Subgroups — C₂×#121×D₂₃ #15686615

Order 2944.

2528 conjugacy classes of subgroups.

The subgroup lattice has 408 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	C₂²×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625101	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625055	C₂	1	2	yes	maximal, complemented
7	C₂×#10625110	C₂	1	2	yes	maximal, complemented
8	C₂×#10625109	C₂	1	1	yes	maximal, characteristic, complemented
9	#121×D₂₃	C₂	1	16	yes	maximal, direct product factor
10	C₂×C₄⋊C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₄×D₂₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₃	C₂²	1	2	yes	—
14	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×D₄×C₂₃	C₂²	1	2	yes	complemented
17	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
21	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₂₃	—	2	16	no	—
23	C₂×D₄×D₂₃	—	2	8	no	—
24	C₂×D₄×D₂₃	C₂²	1	16	yes	complemented
25	C₂×D₄×D₂₃	C₂²	1	8	yes	complemented
26	C₂²×D₉₂	C₂²	1	2	yes	complemented
27	C₂²×D₉₂	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₂₃	—	2	8	no	—
29	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
30	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₂₃	C₂²	1	8	yes	complemented
33	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#121	C₂²	1	8	yes	complemented
36	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
39	#10625110	C₂²	1	16	yes	complemented
40	#10625109	C₂²	1	8	yes	complemented
41	#10625101	C₂²	1	8	yes	complemented
42	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
43	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×Dic₂₃⋊C₄	C₂²	1	2	yes	complemented
46	#10625066	C₂²	1	8	yes	complemented
47	C₄⋊C₄×D₂₃	C₂²	1	8	yes	complemented
48	#10625055	C₂²	1	16	yes	complemented
49	C₂²⋊C₄×D₂₃	C₂²	1	16	yes	complemented
50	C₂⁴×C₂₃	C₂³	1	2	yes	—
51	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
52	C₂³×D₂₃	—	2	4	no	—
53	C₂³×D₂₃	—	2	4	no	—
54	C₂³×D₂₃	—	2	8	no	—
55	C₂³×D₂₃	—	2	8	no	—
56	C₂³×D₂₃	—	2	8	no	—
57	C₂³×D₂₃	D₄	1	8	yes	complemented
58	C₂³×D₂₃	C₂³	1	8	yes	—
59	C₂³×D₂₃	C₂³	1	2	yes	—
60	C₂³×D₂₃	C₂³	1	1	yes	characteristic
61	C₂³×D₂₃	C₂³	1	4	yes	—
62	C₂³×D₂₃	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₂₃	—	2	8	no	—
64	C₂×D₄×C₂₃	—	2	4	no	—
65	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
66	C₂×D₄×C₂₃	C₂³	1	8	yes	complemented
67	C₂²×C₄×C₂₃	—	2	4	no	—
68	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
69	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂³	1	4	yes	complemented
