Subgroups — D₂₃×#554 #15686924

Order 2944.

1200 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093128	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093127	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093126	C₂	1	2	yes	maximal, complemented
4	#13093125	C₂	1	2	yes	maximal, complemented
5	#13093124	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093123	C₂	1	2	yes	maximal, complemented
7	#13093122	C₂	1	2	yes	maximal, complemented
8	#13093121	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#125×D₂₃	C₂	1	2	yes	maximal, complemented
11	C₂²⋊Q₈×D₂₃	C₂	1	4	yes	maximal, complemented
12	C₂²⋊Q₈×D₂₃	C₂	1	2	yes	maximal, complemented
13	C₄×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₂₃	C₂	1	2	yes	maximal
15	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊C₄×D₂₃	C₂	1	2	yes	maximal, complemented
17	C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₂₃	C₂²	1	2	yes	—
20	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
22	C₂²×C₄×D₂₃	C₂²	1	4	yes	—
23	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#125	C₂²	1	2	yes	complemented
25	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
26	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₄×D₄×C₂₃	C₂²	1	2	yes	—
30	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
31	#10625117	C₂²	1	4	yes	complemented
32	#10625117	C₂²	1	2	yes	complemented
33	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
34	#10625115	C₂²	1	2	yes	complemented
35	D₄×Dic₂₃	C₂²	1	2	yes	—
36	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	—
38	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
39	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
40	#10625095	C₂²	1	2	yes	complemented
41	#10625095	C₂²	1	4	yes	complemented
42	C₂×Dic₂₃⋊C₄	C₂²	1	4	yes	complemented
43	#10625068	C₂²	1	2	yes	complemented
44	#10625068	C₂²	1	4	yes	complemented
45	#10625067	C₂²	1	4	yes	complemented
46	#10625067	C₂²	1	4	yes	complemented
47	#10625067	C₂²	1	4	yes	complemented
48	#10625064	C₂²	1	1	yes	characteristic
49	#10625064	C₂²	1	2	yes	—
50	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
51	C₄⋊C₄×D₂₃	C₂²	1	4	yes	—
52	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
53	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
54	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
55	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
56	C₄⋊C₄×D₂₃	C₂²	1	4	yes	—
57	C₄⋊C₄×D₂₃	C₂²	1	4	yes	complemented
58	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
59	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
60	#10625061	C₂²	1	2	yes	complemented
61	#10625061	C₂²	1	2	yes	complemented
