Subgroups — C₂×D₄×C₂²⋊D₂₃ #15686834

Order 2944.

2536 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊D₂₃	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₂₃	C₂	1	16	yes	maximal, direct product factor
4	C₂×#10625111	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625101	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625110	C₂	1	2	yes	maximal, complemented
7	C₂×#10625109	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625124	C₂	1	2	yes	maximal, complemented
9	C₂×#10625108	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×C₂₃	C₂²	1	2	yes	complemented
14	C₂⁴×D₂₃	C₂²	1	2	yes	complemented
15	C₂²×D₄×C₂₃	—	2	8	no	—
16	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₂₃	C₂²	1	2	yes	complemented
18	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₂₃	C₂²	1	8	yes	complemented
20	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₂₃	—	2	16	no	—
22	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₂₃	C₂²	1	16	yes	complemented
29	C₂³×Dic₂₃	C₂²	1	2	yes	complemented
30	C₂×D₄×D₂₃	—	2	8	no	—
31	C₂×D₄×D₂₃	C₂²	1	8	yes	complemented
32	C₂²×D₉₂	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
34	#10625124	C₂²	1	16	yes	complemented
35	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
38	#10625111	C₂²	1	8	yes	complemented
39	#10625110	C₂²	1	16	yes	complemented
40	#10625109	C₂²	1	8	yes	complemented
41	#10625108	C₂²	1	16	yes	complemented
42	D₄×Dic₂₃	C₂²	1	8	yes	complemented
43	#10625101	C₂²	1	8	yes	complemented
44	C₄×C₂²⋊D₂₃	C₂²	1	8	yes	complemented
45	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
47	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
50	C₂⁴×C₂₃	—	2	8	no	—
51	C₂⁴×C₂₃	—	2	8	no	—
52	C₂⁴×C₂₃	—	4	4	no	—
53	C₂⁴×C₂₃	C₂³	1	2	yes	—
54	C₂⁴×C₂₃	C₂³	1	2	yes	—
55	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
56	C₂⁴×C₂₃	C₂³	1	8	yes	complemented
57	C₂³×D₂₃	—	2	8	no	—
58	C₂³×D₂₃	—	2	8	no	—
59	C₂³×D₂₃	—	4	4	no	—
60	C₂³×D₂₃	C₂³	1	2	yes	—
61	C₂³×D₂₃	C₂³	1	1	yes	characteristic
62	C₂³×D₂₃	C₂³	1	8	yes	complemented
63	C₂×D₄×C₂₃	—	2	8	no	—
64	C₂×D₄×C₂₃	—	2	32	no	—
65	C₂×D₄×C₂₃	—	2	4	no	—
66	C₂×D₄×C₂₃	D₄	1	8	yes	complemented
67	C₂×D₄×C₂₃	C₂³	1	4	yes	—
68	C₂×D₄×C₂₃	C₂³	1	8	yes	complemented
69	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
70	C₂²×C₄×C₂₃	—	2	4	no	—
71	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂³	1	4	yes	complemented
74	C₂×C₂²⋊D₂₃	—	2	8	no	—
75	C₂×C₂²⋊D₂₃	—	2	8	no	—
76	C₂×C₂²⋊D₂₃	—	2	8	no	—
77	C₂×C₂²⋊D₂₃	—	2	64	no	—
78	C₂×C₂²⋊D₂₃	—	2	8	no	—
79	C₂×C₂²⋊D₂₃	—	4	4	no	—