72	C₂×C₂²⋊D₂₃	—	2	8	no	—
73	C₂×C₂²⋊D₂₃	—	2	8	no	—
74	C₂×C₂²⋊D₂₃	—	2	8	no	—
75	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
76	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
77	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
78	C₂²×Dic₂₃	—	2	4	no	—
79	C₂²×Dic₂₃	C₂³	1	2	yes	—
80	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
81	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
82	C₂²×Dic₂₃	C₂³	1	4	yes	complemented
83	D₄×D₂₃	—	2	64	no	—
84	D₄×D₂₃	—	2	32	no	—
85	C₂×D₉₂	—	2	8	no	—
86	C₂×D₉₂	—	2	4	no	—
87	C₂×D₉₂	C₂³	1	8	yes	complemented
88	C₂×D₉₂	C₂³	1	4	yes	complemented
89	C₂×C₄×D₂₃	—	2	4	no	—
90	C₂×C₄×D₂₃	—	2	8	no	—
91	C₂×C₄×D₂₃	—	2	4	no	—
92	C₂×C₄×D₂₃	—	2	4	no	—
93	C₂×C₄×D₂₃	—	2	32	no	—
94	C₂×C₄×D₂₃	D₄	1	8	yes	complemented
95	C₂×C₄×D₂₃	C₂³	1	4	yes	—
96	C₂×C₄×D₂₃	C₂³	1	8	yes	—
97	C₂×C₄×D₂₃	C₂³	1	4	yes	—
98	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
99	C₂×C₄×D₂₃	C₂³	1	4	yes	complemented
100	C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
101	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
102	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
103	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
104	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
105	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
106	Dic₂₃⋊C₄	C₂³	1	8	yes	complemented
107	C₂³×C₂₃	—	2	2	no	—
108	C₂³×C₂₃	—	2	2	no	—
109	C₂³×C₂₃	—	2	4	no	—
110	C₂³×C₂₃	—	2	4	no	—
111	C₂³×C₂₃	—	2	4	no	—
112	C₂³×C₂₃	C₂×D₄	1	4	yes	complemented
113	C₂³×C₂₃	C₂⁴	1	4	yes	—
114	C₂³×C₂₃	C₂⁴	1	2	yes	—
115	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
116	C₂²×D₂₃	—	2	2	no	—
117	C₂²×D₂₃	—	2	2	no	—
118	C₂²×D₂₃	—	2	32	no	—
119	C₂²×D₂₃	—	2	8	no	—
120	C₂²×D₂₃	—	2	8	no	—
121	C₂²×D₂₃	—	2	4	no	—
122	C₂²×D₂₃	—	2	4	no	—
123	C₂²×D₂₃	—	2	4	no	—
124	C₂²×D₂₃	—	2	16	no	—
125	C₂²×D₂₃	—	2	16	no	—
126	C₂²×D₂₃	—	2	16	no	—
127	C₂²×D₂₃	—	4	32	no	—
128	C₂²×D₂₃	C₂×D₄	1	4	yes	—
129	C₂²×D₂₃	C₂×D₄	1	4	yes	—
130	C₂²×D₂₃	C₂×D₄	1	16	yes	complemented
131	C₂²×D₂₃	C₂×D₄	1	4	yes	complemented
132	C₂²×D₂₃	#41	1	4	yes	—
133	C₂²×D₂₃	C₂⁴	1	4	yes	—
134	C₂²×D₂₃	C₂⁴	1	2	yes	—
135	C₂²×D₂₃	C₂⁴	1	2	yes	—
136	D₄×C₂₃	—	2	16	no	—
137	D₄×C₂₃	—	2	8	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	4	no	—
140	C₂×C₄×C₂₃	—	2	8	no	—
141	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
142	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
143	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
144	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
