Subgroups — D₄²×D₂₃ #15686832

Order 2944.

2536 conjugacy classes of subgroups.

The subgroup lattice has 356 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	4	yes	maximal, complemented
2	D₄×D₉₂	C₂	1	2	yes	maximal, complemented
3	#13093052	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093051	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊D₂₃	C₂	1	4	yes	maximal, complemented
6	#13093049	C₂	1	4	yes	maximal, complemented
7	#127×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#121×D₂₃	C₂	1	4	yes	maximal, complemented
9	#120×D₂₃	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
11	D₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₂₃	C₂²	1	4	yes	complemented
13	C₂²×D₄×C₂₃	C₂²	1	4	yes	complemented
14	C₂²×C₂²⋊D₂₃	C₂²	1	8	yes	complemented
15	C₂×D₄×D₂₃	—	2	32	no	—
16	C₂×D₄×D₂₃	C₂²	1	2	yes	—
17	C₂×D₄×D₂₃	C₂²	1	8	yes	complemented
18	C₂×D₄×D₂₃	C₂²	1	4	yes	complemented
19	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
20	C₂×D₄×D₂₃	C₂²	1	4	yes	complemented
21	C₂×D₄×D₂₃	C₂²	1	8	yes	complemented
22	C₂×D₄×D₂₃	C₂²	1	4	yes	complemented
23	C₂²×D₉₂	C₂²	1	4	yes	complemented
24	C₂²×C₄×D₂₃	C₂²	1	4	yes	complemented
25	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#121	C₂²	1	4	yes	complemented
27	C₂₃×#120	C₂²	1	4	yes	complemented
28	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
29	#10625124	C₂²	1	4	yes	complemented
30	#10625111	C₂²	1	2	yes	complemented
31	#10625111	C₂²	1	4	yes	complemented
32	#10625110	C₂²	1	8	yes	complemented
33	#10625109	C₂²	1	4	yes	complemented
34	#10625108	C₂²	1	4	yes	complemented
35	#10625108	C₂²	1	8	yes	complemented
36	D₄×Dic₂₃	C₂²	1	2	yes	complemented
37	#10625101	C₂²	1	4	yes	complemented
38	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
39	#10625066	C₂²	1	4	yes	complemented
40	#10625064	C₂²	1	2	yes	complemented
41	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
42	#10625055	C₂²	1	8	yes	complemented
43	#10625053	C₂²	1	8	yes	complemented
44	#10625053	C₂²	1	4	yes	complemented
45	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
46	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	complemented
47	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	complemented
48	#10625045	C₂²	1	1	yes	characteristic, complemented
49	C₄×D₉₂	C₂²	1	2	yes	complemented
50	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
51	C₂⁴×C₂₃	C₂³	1	4	yes	complemented
52	C₂³×D₂₃	—	2	32	no	—