80	C₂×C₂²⋊D₂₃	D₄	1	8	yes	direct product factor
81	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
83	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
84	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
85	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
86	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
87	C₂²×Dic₂₃	—	2	8	no	—
88	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
89	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
90	C₂²×Dic₂₃	C₂³	1	2	yes	—
91	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
92	C₂²×Dic₂₃	C₂³	1	8	yes	complemented
93	D₄×D₂₃	—	2	32	no	—
94	C₂×D₉₂	—	2	4	no	—
95	C₂×D₉₂	C₂³	1	4	yes	complemented
96	C₂×C₄×D₂₃	—	2	4	no	—
97	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
98	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
99	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
100	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
101	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
102	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
103	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
104	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
105	C₄×Dic₂₃	C₂³	1	4	yes	complemented
106	C₂³×C₂₃	—	2	4	no	—
107	C₂³×C₂₃	—	2	2	no	—
108	C₂³×C₂₃	—	2	4	no	—
109	C₂³×C₂₃	—	2	2	no	—
110	C₂³×C₂₃	—	2	4	no	—
111	C₂³×C₂₃	—	2	4	no	—
112	C₂³×C₂₃	—	2	16	no	—
113	C₂³×C₂₃	—	2	16	no	—
114	C₂³×C₂₃	—	2	4	no	—
115	C₂³×C₂₃	—	4	8	no	—
116	C₂³×C₂₃	—	4	32	no	—
117	C₂³×C₂₃	C₂×D₄	1	4	yes	complemented
118	C₂³×C₂₃	C₂×D₄	1	8	yes	complemented
119	C₂³×C₂₃	C₂⁴	1	4	yes	—
120	C₂³×C₂₃	C₂⁴	1	4	yes	—
121	C₂³×C₂₃	C₂⁴	1	2	yes	—
122	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
123	C₂²×D₂₃	—	2	2	no	—
124	C₂²×D₂₃	—	2	2	no	—
125	C₂²×D₂₃	—	2	4	no	—
126	C₂²×D₂₃	—	2	4	no	—
127	C₂²×D₂₃	—	2	16	no	—
128	C₂²×D₂₃	—	2	4	no	—
129	C₂²×D₂₃	—	2	16	no	—
130	C₂²×D₂₃	—	4	8	no	—
131	C₂²×D₂₃	—	4	32	no	—
132	C₂²×D₂₃	C₂×D₄	1	4	yes	complemented
133	C₂²×D₂₃	C₂⁴	1	4	yes	—
134	C₂²×D₂₃	C₂⁴	1	2	yes	—
135	D₄×C₂₃	—	2	16	no	—
136	D₄×C₂₃	—	2	8	no	—
137	D₄×C₂₃	C₂×D₄	1	16	yes	complemented
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	8	no	—
140	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
141	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
143	C₂²⋊D₂₃	—	2	16	no	—
144	C₂²⋊D₂₃	—	2	16	no	—
145	C₂²⋊D₂₃	—	2	16	no	—
146	C₂²⋊D₂₃	—	2	16	no	—
147	C₂²⋊D₂₃	—	4	8	no	—
148	C₂²⋊D₂₃	C₂×D₄	1	16	yes	direct product factor
149	C₂×Dic₂₃	—	2	2	no	—
150	C₂×Dic₂₃	—	2	4	no	—
151	C₂×Dic₂₃	—	2	2	no	—
152	C₂×Dic₂₃	—	2	16	no	—