62	#10625060	C₂²	1	4	yes	complemented
63	#10625060	C₂²	1	4	yes	complemented
64	#10625059	C₂²	1	2	yes	complemented
65	#10625059	C₂²	1	2	yes	complemented
66	#10625058	C₂²	1	2	yes	complemented
67	#10625058	C₂²	1	1	yes	characteristic, complemented
68	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
69	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	—
70	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	—
71	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
72	#10625049	C₂²	1	4	yes	complemented
73	#10625049	C₂²	1	4	yes	complemented
74	#10625049	C₂²	1	4	yes	complemented
75	C₄×D₉₂	C₂²	1	2	yes	—
76	C₄×D₉₂	C₂²	1	1	yes	characteristic
77	C₄²×D₂₃	C₂²	1	2	yes	—
78	C₄²×D₂₃	C₂²	1	1	yes	characteristic
79	#10625041	C₂²	1	2	yes	complemented
80	#10625040	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₄₆	C₂²	1	2	yes	complemented
82	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₂₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
86	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
88	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
90	C₂²×Dic₂₃	C₂³	1	2	yes	—
91	C₂²×Dic₂₃	C₂³	1	4	yes	—
92	Q₈×D₂₃	—	2	4	no	—
93	Q₈×D₂₃	—	4	4	no	—
94	D₄×D₂₃	Q₈	1	8	yes	complemented
95	C₂×D₉₂	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₂₃	—	2	8	no	—
97	C₂×C₄×D₂₃	—	4	8	no	—
98	C₂×C₄×D₂₃	C₂³	1	2	yes	—
99	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₂₃	C₂³	1	2	yes	—
101	C₂×C₄×D₂₃	C₂³	1	2	yes	—
102	C₂×C₄×D₂₃	C₂³	1	2	yes	—
103	C₂×C₄×D₂₃	C₂³	1	4	yes	—
104	C₂×C₄×D₂₃	C₂³	1	2	yes	—
105	C₂×C₄×D₂₃	C₂³	1	4	yes	—
106	C₂×C₄×D₂₃	C₂³	1	4	yes	—
107	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
109	C₂×Dic₄₆	C₂³	1	2	yes	—
110	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
111	C₂×Dic₄₆	C₂³	1	2	yes	—
112	C₂×Dic₄₆	C₂³	1	4	yes	—
113	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
115	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
121	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₄²×C₂₃	C₂³	1	1	yes	characteristic
123	C₄²×C₂₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
125	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
126	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
130	C₄⋊Dic₂₃	C₂³	1	2	yes	—
131	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₂₃	C₂³	1	2	yes	—
133	C₄⋊Dic₂₃	C₂³	1	2	yes	—
134	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₂₃	C₂³	1	4	yes	—
136	C₄⋊Dic₂₃	C₂³	1	4	yes	—
137	Dic₂₃⋊C₄	C₂³	1	2	yes	—
138	Dic₂₃⋊C₄	C₂³	1	2	yes	—
139	Dic₂₃⋊C₄	C₂³	1	2	yes	—
140	Dic₂₃⋊C₄	C₂³	1	4	yes	—
141	Dic₂₃⋊C₄	C₂³	1	4	yes	—
142	Dic₂₃⋊C₄	C₂³	1	4	yes	—
143	Dic₂₃⋊C₄	C₂³	1	4	yes	—