145	C₂²⋊D₂₃	—	2	16	no	—
146	C₂²⋊D₂₃	—	2	16	no	—
147	C₂²⋊D₂₃	—	2	16	no	—
148	C₂×Dic₂₃	—	2	2	no	—
149	C₂×Dic₂₃	—	2	4	no	—
150	C₂×Dic₂₃	—	2	8	no	—
151	C₂×Dic₂₃	C₂×D₄	1	4	yes	complemented
152	C₂×Dic₂₃	C₂⁴	1	4	yes	—
153	C₂×Dic₂₃	C₂⁴	1	2	yes	—
154	C₂×Dic₂₃	C₂⁴	1	2	yes	—
155	D₉₂	—	2	16	no	—
156	D₉₂	—	2	8	no	—
157	C₄×D₂₃	—	2	8	no	—
158	C₄×D₂₃	—	2	16	no	—
159	C₄×D₂₃	—	2	8	no	—
160	C₄×D₂₃	—	2	8	no	—
161	C₄×D₂₃	C₂×D₄	1	16	yes	complemented
162	C₂²×#121	—	23	1	no	maximal, Sylow
163	C₂²×C₂₃	—	2	8	no	—
164	C₂²×C₂₃	—	2	2	no	—
165	C₂²×C₂₃	—	2	2	no	—
166	C₂²×C₂₃	—	2	4	no	—
167	C₂²×C₂₃	—	2	4	no	—
168	C₂²×C₂₃	—	2	4	no	—
169	C₂²×C₂₃	—	4	8	no	—
170	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
171	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
172	C₂²×C₂₃	C₂²×D₄	1	4	yes	complemented
173	C₂²×C₂₃	C₂×#41	1	2	yes	—
174	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
175	C₂×D₂₃	—	2	8	no	—
176	C₂×D₂₃	—	2	2	no	—
177	C₂×D₂₃	—	2	2	no	—
178	C₂×D₂₃	—	2	32	no	—
179	C₂×D₂₃	—	2	4	no	—
180	C₂×D₂₃	—	2	4	no	—
181	C₂×D₂₃	—	2	4	no	—
182	C₂×D₂₃	—	4	8	no	—
183	C₂×D₂₃	—	4	32	no	—
184	C₂×D₂₃	#121	1	16	yes	direct product factor
185	C₂×D₂₃	C₂²×D₄	1	4	yes	—
186	C₂×D₂₃	C₂²×D₄	1	4	yes	—
187	C₂×D₂₃	C₂²×D₄	1	4	yes	complemented
188	C₂×D₂₃	C₂×#41	1	4	yes	—
189	C₄×C₂₃	—	2	2	no	—
190	C₄×C₂₃	—	2	4	no	—
191	C₄×C₂₃	C₂²×D₄	1	4	yes	complemented
192	Dic₂₃	—	2	2	no	—
193	Dic₂₃	—	2	4	no	—
194	Dic₂₃	C₂²×D₄	1	4	yes	complemented
195	C₂³×D₄	—	23	1	no	—
196	C₂³×D₄	—	23	2	no	—
197	C₂⁴×C₄	—	23	1	no	—
198	C₂×#121	—	23	1	no	—
199	C₂×#121	—	23	2	no	—
200	C₂×#121	—	23	1	no	—
201	C₂×#121	—	23	16	no	—
202	C₂×#121	—	23	1	no	—
203	C₂×#121	—	23	2	no	—
204	C₂×#121	D₂₃	1	1	yes	characteristic, direct product factor
205	C₂²×C₄⋊C₄	—	23	1	no	—
206	C₂²×C₂²⋊C₄	—	23	2	no	—
207	C₂×C₂₃	—	2	4	no	—
208	C₂×C₂₃	—	4	4	no	—
209	C₂×C₂₃	C₂×#121	1	4	yes	complemented
210	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
211	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
212	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
213	D₂₃	—	2	4	no	—
214	D₂₃	—	4	4	no	—
215	D₂₃	C₂×#121	1	8	yes	direct product factor
216	C₂⁵	—	23	1	no	—
217	C₂⁵	—	23	2	no	—
218	C₂²×D₄	—	23	2	no	—
219	C₂²×D₄	—	23	2	no	—
220	C₂²×D₄	—	23	2	no	—
221	C₂²×D₄	—	23	8	no	—
222	C₂²×D₄	—	23	16	no	—
223	C₂²×D₄	—	23	2	no	—
224	C₂²×D₄	—	23	1	no	—
225	C₂²×D₄	—	46	8	no	—
226	C₂²×D₄	—	46	16	no	—
227	C₂²×D₄	C₂×D₂₃	1	2	yes	complemented
228	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
229	C₂³×C₄	—	23	1	no	—
230	C₂³×C₄	—	23	1	no	—