153	C₂×Dic₂₃	C₂×D₄	1	4	yes	complemented
154	C₂×Dic₂₃	C₂⁴	1	2	yes	—
155	C₂×Dic₂₃	C₂⁴	1	2	yes	—
156	C₂×Dic₂₃	C₂⁴	1	4	yes	—
157	C₂×Dic₂₃	C₂⁴	1	2	yes	—
158	D₉₂	—	2	8	no	—
159	C₄×D₂₃	—	2	8	no	—
160	C₂×D₄²	—	23	1	no	maximal, Sylow
161	C₂²×C₂₃	—	2	16	no	—
162	C₂²×C₂₃	—	2	8	no	—
163	C₂²×C₂₃	—	2	4	no	—
164	C₂²×C₂₃	—	2	2	no	—
165	C₂²×C₂₃	—	2	4	no	—
166	C₂²×C₂₃	—	2	2	no	—
167	C₂²×C₂₃	—	2	4	no	—
168	C₂²×C₂₃	—	2	4	no	—
169	C₂²×C₂₃	—	2	4	no	—
170	C₂²×C₂₃	—	4	32	no	—
171	C₂²×C₂₃	—	4	8	no	—
172	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
173	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
174	C₂²×C₂₃	C₂²×D₄	1	4	yes	complemented
175	C₂²×C₂₃	C₂²×D₄	1	8	yes	complemented
176	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
177	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
178	C₂×D₂₃	—	2	8	no	—
179	C₂×D₂₃	—	2	2	no	—
180	C₂×D₂₃	—	2	2	no	—
181	C₂×D₂₃	—	2	4	no	—
182	C₂×D₂₃	—	2	4	no	—
183	C₂×D₂₃	—	2	4	no	—
184	C₂×D₂₃	—	4	32	no	—
185	C₂×D₂₃	—	4	8	no	—
186	C₂×D₂₃	C₂²×D₄	1	4	yes	complemented
187	C₄×C₂₃	—	2	2	no	—
188	C₄×C₂₃	C₂²×D₄	1	4	yes	complemented
189	Dic₂₃	—	2	2	no	—
190	Dic₂₃	—	2	4	no	—
191	Dic₂₃	—	2	2	no	—
192	Dic₂₃	C₂²×D₄	1	4	yes	complemented
193	C₂³×D₄	—	23	2	no	—
194	C₂³×D₄	—	23	1	no	—
195	C₂³×D₄	D₂₃	1	1	yes	characteristic, complemented
196	D₄²	—	23	16	no	—
197	C₂×#127	—	23	1	no	—
198	C₂×#121	—	23	1	no	—
199	C₂×#121	—	23	2	no	—
200	C₂×#121	—	23	1	no	—
201	C₂×#120	—	23	2	no	—
202	C₂×#120	—	23	2	no	—
203	C₂×C₄×D₄	—	23	1	no	—
204	C₂×C₄×D₄	—	23	1	no	—
205	C₂×C₂₃	—	2	8	no	—
206	C₂×C₂₃	—	2	4	no	—
207	C₂×C₂₃	—	4	4	no	—
208	C₂×C₂₃	D₄²	1	4	yes	complemented
209	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
210	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
211	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
212	D₂₃	—	2	4	no	—
213	D₂₃	—	4	4	no	—
214	C₂⁵	—	23	2	no	—
215	C₂⁵	C₂×D₂₃	1	2	yes	complemented
216	C₂²×D₄	—	2	8	no	—
217	C₂²×D₄	—	23	1	no	—
218	C₂²×D₄	—	23	2	no	—
219	C₂²×D₄	—	23	2	no	—
220	C₂²×D₄	—	23	2	no	—
221	C₂²×D₄	—	23	2	no	—
222	C₂²×D₄	—	23	16	no	—
223	C₂²×D₄	—	23	2	no	—
224	C₂²×D₄	—	23	8	no	—
225	C₂²×D₄	—	23	1	no	—
226	C₂²×D₄	—	46	16	no	—
227	C₂²×D₄	—	46	8	no	—
228	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
229	C₂²×D₄	C₂×D₂₃	1	2	yes	complemented
230	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
231	C₂²×D₄	C₂×D₂₃	1	8	yes	complemented
232	C₂³×C₄	—	23	2	no	—
233	C₂³×C₄	—	23	1	no	—
234	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
235	#127	—	23	8	no	—
236	#121	—	23	8	no	—
237	#121	—	23	16	no	—