144	Dic₂₃⋊C₄	C₂³	1	4	yes	—
145	Dic₂₃⋊C₄	C₂³	1	4	yes	—
146	Dic₂₃⋊C₄	C₂³	1	2	yes	—
147	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₂₃	C₂³	1	2	yes	—
149	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₂₃	C₂³	1	2	yes	—
151	C₄×Dic₂₃	C₂³	1	2	yes	—
152	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
153	C₂³×C₂₃	C₂⁴	1	2	yes	—
154	C₂²×D₂₃	—	2	4	no	—
155	C₂²×D₂₃	—	2	4	no	—
156	C₂²×D₂₃	C₂×Q₈	1	8	yes	—
157	C₂²×D₂₃	C₂⁴	1	2	yes	—
158	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
159	Q₈×C₂₃	—	2	2	no	—
160	Q₈×C₂₃	—	4	2	no	—
161	D₄×C₂₃	C₂×Q₈	1	4	yes	complemented
162	C₂×C₄×C₂₃	—	2	4	no	—
163	C₂×C₄×C₂₃	—	4	4	no	—
164	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
169	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₂₃	C₂×Q₈	1	8	yes	complemented
172	C₂×Dic₂₃	—	2	4	no	—
173	C₂×Dic₂₃	—	4	4	no	—
174	C₂×Dic₂₃	C₂⁴	1	2	yes	—
175	C₂×Dic₂₃	C₂⁴	1	2	yes	—
176	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₂₃	C₂⁴	1	2	yes	—
178	C₂×Dic₂₃	C₂⁴	1	4	yes	—
179	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
181	D₉₂	C₂×Q₈	1	4	yes	complemented
182	C₄×D₂₃	—	2	4	no	—
183	C₄×D₂₃	—	2	4	no	—
184	C₄×D₂₃	—	2	4	no	—
185	C₄×D₂₃	—	2	8	no	—
186	C₄×D₂₃	—	2	2	no	—
187	C₄×D₂₃	—	2	4	no	—
188	C₄×D₂₃	—	2	4	no	—
189	C₄×D₂₃	—	4	4	no	—
190	C₄×D₂₃	—	4	4	no	—
191	C₄×D₂₃	C₂×Q₈	1	4	yes	—
192	C₄×D₂₃	#41	1	4	yes	—
193	Dic₄₆	—	2	2	no	—
194	Dic₄₆	—	2	4	no	—
195	Dic₄₆	—	4	4	no	—
196	Dic₄₆	—	4	2	no	—
197	C₂×#554	—	23	1	no	maximal, Sylow
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	2	2	no	—
200	C₂²×C₂₃	C₂²×Q₈	1	4	yes	—
201	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₂₃	—	2	2	no	—
203	C₂×D₂₃	—	2	2	no	—
204	C₂×D₂₃	—	2	16	no	—
205	C₂×D₂₃	C₂²×Q₈	1	4	yes	—
206	C₂×D₂₃	C₂²×Q₈	1	2	yes	—
207	C₂×D₂₃	C₂×#41	1	2	yes	—
208	C₂×D₂₃	H(5,𝔽₂)	1	2	yes	—
209	C₄×C₂₃	—	2	2	no	—
210	C₄×C₂₃	—	2	2	no	—
211	C₄×C₂₃	—	2	1	no	—
212	C₄×C₂₃	—	2	4	no	—
213	C₄×C₂₃	—	2	2	no	—
214	C₄×C₂₃	C₂²×Q₈	1	2	yes	—
215	C₄×C₂₃	C₂×#41	1	2	yes	—
216	Dic₂₃	—	2	2	no	—
217	Dic₂₃	—	2	2	no	—
218	Dic₂₃	—	2	1	no	—
219	Dic₂₃	—	2	4	no	—
220	Dic₂₃	—	2	2	no	—
221	Dic₂₃	C₂²×Q₈	1	2	yes	—
222	Dic₂₃	C₂×#41	1	2	yes	—
223	#554	—	23	1	no	—
224	#554	—	23	2	no	—
225	#554	—	23	4	no	—
226	#554	—	23	2	no	—
227	#554	—	23	1	no	—
228	#554	—	23	1	no	—
229	#554	—	23	2	no	—
230	#554	—	23	2	no	—
231	#554	D₂₃	1	1	yes	characteristic, direct product factor
232	C₂×C₄⋊Q₈	—	23	1	no	—
233	C₂×#125	—	23	2	no	—
234	C₂×C₂²⋊Q₈	—	23	4	no	—
235	C₂×C₂²⋊Q₈	—	23	2	no	—
236	C₂×C₄×Q₈	—	23	1	no	—
237	C₂×C₄×D₄	—	23	2	no	—
238	C₂×C₄×D₄	—	23	1	no	—
239	C₂²×C₄⋊C₄	—	23	2	no	—
240	C₂×C₂₃	—	2	4	no	—
241	C₂×C₂₃	C₂³×Q₈	1	1	yes	characteristic