231	C₂³×C₄	—	23	1	no	—
232	C₂³×C₄	—	23	2	no	—
233	C₂³×C₄	—	23	1	no	—
234	C₂³×C₄	—	23	1	no	—
235	C₂³×C₄	—	23	8	no	—
236	C₂³×C₄	—	46	8	no	—
237	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
238	#121	—	23	8	no	—
239	#121	—	23	16	no	—
240	#121	—	23	8	no	—
241	#121	—	23	8	no	—
242	#121	—	23	16	no	—
243	#121	C₂×D₂₃	1	8	yes	direct product factor
244	C₂×C₄⋊C₄	—	23	2	no	—
245	C₂×C₄⋊C₄	—	23	1	no	—
246	C₂×C₄⋊C₄	—	23	8	no	—
247	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
248	C₂×C₂²⋊C₄	—	23	2	no	—
249	C₂×C₂²⋊C₄	—	23	2	no	—
250	C₂×C₂²⋊C₄	—	23	2	no	—
251	C₂×C₂²⋊C₄	—	23	16	no	—
252	C₂×C₂²⋊C₄	C₂×D₂₃	1	2	yes	complemented
253	C₂₃	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
254	C₂⁴	—	23	1	no	—
255	C₂⁴	—	23	8	no	—
256	C₂⁴	—	23	4	no	—
257	C₂⁴	—	23	1	no	—
258	C₂⁴	—	23	8	no	—
259	C₂⁴	—	23	2	no	—
260	C₂⁴	—	46	4	no	—
261	C₂⁴	—	46	4	no	—
262	C₂⁴	—	46	8	no	—
263	C₂⁴	—	46	8	no	—
264	C₂⁴	—	46	8	no	—
265	C₂⁴	C₂²×D₂₃	1	2	yes	—
266	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	23	8	no	—
270	C₂×D₄	—	23	8	no	—
271	C₂×D₄	—	23	8	no	—
272	C₂×D₄	—	23	8	no	—
273	C₂×D₄	—	23	4	no	—
274	C₂×D₄	—	46	8	no	—
275	C₂×D₄	—	46	32	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	4	no	—
281	C₂×D₄	C₂²×D₂₃	1	8	yes	complemented
282	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	23	1	no	—
285	C₂²×C₄	—	23	8	no	—
286	C₂²×C₄	—	23	4	no	—
287	C₂²×C₄	—	23	4	no	—
288	C₂²×C₄	—	23	1	no	—
289	C₂²×C₄	—	23	2	no	—
290	C₂²×C₄	—	23	4	no	—
291	C₂²×C₄	—	23	8	no	—
292	C₂²×C₄	—	23	4	no	—
293	C₂²×C₄	—	23	4	no	—
294	C₂²×C₄	—	46	4	no	—
295	C₂²×C₄	—	46	32	no	—
296	C₂²×C₄	—	46	4	no	—
297	C₂²×C₄	—	46	8	no	—
298	C₂²×C₄	—	46	4	no	—
299	C₂²×C₄	—	46	4	no	—
300	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
302	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₂₃	1	4	yes	complemented
304	C₄⋊C₄	—	23	8	no	—
305	C₄⋊C₄	—	23	4	no	—
306	C₄⋊C₄	C₂²×D₂₃	1	4	yes	complemented
307	C₂²⋊C₄	—	23	8	no	—
308	C₂²⋊C₄	—	23	8	no	—
309	C₂²⋊C₄	—	23	8	no	—
310	C₂²⋊C₄	C₂²×D₂₃	1	8	yes	complemented
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	23	4	no	—
317	C₂³	—	23	4	no	—
318	C₂³	—	23	4	no	—
319	C₂³	—	23	2	no	—
320	C₂³	—	23	4	no	—
321	C₂³	—	23	16	no	—
322	C₂³	—	23	2	no	—
323	C₂³	—	23	4	no	—
324	C₂³	—	46	8	no	—
325	C₂³	—	46	32	no	—
326	C₂³	—	46	8	no	—
327	C₂³	—	46	16	no	—
328	C₂³	—	46	16	no	—
329	C₂³	—	46	16	no	—
330	C₂³	—	46	2	no	—
331	C₂³	—	46	2	no	—
332	C₂³	—	46	4	no	—
333	C₂³	—	46	4	no	—
334	C₂³	—	46	4	no	—
335	C₂³	—	92	32	no	—
336	C₂³	D₄×D₂₃	1	4	yes	complemented