53	C₂³×D₂₃	—	4	8	no	—
54	C₂³×D₂₃	C₂³	1	4	yes	—
55	C₂³×D₂₃	C₂³	1	4	yes	—
56	C₂³×D₂₃	C₂³	1	8	yes	complemented
57	C₂³×D₂₃	C₂³	1	4	yes	complemented
58	C₂×D₄×C₂₃	—	2	16	no	—
59	C₂×D₄×C₂₃	C₂³	1	2	yes	—
60	C₂×D₄×C₂₃	C₂³	1	8	yes	complemented
61	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
62	C₂×D₄×C₂₃	C₂³	1	2	yes	complemented
63	C₂²×C₄×C₂₃	C₂³	1	4	yes	complemented
64	C₂×C₂²⋊D₂₃	—	2	32	no	—
65	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
66	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
67	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
68	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
69	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	complemented
70	C₂²×Dic₂₃	C₂³	1	4	yes	complemented
71	D₄×D₂₃	—	2	32	no	—
72	D₄×D₂₃	—	2	16	no	—
73	D₄×D₂₃	—	2	32	no	—
74	D₄×D₂₃	—	2	16	no	—
75	D₄×D₂₃	—	2	16	no	—
76	D₄×D₂₃	—	4	4	no	—
77	D₄×D₂₃	D₄	1	16	yes	direct product factor
78	C₂×D₉₂	—	2	16	no	—
79	C₂×D₉₂	C₂³	1	2	yes	—
80	C₂×D₉₂	C₂³	1	4	yes	complemented
81	C₂×D₉₂	C₂³	1	8	yes	complemented
82	C₂×D₉₂	C₂³	1	2	yes	complemented
83	C₂×C₄×D₂₃	—	2	16	no	—
84	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₂₃	C₂³	1	4	yes	—
86	C₂×C₄×D₂₃	C₂³	1	2	yes	—
87	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
88	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
89	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
90	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
91	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
92	C₄²×C₂₃	C₂³	1	1	yes	characteristic, complemented
93	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
94	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
95	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
96	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
97	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
98	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
99	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
100	C₄×Dic₂₃	C₂³	1	1	yes	characteristic, complemented
101	C₄×Dic₂₃	C₂³	1	2	yes	complemented
102	C₂³×C₂₃	—	2	16	no	—
103	C₂³×C₂₃	—	4	4	no	—
104	C₂³×C₂₃	C₂⁴	1	4	yes	—
105	C₂³×C₂₃	C₂⁴	1	4	yes	—
106	C₂²×D₂₃	—	2	8	no	—
107	C₂²×D₂₃	—	2	8	no	—
108	C₂²×D₂₃	—	2	16	no	—
109	C₂²×D₂₃	—	2	16	no	—
110	C₂²×D₂₃	—	2	16	no	—
111	C₂²×D₂₃	—	2	16	no	—
112	C₂²×D₂₃	—	2	8	no	—
113	C₂²×D₂₃	—	4	4	no	—
114	C₂²×D₂₃	—	4	8	no	—
115	C₂²×D₂₃	—	4	64	no	—
116	C₂²×D₂₃	C₂×D₄	1	16	yes	complemented
