C₂³	—	23	8	no	—
306	C₂³	—	23	4	no	—
307	C₂³	—	46	4	no	—
308	C₂³	—	46	8	no	—
309	C₂³	—	46	8	no	—
310	C₂³	—	46	8	no	—
311	C₂³	—	46	16	no	—
312	C₂³	—	46	4	no	—
313	C₂³	—	92	2	no	—
314	C₂³	—	92	4	no	—
315	C₂³	—	92	4	no	—
316	C₂³	—	92	8	no	—
317	C₂³	—	92	16	no	—
318	C₂³	—	92	32	no	—
319	C₂³	D₄×D₂₃	1	4	yes	complemented
320	C₂³	C₂³×D₂₃	1	4	yes	—
321	C₂³	C₂³×D₂₃	1	2	yes	—
322	C₂³	C₂³×D₂₃	1	1	yes	characteristic
323	D₄	—	2	8	no	—
324	D₄	—	2	8	no	—
325	D₄	—	4	4	no	—
326	D₄	—	46	8	no	—
327	D₄	—	46	8	no	—
328	D₄	—	46	8	no	—
329	D₄	—	46	8	no	—
330	D₄	—	46	8	no	—
331	D₄	—	46	8	no	—
332	D₄	—	92	4	no	—
333	D₄	—	92	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	23	4	no	—
337	C₂×C₄	—	23	4	no	—
338	C₂×C₄	—	46	8	no	—
339	C₂×C₄	—	46	8	no	—
340	C₂×C₄	—	46	8	no	—
341	C₂×C₄	—	46	4	no	—
342	C₂×C₄	—	92	4	no	—
343	C₂×C₄	—	92	2	no	—
344	C₂×C₄	C₂³×D₂₃	1	4	yes	—
345	C₂×C₄	C₂³×D₂₃	1	4	yes	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	8	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	23	2	no	—
353	C₂²	—	23	4	no	—
354	C₂²	—	23	4	no	—
355	C₂²	—	23	2	no	—
356	C₂²	—	46	16	no	—
357	C₂²	—	46	8	no	—
358	C₂²	—	46	2	no	—
359	C₂²	—	46	4	no	—
360	C₂²	—	46	4	no	—
361	C₂²	—	46	8	no	—
362	C₂²	—	92	8	no	—
363	C₂²	—	92	4	no	—
364	C₂²	—	92	8	no	—
365	C₂²	—	92	16	no	—
366	C₂²	—	92	16	no	—
367	C₂²	C₂×D₄×D₂₃	1	4	yes	—
368	C₂²	C₂×D₄×D₂₃	1	2	yes	—
369	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
370	C₄	—	2	4	no	—
371	C₄	—	2	4	no	—
372	C₄	—	46	4	no	—
373	C₄	—	46	4	no	—
374	C₂	—	2	4	no	—
375	C₂	—	2	2	no	—
376	C₂	—	4	4	no	—
377	C₂	—	23	4	no	—
378	C₂	—	46	4	no	—
379	C₂	—	46	2	no	—
380	C₂	—	92	4	no	—
381	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
382	C₂	H(5,𝔽₂)×D₂₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#534	C₂
hypercenter	#534	D₂₃
hypocenter	C₂₃	C₂×#534
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₂₃	C₂	semidirect
2. #13092979	C₂	semidirect
3. #13092978	C₂	semidirect
4. #13092977	C₂	semidirect
5. #13092976	C₂	semidirect
6. #13092975	C₂	semidirect
7. #123×D₂₃	C₂	semidirect
8. #121×D₂₃	C₂	semidirect
9. #120×D₂₃	C₂	semidirect
10. C₂×C₂²⋊C₄×D₂₃	C₂	semidirect
11. C₂₃×#534	C₂	semidirect
13. C₂⁴×D₂₃	C₂²	semidirect
14. C₂²×D₄×C₂₃	C₂²	semidirect
15. C₂²×C₂²⋊D₂₃	C₂²	semidirect
16. C₂²×C₂²⋊D₂₃	C₂²	semidirect
19. C₂×D₄×D₂₃	C₂²	semidirect
20. C₂×D₄×D₂₃	C₂²	semidirect
21. C₂×D₄×D₂₃	C₂²	semidirect
22. C₂×D₄×D₂₃	C₂²	semidirect
23. C₂²×D₉₂	C₂²	semidirect
24. C₂²×C₄×D₂₃	C₂²	semidirect
25. C₂²×C₄×D₂₃	C₂²	semidirect
26. C₂₃×#123	C₂²	semidirect