242	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
243	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	D₂₃	—	2	4	no	—
245	D₂₃	#554	1	4	yes	direct product factor
246	C₂²×Q₈	—	23	1	no	—
247	C₂²×Q₈	—	23	2	no	—
248	C₂²×D₄	—	23	1	no	—
249	C₂³×C₄	—	23	2	no	—
250	C₂³×C₄	—	23	4	no	—
251	C₄⋊Q₈	—	23	2	no	—
252	C₄⋊Q₈	—	23	2	no	—
253	C₄⋊Q₈	—	23	2	no	—
254	C₄⋊Q₈	—	23	1	no	—
255	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
256	#125	—	23	4	no	—
257	#125	—	23	4	no	—
258	#125	—	23	2	no	—
259	#125	—	23	2	no	—
260	#125	—	23	2	no	—
261	#125	C₂×D₂₃	1	2	yes	complemented
262	C₂²⋊Q₈	—	23	4	no	—
263	C₂²⋊Q₈	—	23	2	no	—
264	C₂²⋊Q₈	—	23	4	no	—
265	C₂²⋊Q₈	—	23	2	no	—
266	C₂²⋊Q₈	—	23	4	no	—
267	C₂²⋊Q₈	—	23	4	no	—
268	C₂²⋊Q₈	—	23	4	no	—
269	C₂²⋊Q₈	—	23	4	no	—
270	C₂²⋊Q₈	—	23	2	no	—
271	C₂²⋊Q₈	—	23	4	no	—
272	C₂²⋊Q₈	—	23	4	no	—
273	C₂²⋊Q₈	—	23	4	no	—
274	C₂²⋊Q₈	C₂×D₂₃	1	4	yes	complemented
275	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	complemented
276	C₄×Q₈	—	23	1	no	—
277	C₄×Q₈	—	23	2	no	—
278	C₄×Q₈	—	23	1	no	—
279	C₄×Q₈	—	23	1	no	—
280	C₄×Q₈	—	23	2	no	—
281	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
282	C₄×D₄	—	23	2	no	—
283	C₄×D₄	—	23	1	no	—
284	C₄×D₄	—	23	4	no	—
285	C₄×D₄	—	23	2	no	—
286	C₄×D₄	—	23	2	no	—
287	C₄×D₄	—	23	1	no	—
288	C₄×D₄	—	23	4	no	—
289	C₄×D₄	—	23	2	no	—
290	C₄×D₄	—	23	2	no	—
291	C₄×D₄	—	23	1	no	—
292	C₄×D₄	C₂×D₂₃	1	2	yes	—
293	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	23	4	no	—
295	C₂×C₄⋊C₄	—	23	2	no	—
296	C₂×C₄⋊C₄	—	23	1	no	—
297	C₂×C₄⋊C₄	—	23	4	no	—
298	C₂×C₄⋊C₄	—	23	2	no	—
299	C₂×C₄⋊C₄	—	23	4	no	—
300	C₂×C₄⋊C₄	—	23	2	no	—
301	C₂×C₄⋊C₄	—	23	2	no	—
302	C₂×C₄⋊C₄	—	23	1	no	—
303	C₂×C₄⋊C₄	—	23	2	no	—
304	C₂×C₄⋊C₄	—	23	2	no	—
305	C₂×C₄⋊C₄	—	23	4	no	—
306	C₂×C₄⋊C₄	C₂×D₂₃	1	2	yes	complemented
307	C₂×C₂²⋊C₄	—	23	4	no	—
308	C₂×C₂²⋊C₄	—	23	2	no	—
309	C₂×C₄²	—	23	2	no	—
310	C₂×C₄²	—	23	1	no	—
311	C₂₃	C₂×#554	1	1	yes	characteristic, complemented, Sylow
312	C₂⁴	—	23	2	no	—
313	C₂×Q₈	—	23	2	no	—
314	C₂×Q₈	—	23	1	no	—
315	C₂×Q₈	—	23	4	no	—
316	C₂×Q₈	—	23	2	no	—
317	C₂×Q₈	—	46	4	no	—
318	C₂×Q₈	—	92	4	no	—
319	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
320	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
321	C₂×D₄	—	23	2	no	—
322	C₂×D₄	—	23	8	no	—
323	C₂×D₄	—	23	1	no	—
324	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
325	C₂²×C₄	—	23	1	no	—
326	C₂²×C₄	—	23	1	no	—
327	C₂²×C₄	—	23	2	no	—
328	C₂²×C₄	—	23	4	no	—
329	C₂²×C₄	—	23	2	no	—
330	C₂²×C₄	—	23	1	no	—
331	C₂²×C₄	—	23	2	no	—
332	C₂²×C₄	—	23	2	no	—
333	C₂²×C₄	—	23	4	no	—
334	C₂²×C₄	—	23	2	no	—
335	C₂²×C₄	—	23	2	no	—
336	C₂²×C₄	—	23	4	no	—
337	C₂²×C₄	—	23	4	no	—