117	C₂²×D₂₃	C₂⁴	1	4	yes	—
118	C₂²×D₂₃	C₂⁴	1	4	yes	—
119	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
120	D₄×C₂₃	—	2	16	no	—
121	D₄×C₂₃	—	2	8	no	—
122	D₄×C₂₃	—	4	2	no	—
123	D₄×C₂₃	C₂×D₄	1	8	yes	complemented
124	C₂×C₄×C₂₃	—	2	8	no	—
125	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
126	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
127	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
128	C₂²⋊D₂₃	—	2	16	no	—
129	C₂²⋊D₂₃	—	2	16	no	—
130	C₂²⋊D₂₃	—	2	16	no	—
131	C₂²⋊D₂₃	—	4	4	no	—
132	C₂²⋊D₂₃	C₂×D₄	1	16	yes	complemented
133	C₂×Dic₂₃	—	2	8	no	—
134	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
135	C₂×Dic₂₃	C₂⁴	1	4	yes	—
136	C₂×Dic₂₃	C₂⁴	1	2	yes	—
137	D₉₂	—	2	16	no	—
138	D₉₂	—	2	8	no	—
139	D₉₂	—	4	2	no	—
140	D₉₂	C₂×D₄	1	8	yes	complemented
141	C₄×D₂₃	—	2	8	no	—
142	C₄×D₂₃	—	2	2	no	—
143	C₄×D₂₃	—	2	8	no	—
144	C₄×D₂₃	—	2	8	no	—
145	C₄×D₂₃	C₂×D₄	1	8	yes	complemented
146	C₂×D₄²	—	23	1	no	maximal, Sylow
147	C₂²×C₂₃	—	2	4	no	—
148	C₂²×C₂₃	—	2	4	no	—
149	C₂²×C₂₃	—	2	8	no	—
150	C₂²×C₂₃	—	2	4	no	—
151	C₂²×C₂₃	—	4	16	no	—
152	C₂²×C₂₃	C₂²×D₄	1	8	yes	complemented
153	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
154	C₂×D₂₃	—	2	4	no	—
155	C₂×D₂₃	—	2	4	no	—
156	C₂×D₂₃	—	2	32	no	—
157	C₂×D₂₃	—	2	8	no	—
158	C₂×D₂₃	—	2	4	no	—
159	C₂×D₂₃	—	4	16	no	—
160	C₂×D₂₃	—	4	32	no	—
161	C₂×D₂₃	—	4	16	no	—
162	C₂×D₂₃	C₂²×D₄	1	4	yes	—
163	C₂×D₂₃	C₂²×D₄	1	8	yes	complemented
164	C₂×D₂₃	H(5,𝔽₂)	1	2	yes	—
165	C₄×C₂₃	—	2	4	no	—
166	C₄×C₂₃	—	2	1	no	—
167	C₄×C₂₃	C₂²×D₄	1	4	yes	complemented
168	Dic₂₃	—	2	4	no	—
169	Dic₂₃	—	2	1	no	—
170	Dic₂₃	C₂²×D₄	1	4	yes	complemented
171	C₂³×D₄	—	23	4	no	—
172	D₄²	—	23	4	no	—
173	D₄²	—	23	1	no	—
174	D₄²	—	23	4	no	—
175	D₄²	—	23	4	no	—
176	D₄²	—	23	2	no	—
177	D₄²	D₂₃	1	1	yes	characteristic, direct product factor
178	C₂×#127	—	23	1	no	—
179	C₂×#121	—	23	4	no	—
180	C₂×#120	—	23	4	no	—
181	C₂×C₄×D₄	—	23	2	no	—
182	C₂×C₂₃	—	2	8	no	—
183	C₂×C₂₃	—	4	4	no	—
184	C₂×C₂₃	C₂³×D₄	1	2	yes	—
185	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
186	D₂₃	—	2	8	no	—
187	D₂₃	—	4	4	no	—
188	D₂₃	D₄²	1	4	yes	direct product factor
189	C₂⁵	—	23	4	no	—
190	C₂²×D₄	—	23	2	no	—
191	C₂²×D₄	—	23	8	no	—
192	C₂²×D₄	—	23	4	no	—
193	C₂²×D₄	—	23	8	no	—
194	C₂²×D₄	—	23	4	no	—
195	C₂²×D₄	—	23	8	no	—
196	C₂²×D₄	—	23	4	no	—
197	C₂²×D₄	—	23	2	no	—
198	C₂²×D₄	—	23	4	no	—
199	C₂²×D₄	—	46	32	no	—
200	C₂²×D₄	C₂×D₂₃	1	4	yes	complemented
201	C₂³×C₄	—	23	4	no	—