27. C₂₃×#121	C₂²	semidirect
28. C₂₃×#120	C₂²	semidirect
29. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
30. #10625124	C₂²	semidirect
31. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
32. #10625110	C₂²	semidirect
33. #10625109	C₂²	semidirect
34. #10625108	C₂²	semidirect
35. #10625108	C₂²	semidirect
36. #10625106	C₂²	semidirect
37. #10625101	C₂²	semidirect
38. #10625100	C₂²	semidirect
39. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
40. #10625066	C₂²	semidirect
41. #10625065	C₂²	semidirect
42. C₄⋊C₄×D₂₃	C₂²	semidirect
43. #10625057	C₂²	semidirect
44. #10625055	C₂²	semidirect
45. #10625054	C₂²	semidirect
46. #10625053	C₂²	semidirect
47. #10625053	C₂²	semidirect
48. C₂²⋊C₄×D₂₃	C₂²	semidirect
49. C₂²⋊C₄×D₂₃	C₂²	semidirect
50. C₂²⋊C₄×D₂₃	C₂²	semidirect
52. C₂⁴×C₂₃	C₂³	semidirect
56. C₂³×D₂₃	D₄	semidirect
62. C₂³×D₂₃	C₂³	semidirect
63. C₂³×D₂₃	C₂³	semidirect
66. C₂×D₄×C₂₃	C₂³	semidirect
67. C₂×D₄×C₂₃	C₂³	semidirect
68. C₂²×C₄×C₂₃	C₂³	semidirect
69. C₂²×C₄×C₂₃	C₂³	semidirect
74. C₂×C₂²⋊D₂₃	C₂³	semidirect
75. C₂×C₂²⋊D₂₃	C₂³	semidirect
76. C₂×C₂²⋊D₂₃	C₂³	semidirect
77. C₂²×Dic₂₃	C₂³	semidirect
78. C₂²×Dic₂₃	C₂³	semidirect
86. C₂×D₉₂	C₂³	semidirect
87. C₂×D₉₂	C₂³	semidirect
92. C₂×C₄×D₂₃	C₂³	semidirect
93. C₂×C₄×D₂₃	C₂³	semidirect
94. C₄⋊C₄×C₂₃	C₂³	semidirect
95. C₂²⋊C₄×C₂₃	C₂³	semidirect
96. C₂²⋊C₄×C₂₃	C₂³	semidirect
97. C₂²⋊Dic₂₃	C₂³	semidirect
98. C₂²⋊Dic₂₃	C₂³	semidirect
99. (C₂×D₂₃)⋊C₄	C₂³	semidirect
100. (C₂×D₂₃)⋊C₄	C₂³	semidirect
101. (C₂×D₂₃)⋊C₄	C₂³	semidirect
102. C₄⋊Dic₂₃	C₂³	semidirect
103. Dic₂₃⋊C₄	C₂³	semidirect
107. C₂³×C₂₃	C₂×D₄	semidirect
125. C₂²×D₂₃	C₂×D₄	semidirect
126. C₂²×D₂₃	C₂×D₄	semidirect
189. #534	D₂₃	direct (N × H)
202. D₂₃	#534	direct (N × H)
214. C₂²×D₄	C₂×D₂₃	semidirect
222. #123	C₂×D₂₃	semidirect
228. #121	C₂×D₂₃	semidirect
234. #120	C₂×D₂₃	semidirect
241. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
242. C₂₃	C₂×#534	semidirect
255. C₂⁴	C₂²×D₂₃	semidirect
274. C₂×D₄	C₂²×D₂₃	semidirect
275. C₂×D₄	C₂²×D₂₃	semidirect
284. C₂²×C₄	C₂²×D₂₃	semidirect
285. C₂²×C₄	C₂²×D₂₃	semidirect
288. C₄⋊C₄	C₂²×D₂₃	semidirect
294. C₂²⋊C₄	C₂²×D₂₃	semidirect
295. C₂²⋊C₄	C₂²×D₂₃	semidirect
319. C₂³	D₄×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×D₂₃	2
#13092979	2
#13092978	2
#13092977	2
#13092976	2
#13092975	2
#123×D₂₃	2
#121×D₂₃	2
#120×D₂₃	2
C₂×C₂²⋊C₄×D₂₃	2
C₂₃×#534	2
C₂×#534	23

Subgroups — D23×#534 #15686695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#534 #15686695