337	C₂³	C₂³×D₂₃	1	4	yes	—
338	C₂³	C₂³×D₂₃	1	2	yes	—
339	C₂³	C₂³×D₂₃	1	1	yes	characteristic
340	D₄	—	2	16	no	—
341	D₄	—	2	8	no	—
342	D₄	—	46	16	no	—
343	D₄	—	46	16	no	—
344	D₄	—	46	16	no	—
345	D₄	—	46	16	no	—
346	D₄	—	46	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	23	4	no	—
351	C₂×C₄	—	23	2	no	—
352	C₂×C₄	—	23	16	no	—
353	C₂×C₄	—	23	2	no	—
354	C₂×C₄	—	23	4	no	—
355	C₂×C₄	—	46	8	no	—
356	C₂×C₄	—	46	8	no	—
357	C₂×C₄	—	46	16	no	—
358	C₂×C₄	—	46	8	no	—
359	C₂×C₄	—	46	2	no	—
360	C₂×C₄	—	46	4	no	—
361	C₂×C₄	—	46	8	no	—
362	C₂×C₄	D₄×D₂₃	1	4	yes	complemented
363	C₂×C₄	C₂³×D₂₃	1	2	yes	—
364	C₂×C₄	C₂³×D₂₃	1	4	yes	—
365	C₂×C₄	C₂³×D₂₃	1	2	yes	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	23	16	no	—
374	C₂²	—	23	4	no	—
375	C₂²	—	23	4	no	—
376	C₂²	—	23	4	no	—
377	C₂²	—	23	4	no	—
378	C₂²	—	46	32	no	—
379	C₂²	—	46	8	no	—
380	C₂²	—	46	2	no	—
381	C₂²	—	46	2	no	—
382	C₂²	—	46	4	no	—
383	C₂²	—	46	4	no	—
384	C₂²	—	46	4	no	—
385	C₂²	—	92	32	no	—
386	C₂²	—	92	8	no	—
387	C₂²	C₂×D₄×D₂₃	1	2	yes	—
388	C₂²	C₂×D₄×D₂₃	1	2	yes	—
389	C₂²	C₂×D₄×D₂₃	1	4	yes	complemented
390	C₂²	#41×D₂₃	1	2	yes	—
391	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	4	no	—
394	C₄	—	23	4	no	—
395	C₄	—	46	2	no	—
396	C₄	—	46	4	no	—
397	C₄	C₂×D₄×D₂₃	1	4	yes	complemented
398	C₂	—	2	4	no	—
399	C₂	—	4	4	no	—
400	C₂	—	23	8	no	—
401	C₂	—	46	4	no	—
402	C₂	—	92	4	no	—
403	C₂	#121×D₂₃	1	4	yes	direct product factor
404	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
405	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
406	C₂	C₂×#41×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₂₃×#121	C₂
socle	C₂³×C₂₃	C₂⁴
hypercenter	C₂×#121	D₂₃
hypocenter	C₂₃	C₂²×#121
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₂₃	C₂	semidirect
2. C₂²×D₄×D₂₃	C₂	semidirect
3. C₂³×C₄×D₂₃	C₂	semidirect
4. C₂×#10625066	C₂	semidirect
5. C₂×#10625101	C₂	semidirect
6. C₂×#10625055	C₂	semidirect
7. C₂×#10625110	C₂	semidirect
8. C₂×#10625109	C₂	semidirect
9. #121×D₂₃	C₂	direct (N × H)
10. C₂×C₄⋊C₄×D₂₃	C₂	semidirect
11. C₂×C₂²⋊C₄×D₂₃	C₂	semidirect
12. C₂×C₂₃×#121	C₂	semidirect
15. C₂²×D₄×C₂₃	C₂²	semidirect
16. C₂²×D₄×C₂₃	C₂²	semidirect
17. C₂³×C₄×C₂₃	C₂²	semidirect
18. C₂²×C₂²⋊D₂₃	C₂²	semidirect
19. C₂²×C₂²⋊D₂₃	C₂²	semidirect
20. C₂²×C₂²⋊D₂₃	C₂²	semidirect
21. C₂³×Dic₂₃	C₂²	semidirect
24. C₂×D₄×D₂₃	C₂²	semidirect
25. C₂×D₄×D₂₃	C₂²	semidirect
26. C₂²×D₉₂	C₂²	semidirect
27. C₂²×D₉₂	C₂²	semidirect
32. C₂²×C₄×D₂₃	C₂²	semidirect
33. C₂²×C₄×D₂₃	C₂²	semidirect
34. C₂²×C₄×D₂₃	C₂²	semidirect