202	#127	—	23	2	no	—
203	#127	—	23	4	no	—
204	#127	—	23	1	no	—
205	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
206	#121	—	23	4	no	—
207	#121	—	23	8	no	—
208	#121	—	23	4	no	—
209	#121	—	23	4	no	—
210	#121	—	23	8	no	—
211	#121	C₂×D₂₃	1	4	yes	complemented
212	#120	—	23	4	no	—
213	#120	—	23	8	no	—
214	#120	—	23	4	no	—
215	#120	—	23	4	no	—
216	#120	—	23	8	no	—
217	#120	C₂×D₂₃	1	4	yes	complemented
218	C₄×D₄	—	23	2	no	—
219	C₄×D₄	—	23	4	no	—
220	C₄×D₄	—	23	2	no	—
221	C₄×D₄	—	23	4	no	—
222	C₄×D₄	—	23	2	no	—
223	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
224	C₂×C₄⋊C₄	—	23	2	no	—
225	C₂×C₂²⋊C₄	—	23	4	no	—
226	C₂×C₂²⋊C₄	—	23	4	no	—
227	C₂×C₄²	—	23	1	no	—
228	C₂₃	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
229	C₂⁴	—	23	4	no	—
230	C₂⁴	—	23	4	no	—
231	C₂⁴	—	23	4	no	—
232	C₂⁴	—	23	8	no	—
233	C₂⁴	—	46	32	no	—
234	C₂⁴	—	92	8	no	—
235	C₂⁴	C₂²×D₂₃	1	4	yes	complemented
236	C₂×D₄	—	2	16	no	—
237	C₂×D₄	—	23	4	no	—
238	C₂×D₄	—	23	16	no	—
239	C₂×D₄	—	23	8	no	—
240	C₂×D₄	—	23	8	no	—
241	C₂×D₄	—	23	8	no	—
242	C₂×D₄	—	23	4	no	—
243	C₂×D₄	—	23	2	no	—
244	C₂×D₄	—	23	8	no	—
245	C₂×D₄	—	23	4	no	—
246	C₂×D₄	—	23	2	no	—
247	C₂×D₄	—	46	16	no	—
248	C₂×D₄	—	46	16	no	—
249	C₂×D₄	—	46	32	no	—
250	C₂×D₄	—	46	16	no	—
251	C₂×D₄	—	46	32	no	—
252	C₂×D₄	—	46	32	no	—
253	C₂×D₄	—	46	16	no	—
254	C₂×D₄	—	92	4	no	—
255	C₂×D₄	C₂²×D₂₃	1	2	yes	—
256	C₂×D₄	C₂²×D₂₃	1	8	yes	complemented
257	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
258	C₂×D₄	C₂²×D₂₃	1	2	yes	complemented
259	C₂²×C₄	—	23	2	no	—
260	C₂²×C₄	—	23	4	no	—
261	C₂²×C₄	—	23	1	no	—
262	C₂²×C₄	—	23	4	no	—
263	C₂²×C₄	—	23	4	no	—
264	C₂²×C₄	—	23	4	no	—
265	C₂²×C₄	—	46	16	no	—
266	C₂²×C₄	C₂²×D₂₃	1	4	yes	complemented
267	C₄⋊C₄	—	23	4	no	—
268	C₄⋊C₄	—	23	2	no	—
269	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
270	C₂²⋊C₄	—	23	4	no	—
271	C₂²⋊C₄	—	23	4	no	—
272	C₂²⋊C₄	—	23	4	no	—
273	C₂²⋊C₄	—	23	4	no	—
274	C₂²⋊C₄	—	23	8	no	—
275	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
276	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
277	C₄²	—	23	1	no	—
278	C₄²	—	23	2	no	—
279	C₄²	C₂²×D₂₃	1	1	yes	characteristic, complemented
280	C₂³	—	2	16	no	—
281	C₂³	—	4	4	no	—
282	C₂³	—	23	1	no	—
283	C₂³	—	23	16	no	—
284	C₂³	—	23	4	no	—
285	C₂³	—	23	4	no	—
286	C₂³	—	46	8	no	—
287	C₂³	—	46	8	no	—
288	C₂³	—	46	16	no	—
289	C₂³	—	46	16	no	—
290	C₂³	—	46	16	no	—
291	C₂³	—	46	8	no	—
292	C₂³	—	46	16	no	—
293	C₂³	—	92	8	no	—