238	#121	—	23	8	no	—
239	#120	—	23	16	no	—
240	#120	—	23	16	no	—
241	C₄×D₄	—	23	8	no	—
242	C₄×D₄	—	23	8	no	—
243	C₂×C₄⋊C₄	—	23	1	no	—
244	C₂×C₄⋊C₄	—	23	1	no	—
245	C₂×C₂²⋊C₄	—	23	1	no	—
246	C₂×C₂²⋊C₄	—	23	2	no	—
247	C₂×C₂²⋊C₄	—	23	2	no	—
248	C₂×C₂²⋊C₄	—	23	1	no	—
249	C₂×C₂²⋊C₄	—	23	2	no	—
250	C₂×C₄²	—	23	1	no	—
251	C₂₃	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
252	C₂⁴	—	2	8	no	—
253	C₂⁴	—	2	8	no	—
254	C₂⁴	—	4	4	no	—
255	C₂⁴	—	23	1	no	—
256	C₂⁴	—	23	2	no	—
257	C₂⁴	—	23	8	no	—
258	C₂⁴	—	46	8	no	—
259	C₂⁴	—	46	8	no	—
260	C₂⁴	—	92	4	no	—
261	C₂⁴	C₂²×D₂₃	1	2	yes	—
262	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
263	C₂⁴	C₂²×D₂₃	1	2	yes	—
264	C₂⁴	C₂²×D₂₃	1	8	yes	complemented
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	32	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	23	8	no	—
269	C₂×D₄	—	23	4	no	—
270	C₂×D₄	—	23	8	no	—
271	C₂×D₄	—	23	8	no	—
272	C₂×D₄	—	23	8	no	—
273	C₂×D₄	—	23	8	no	—
274	C₂×D₄	—	23	8	no	—
275	C₂×D₄	—	23	4	no	—
276	C₂×D₄	—	46	8	no	—
277	C₂×D₄	—	46	64	no	—
278	C₂×D₄	—	46	8	no	—
279	C₂×D₄	—	46	8	no	—
280	C₂×D₄	—	46	8	no	—
281	C₂×D₄	—	46	32	no	—
282	C₂×D₄	—	46	4	no	—
283	C₂×D₄	—	92	4	no	—
284	C₂×D₄	C₂²⋊D₂₃	1	8	yes	direct product factor
285	C₂×D₄	C₂²×D₂₃	1	4	yes	—
286	C₂×D₄	C₂²×D₂₃	1	8	yes	complemented
287	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	23	1	no	—
290	C₂²×C₄	—	23	8	no	—
291	C₂²×C₄	—	23	1	no	—
292	C₂²×C₄	—	23	2	no	—
293	C₂²×C₄	—	23	1	no	—
294	C₂²×C₄	—	23	4	no	—
295	C₂²×C₄	—	46	8	no	—
296	C₂²×C₄	—	46	4	no	—
297	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₂₃	1	4	yes	complemented
300	C₄⋊C₄	—	23	4	no	—
301	C₄⋊C₄	—	23	4	no	—
302	C₂²⋊C₄	—	23	4	no	—
303	C₂²⋊C₄	—	23	8	no	—
304	C₂²⋊C₄	—	23	8	no	—
305	C₂²⋊C₄	—	23	4	no	—
306	C₂²⋊C₄	—	23	8	no	—
307	C₄²	—	23	4	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	16	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	16	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	32	no	—
319	C₂³	—	23	4	no	—
320	C₂³	—	23	2	no	—
321	C₂³	—	23	4	no	—
322	C₂³	—	46	16	no	—
323	C₂³	—	46	2	no	—
324	C₂³	—	46	2	no	—
325	C₂³	—	46	4	no	—
326	C₂³	—	46	4	no	—
327	C₂³	—	46	4	no	—
328	C₂³	—	46	16	no	—
329	C₂³	—	92	8	no	—
330	C₂³	—	92	32	no	—
331	C₂³	D₄×D₂₃	1	4	yes	complemented
332	C₂³	C₂×C₂²⋊D₂₃	1	8	yes	complemented
333	C₂³	C₂³×D₂₃	1	4	yes	—
334	C₂³	C₂³×D₂₃	1	2	yes	—
335	C₂³	C₂³×D₂₃	1	4	yes	—
336	C₂³	C₂³×D₂₃	1	1	yes	characteristic
337	D₄	—	2	16	no	—
338	D₄	—	2	8	no	—
339	D₄	—	23	16	no	—
340	D₄	—	46	16	no	—
341	D₄	—	46	16	no	—
342	D₄	—	46	16	no	—
343	D₄	—	46	16	no	—