35. C₂₃×#121	C₂²	semidirect
36. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
37. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
38. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
39. #10625110	C₂²	semidirect
40. #10625109	C₂²	semidirect
41. #10625101	C₂²	semidirect
42. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
43. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
44. C₂×C₄⋊Dic₂₃	C₂²	semidirect
45. C₂×Dic₂₃⋊C₄	C₂²	semidirect
46. #10625066	C₂²	semidirect
47. C₄⋊C₄×D₂₃	C₂²	semidirect
48. #10625055	C₂²	semidirect
49. C₂²⋊C₄×D₂₃	C₂²	semidirect
57. C₂³×D₂₃	D₄	semidirect
65. C₂×D₄×C₂₃	C₂³	semidirect
66. C₂×D₄×C₂₃	C₂³	semidirect
71. C₂²×C₄×C₂₃	C₂³	semidirect
75. C₂×C₂²⋊D₂₃	C₂³	semidirect
76. C₂×C₂²⋊D₂₃	C₂³	semidirect
77. C₂×C₂²⋊D₂₃	C₂³	semidirect
82. C₂²×Dic₂₃	C₂³	semidirect
87. C₂×D₉₂	C₂³	semidirect
88. C₂×D₉₂	C₂³	semidirect
94. C₂×C₄×D₂₃	D₄	semidirect
98. C₂×C₄×D₂₃	C₂³	semidirect
99. C₂×C₄×D₂₃	C₂³	semidirect
100. C₄⋊C₄×C₂₃	C₂³	semidirect
101. C₂²⋊C₄×C₂₃	C₂³	semidirect
102. C₂²⋊Dic₂₃	C₂³	semidirect
103. (C₂×D₂₃)⋊C₄	C₂³	semidirect
104. (C₂×D₂₃)⋊C₄	C₂³	semidirect
105. C₄⋊Dic₂₃	C₂³	semidirect
106. Dic₂₃⋊C₄	C₂³	semidirect
112. C₂³×C₂₃	C₂×D₄	semidirect
130. C₂²×D₂₃	C₂×D₄	semidirect
131. C₂²×D₂₃	C₂×D₄	semidirect
141. C₂×C₄×C₂₃	C₂×D₄	semidirect
151. C₂×Dic₂₃	C₂×D₄	semidirect
161. C₄×D₂₃	C₂×D₄	semidirect
172. C₂²×C₂₃	C₂²×D₄	semidirect
184. C₂×D₂₃	#121	direct (N × H)
187. C₂×D₂₃	C₂²×D₄	semidirect
191. C₄×C₂₃	C₂²×D₄	semidirect
194. Dic₂₃	C₂²×D₄	semidirect
204. C₂×#121	D₂₃	direct (N × H)
209. C₂×C₂₃	C₂×#121	semidirect
215. D₂₃	C₂×#121	direct (N × H)
227. C₂²×D₄	C₂×D₂₃	semidirect
228. C₂²×D₄	C₂×D₂₃	semidirect
237. C₂³×C₄	C₂×D₂₃	semidirect
243. #121	C₂×D₂₃	direct (N × H)
247. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
252. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
253. C₂₃	C₂²×#121	semidirect
281. C₂×D₄	C₂²×D₂₃	semidirect
282. C₂×D₄	C₂²×D₂₃	semidirect
303. C₂²×C₄	C₂²×D₂₃	semidirect
306. C₄⋊C₄	C₂²×D₂₃	semidirect
310. C₂²⋊C₄	C₂²×D₂₃	semidirect
336. C₂³	D₄×D₂₃	semidirect
362. C₂×C₄	D₄×D₂₃	semidirect
389. C₂²	C₂×D₄×D₂₃	semidirect
397. C₄	C₂×D₄×D₂₃	semidirect
403. C₂	#121×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
C₂²×D₄×D₂₃	2
C₂³×C₄×D₂₃	2
C₂×#10625066	2
C₂×#10625101	2
C₂×#10625055	2
C₂×#10625110	2
C₂×#10625109	2
#121×D₂₃	2
C₂×C₄⋊C₄×D₂₃	2
C₂×C₂²⋊C₄×D₂₃	2
C₂×C₂₃×#121	2
C₂²×#121	23

Subgroups — C2×#121×D23 #15686615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#121×D₂₃ #15686615