294	C₂³	—	92	4	no	—
295	C₂³	—	92	64	no	—
296	C₂³	C₂³×D₂₃	1	4	yes	—
297	C₂³	C₂³×D₂₃	1	4	yes	—
298	D₄	—	2	16	no	—
299	D₄	—	2	8	no	—
300	D₄	—	4	2	no	—
301	D₄	—	23	16	no	—
302	D₄	—	23	8	no	—
303	D₄	—	46	16	no	—
304	D₄	—	46	16	no	—
305	D₄	—	46	16	no	—
306	D₄	—	46	16	no	—
307	D₄	—	46	8	no	—
308	D₄	—	92	2	no	—
309	D₄	—	92	4	no	—
310	D₄	D₄×D₂₃	1	8	yes	direct product factor
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	23	2	no	—
313	C₂×C₄	—	23	8	no	—
314	C₂×C₄	—	23	1	no	—
315	C₂×C₄	—	23	4	no	—
316	C₂×C₄	—	46	8	no	—
317	C₂×C₄	—	46	8	no	—
318	C₂×C₄	—	46	2	no	—
319	C₂×C₄	—	46	8	no	—
320	C₂×C₄	—	46	8	no	—
321	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
322	C₂×C₄	C₂³×D₂₃	1	4	yes	—
323	C₂×C₄	C₂³×D₂₃	1	2	yes	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	4	16	no	—
329	C₂²	—	23	4	no	—
330	C₂²	—	23	2	no	—
331	C₂²	—	23	8	no	—
332	C₂²	—	46	32	no	—
333	C₂²	—	46	4	no	—
334	C₂²	—	46	4	no	—
335	C₂²	—	46	8	no	—
336	C₂²	—	46	4	no	—
337	C₂²	—	92	32	no	—
338	C₂²	—	92	16	no	—
339	C₂²	—	92	16	no	—
340	C₂²	C₂×D₄×D₂₃	1	8	yes	complemented
341	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
342	C₄	—	2	4	no	—
343	C₄	—	2	1	no	—
344	C₄	—	23	4	no	—
345	C₄	—	46	4	no	—
346	C₄	—	46	1	no	—
347	C₄	C₂×D₄×D₂₃	1	4	yes	complemented
348	C₂	—	2	8	no	—
349	C₂	—	4	4	no	—
350	C₂	—	23	4	no	—
351	C₂	—	46	8	no	—
352	C₂	—	92	4	no	—
353	C₂	C₂²×D₄×D₂₃	1	2	yes	—
354	C₂	H(5,𝔽₂)×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	D₄²×C₂₃	C₂
hypercenter	D₄²	D₂₃
hypocenter	C₂₃	C₂×D₄²
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₂₃	C₂	semidirect
2. D₄×D₉₂	C₂	semidirect
3. #13093052	C₂	semidirect
4. #13093051	C₂	semidirect
5. D₄×C₂²⋊D₂₃	C₂	semidirect
6. #13093049	C₂	semidirect
7. #127×D₂₃	C₂	semidirect
8. #121×D₂₃	C₂	semidirect
9. #120×D₂₃	C₂	semidirect
10. C₄×D₄×D₂₃	C₂	semidirect
11. D₄²×C₂₃	C₂	semidirect
12. C₂⁴×D₂₃	C₂²	semidirect
13. C₂²×D₄×C₂₃	C₂²	semidirect
14. C₂²×C₂²⋊D₂₃	C₂²	semidirect
17. C₂×D₄×D₂₃	C₂²	semidirect
18. C₂×D₄×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. C₂₃×#127	C₂²	semidirect
26. C₂₃×#121	C₂²	semidirect
27. C₂₃×#120	C₂²	semidirect
28. C₄×D₄×C₂₃	C₂²	semidirect
29. #10625124	C₂²	semidirect
30. #10625111	C₂²	semidirect
31. #10625111	C₂²	semidirect
32. #10625110	C₂²	semidirect
33. #10625109	C₂²	semidirect
34. #10625108	C₂²	semidirect
35. #10625108	C₂²	semidirect
36. D₄×Dic₂₃	C₂²	semidirect
37. #10625101	C₂²	semidirect
38. C₄×C₂²⋊D₂₃	C₂²	semidirect