344	D₄	—	46	8	no	—
345	D₄	—	92	8	no	—
346	D₄	C₂×C₂²⋊D₂₃	1	16	yes	direct product factor
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	23	4	no	—
350	C₂×C₄	—	23	2	no	—
351	C₂×C₄	—	23	2	no	—
352	C₂×C₄	—	23	4	no	—
353	C₂×C₄	—	23	2	no	—
354	C₂×C₄	—	46	16	no	—
355	C₂×C₄	—	46	4	no	—
356	C₂×C₄	—	46	2	no	—
357	C₂×C₄	—	46	2	no	—
358	C₂×C₄	—	46	8	no	—
359	C₂×C₄	C₂×C₂²⋊D₂₃	1	4	yes	complemented
360	C₂×C₄	C₂³×D₂₃	1	2	yes	—
361	C₂×C₄	C₂³×D₂₃	1	2	yes	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	16	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	4	32	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	23	4	no	—
374	C₂²	—	46	2	no	—
375	C₂²	—	46	2	no	—
376	C₂²	—	46	8	no	—
377	C₂²	—	46	4	no	—
378	C₂²	—	46	4	no	—
379	C₂²	—	46	4	no	—
380	C₂²	—	92	32	no	—
381	C₂²	—	92	8	no	—
382	C₂²	C₂×D₄×D₂₃	1	2	yes	—
383	C₂²	C₂×D₄×D₂₃	1	4	yes	complemented
384	C₂²	#10625155	1	2	yes	—
385	C₂²	C₂²×C₂²⋊D₂₃	1	2	yes	—
386	C₂²	C₂²×C₂²⋊D₂₃	1	8	yes	complemented
387	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	23	4	no	—
390	C₄	—	46	4	no	—
391	C₄	—	46	2	no	—
392	C₄	—	46	2	no	—
393	C₄	C₂²×C₂²⋊D₂₃	1	4	yes	complemented
394	C₂	—	2	4	no	—
395	C₂	—	2	8	no	—
396	C₂	—	4	4	no	—
397	C₂	—	46	4	no	—
398	C₂	—	92	4	no	—
399	C₂	D₄×C₂²⋊D₂₃	1	4	yes	direct product factor
400	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
401	C₂	C₂³×C₂²⋊D₂₃	1	1	yes	characteristic
402	C₂	C₂×#10625155	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂³×D₄×C₂₃	C₂
socle	C₂³×C₂₃	C₂⁴
hypercenter	C₂³×D₄	D₂₃
hypocenter	C₂₃	C₂×D₄²
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂²⋊D₂₃	C₂	semidirect
2. C₂²×D₄×D₂₃	C₂	semidirect
3. D₄×C₂²⋊D₂₃	C₂	direct (N × H)
4. C₂×#10625111	C₂	semidirect
5. C₂×#10625101	C₂	semidirect
6. C₂×#10625110	C₂	semidirect
7. C₂×#10625109	C₂	semidirect
8. C₂×#10625124	C₂	semidirect
9. C₂×#10625108	C₂	semidirect
10. C₂×D₄×Dic₂₃	C₂	semidirect
11. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
12. C₂³×D₄×C₂₃	C₂	semidirect
13. C₂⁵×C₂₃	C₂²	semidirect
14. C₂⁴×D₂₃	C₂²	semidirect
17. C₂²×D₄×C₂₃	C₂²	semidirect
18. C₂²×D₄×C₂₃	C₂²	semidirect
19. C₂²×D₄×C₂₃	C₂²	semidirect
20. C₂³×C₄×C₂₃	C₂²	semidirect
23. C₂²×C₂²⋊D₂₃	C₂²	semidirect
24. C₂²×C₂²⋊D₂₃	C₂²	semidirect
25. C₂²×C₂²⋊D₂₃	C₂²	semidirect
26. C₂²×C₂²⋊D₂₃	C₂²	semidirect
27. C₂²×C₂²⋊D₂₃	C₂²	semidirect
28. C₂²×C₂²⋊D₂₃	C₂²	semidirect
29. C₂³×Dic₂₃	C₂²	semidirect
31. C₂×D₄×D₂₃	C₂²	semidirect
32. C₂²×D₉₂	C₂²	semidirect
33. C₂²×C₄×D₂₃	C₂²	semidirect
34. #10625124	C₂²	semidirect
35. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
36. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
38. #10625111	C₂²	semidirect
39. #10625110	C₂²	semidirect
40. #10625109	C₂²	semidirect
41. #10625108	C₂²	semidirect
42. D₄×Dic₂₃	C₂²	semidirect
43. #10625101	C₂²	semidirect
44. C₄×C₂²⋊D₂₃	C₂²	semidirect
45. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
46. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
47. C₂×C₄⋊Dic₂₃	C₂²	semidirect
48. C₂×Dic₂₃⋊C₄	C₂²	semidirect
49. C₂×C₄×Dic₂₃	C₂²	semidirect
56. C₂⁴×C₂₃	C₂³	semidirect
62. C₂³×D₂₃	C₂³	semidirect
66. C₂×D₄×C₂₃	D₄	semidirect
68. C₂×D₄×C₂₃	C₂³	semidirect
69. C₂×D₄×C₂₃	C₂³	semidirect
73. C₂²×C₄×C₂₃	C₂³	semidirect
80. C₂×C₂²⋊D₂₃	D₄	direct (N × H)
82. C₂×C₂²⋊D₂₃	C₂³	semidirect
83. C₂×C₂²⋊D₂₃	C₂³	semidirect
84. C₂×C₂²⋊D₂₃	C₂³	semidirect
85. C₂×C₂²⋊D₂₃	C₂³	semidirect
86. C₂×C₂²⋊D₂₃	C₂³	semidirect
92. C₂²×Dic₂₃	C₂³	semidirect
95. C₂×D₉₂	C₂³	semidirect
97. C₂×C₄×D₂₃	C₂³	semidirect
98. C₂²⋊Dic₂₃	C₂³	semidirect
99. C₂²⋊Dic₂₃	C₂³	semidirect
100. C₂²⋊Dic₂₃	C₂³	semidirect
101. (C₂×D₂₃)⋊C₄	C₂³	semidirect
102. (C₂×D₂₃)⋊C₄	C₂³	semidirect
103. C₄⋊Dic₂₃	C₂³	semidirect
104. Dic₂₃⋊C₄	C₂³	semidirect
105. C₄×Dic₂₃	C₂³	semidirect
117. C₂³×C₂₃	C₂×D₄	semidirect
118. C₂³×C₂₃	C₂×D₄	semidirect
132. C₂²×D₂₃	C₂×D₄	semidirect
137. D₄×C₂₃	C₂×D₄	semidirect
140. C₂×C₄×C₂₃	C₂×D₄	semidirect
148. C₂²⋊D₂₃	C₂×D₄	direct (N × H)
153. C₂×Dic₂₃	C₂×D₄	semidirect
174. C₂²×C₂₃	C₂²×D₄	semidirect
175. C₂²×C₂₃	C₂²×D₄	semidirect
186. C₂×D₂₃	C₂²×D₄	semidirect
188. C₄×C₂₃	C₂²×D₄	semidirect
192. Dic₂₃	C₂²×D₄	semidirect
195. C₂³×D₄	D₂₃	semidirect
208. C₂×C₂₃	D₄²	semidirect
215. C₂⁵	C₂×D₂₃	semidirect
229. C₂²×D₄	C₂×D₂₃	semidirect
230. C₂²×D₄	C₂×D₂₃	semidirect
231. C₂²×D₄	C₂×D₂₃	semidirect
234. C₂³×C₄	C₂×D₂₃	semidirect
251. C₂₃	C₂×D₄²	semidirect
264. C₂⁴	C₂²×D₂₃	semidirect
284. C₂×D₄	C₂²⋊D₂₃	direct (N × H)
286. C₂×D₄	C₂²×D₂₃	semidirect
287. C₂×D₄	C₂²×D₂₃	semidirect
299. C₂²×C₄	C₂²×D₂₃	semidirect
331. C₂³	D₄×D₂₃	semidirect
332. C₂³	C₂×C₂²⋊D₂₃	semidirect
346. D₄	C₂×C₂²⋊D₂₃	direct (N × H)
359. C₂×C₄	C₂×C₂²⋊D₂₃	semidirect
383. C₂²	C₂×D₄×D₂₃	semidirect
386. C₂²	C₂²×C₂²⋊D₂₃	semidirect
393. C₄	C₂²×C₂²⋊D₂₃	semidirect
399. C₂	D₄×C₂²⋊D₂₃	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×C₂²⋊D₂₃	2
C₂²×D₄×D₂₃	2
D₄×C₂²⋊D₂₃	2
C₂×#10625111	2
C₂×#10625101	2
C₂×#10625110	2
C₂×#10625109	2
C₂×#10625124	2
C₂×#10625108	2
C₂×D₄×Dic₂₃	2
C₂×C₄×C₂²⋊D₂₃	2
C₂³×D₄×C₂₃	2
C₂×D₄²	23

Subgroups — C2×D4×C22⋊D23 #15686834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₂²⋊D₂₃ #15686834