39. #10625066	C₂²	semidirect
40. #10625064	C₂²	semidirect
41. C₄⋊C₄×D₂₃	C₂²	semidirect
42. #10625055	C₂²	semidirect
43. #10625053	C₂²	semidirect
44. #10625053	C₂²	semidirect
45. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
46. C₂²⋊C₄×D₂₃	C₂²	semidirect
47. C₂²⋊C₄×D₂₃	C₂²	semidirect
48. #10625045	C₂²	semidirect
49. C₄×D₉₂	C₂²	semidirect
50. C₄²×D₂₃	C₂²	semidirect
51. C₂⁴×C₂₃	C₂³	semidirect
56. C₂³×D₂₃	C₂³	semidirect
57. C₂³×D₂₃	C₂³	semidirect
60. C₂×D₄×C₂₃	C₂³	semidirect
61. C₂×D₄×C₂₃	C₂³	semidirect
62. C₂×D₄×C₂₃	C₂³	semidirect
63. C₂²×C₄×C₂₃	C₂³	semidirect
66. C₂×C₂²⋊D₂₃	C₂³	semidirect
67. C₂×C₂²⋊D₂₃	C₂³	semidirect
68. C₂×C₂²⋊D₂₃	C₂³	semidirect
69. C₂×C₂²⋊D₂₃	C₂³	semidirect
70. C₂²×Dic₂₃	C₂³	semidirect
77. D₄×D₂₃	D₄	direct (N × H)
80. C₂×D₉₂	C₂³	semidirect
81. C₂×D₉₂	C₂³	semidirect
82. C₂×D₉₂	C₂³	semidirect
87. C₂×C₄×D₂₃	C₂³	semidirect
88. C₂×C₄×D₂₃	C₂³	semidirect
89. C₄⋊C₄×C₂₃	C₂³	semidirect
90. C₂²⋊C₄×C₂₃	C₂³	semidirect
91. C₂²⋊C₄×C₂₃	C₂³	semidirect
92. C₄²×C₂₃	C₂³	semidirect
93. C₂²⋊Dic₂₃	C₂³	semidirect
94. C₂²⋊Dic₂₃	C₂³	semidirect
95. (C₂×D₂₃)⋊C₄	C₂³	semidirect
96. (C₂×D₂₃)⋊C₄	C₂³	semidirect
97. (C₂×D₂₃)⋊C₄	C₂³	semidirect
98. C₄⋊Dic₂₃	C₂³	semidirect
99. Dic₂₃⋊C₄	C₂³	semidirect
100. C₄×Dic₂₃	C₂³	semidirect
101. C₄×Dic₂₃	C₂³	semidirect
116. C₂²×D₂₃	C₂×D₄	semidirect
123. D₄×C₂₃	C₂×D₄	semidirect
132. C₂²⋊D₂₃	C₂×D₄	semidirect
140. D₉₂	C₂×D₄	semidirect
145. C₄×D₂₃	C₂×D₄	semidirect
152. C₂²×C₂₃	C₂²×D₄	semidirect
163. C₂×D₂₃	C₂²×D₄	semidirect
167. C₄×C₂₃	C₂²×D₄	semidirect
170. Dic₂₃	C₂²×D₄	semidirect
177. D₄²	D₂₃	direct (N × H)
188. D₂₃	D₄²	direct (N × H)
200. C₂²×D₄	C₂×D₂₃	semidirect
205. #127	C₂×D₂₃	semidirect
211. #121	C₂×D₂₃	semidirect
217. #120	C₂×D₂₃	semidirect
223. C₄×D₄	C₂×D₂₃	semidirect
228. C₂₃	C₂×D₄²	semidirect
235. C₂⁴	C₂²×D₂₃	semidirect
256. C₂×D₄	C₂²×D₂₃	semidirect
257. C₂×D₄	C₂²×D₂₃	semidirect
258. C₂×D₄	C₂²×D₂₃	semidirect
266. C₂²×C₄	C₂²×D₂₃	semidirect
269. C₄⋊C₄	C₂²×D₂₃	semidirect
275. C₂²⋊C₄	C₂²×D₂₃	semidirect
276. C₂²⋊C₄	C₂²×D₂₃	semidirect
279. C₄²	C₂²×D₂₃	semidirect
310. D₄	D₄×D₂₃	direct (N × H)
340. C₂²	C₂×D₄×D₂₃	semidirect
347. C₄	C₂×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
D₄×D₉₂	2
#13093052	2
#13093051	2
D₄×C₂²⋊D₂₃	2
#13093049	2
#127×D₂₃	2
#121×D₂₃	2
#120×D₂₃	2
C₄×D₄×D₂₃	2
D₄²×C₂₃	2
C₂×D₄²	23

Subgroups — D42×D23 #15686832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄²×D₂₃ #15686832