338	C₂²×C₄	—	46	8	no	—
339	C₂²×C₄	—	92	8	no	—
340	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
341	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
342	C₄⋊C₄	—	23	2	no	—
343	C₄⋊C₄	—	23	1	no	—
344	C₄⋊C₄	—	23	4	no	—
345	C₄⋊C₄	—	23	4	no	—
346	C₄⋊C₄	—	23	4	no	—
347	C₄⋊C₄	—	23	4	no	—
348	C₄⋊C₄	—	23	2	no	—
349	C₄⋊C₄	—	23	2	no	—
350	C₄⋊C₄	—	23	1	no	—
351	C₄⋊C₄	—	23	4	no	—
352	C₄⋊C₄	—	23	2	no	—
353	C₄⋊C₄	—	23	2	no	—
354	C₄⋊C₄	—	23	2	no	—
355	C₄⋊C₄	—	23	2	no	—
356	C₄⋊C₄	—	23	4	no	—
357	C₄⋊C₄	—	23	4	no	—
358	C₄⋊C₄	—	23	4	no	—
359	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
361	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
362	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
364	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
365	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
366	C₂²⋊C₄	—	23	4	no	—
367	C₂²⋊C₄	—	23	2	no	—
368	C₂²⋊C₄	—	23	4	no	—
369	C₂²⋊C₄	—	23	2	no	—
370	C₂²⋊C₄	—	23	2	no	—
371	C₂²⋊C₄	—	23	4	no	—
372	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
373	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
374	C₄²	—	23	2	no	—
375	C₄²	—	23	2	no	—
376	C₄²	—	23	2	no	—
377	C₄²	—	23	1	no	—
378	C₄²	—	23	1	no	—
379	C₄²	—	23	1	no	—
380	C₄²	C₂²×D₂₃	1	2	yes	—
381	C₄²	C₂²×D₂₃	1	1	yes	characteristic
382	C₂³	—	23	1	no	—
383	C₂³	—	23	8	no	—
384	C₂³	—	23	2	no	—
385	C₂³	—	46	4	no	—
386	C₂³	—	46	4	no	—
387	C₂³	C₂³×D₂₃	1	2	yes	—
388	Q₈	—	2	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	46	4	no	—
391	Q₈	—	46	2	no	—
392	Q₈	—	92	4	no	—
393	Q₈	—	92	2	no	—
394	D₄	—	23	8	no	—
395	D₄	—	23	4	no	—
396	D₄	Q₈×D₂₃	1	4	yes	complemented
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	23	1	no	—
400	C₂×C₄	—	23	1	no	—
401	C₂×C₄	—	23	4	no	—
402	C₂×C₄	—	23	4	no	—
403	C₂×C₄	—	23	2	no	—
404	C₂×C₄	—	23	1	no	—
405	C₂×C₄	—	23	2	no	—
406	C₂×C₄	—	23	2	no	—
407	C₂×C₄	—	23	4	no	—
408	C₂×C₄	—	46	4	no	—
409	C₂×C₄	—	46	4	no	—
410	C₂×C₄	—	46	4	no	—
411	C₂×C₄	—	46	8	no	—
412	C₂×C₄	—	46	4	no	—
413	C₂×C₄	—	46	2	no	—
414	C₂×C₄	—	46	4	no	—
415	C₂×C₄	—	46	4	no	—
416	C₂×C₄	—	92	4	no	—
417	C₂×C₄	—	92	4	no	—
418	C₂×C₄	—	92	4	no	—
419	C₂×C₄	C₂³×D₂₃	1	2	yes	—
420	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₂₃	1	2	yes	—
422	C₂×C₄	C₂³×D₂₃	1	2	yes	—
423	C₂×C₄	C₂³×D₂₃	1	4	yes	—
424	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	23	2	no	—
429	C₂²	—	23	2	no	—
430	C₂²	—	23	2	no	—
431	C₂²	—	23	4	no	—
432	C₂²	—	46	16	no	—
433	C₂²	—	46	2	no	—
434	C₂²	—	46	2	no	—
435	C₂²	C₂×Q₈×D₂₃	1	4	yes	—
436	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	1	no	—
442	C₄	—	23	2	no	—
443	C₄	—	23	2	no	—
444	C₄	—	46	2	no	—
445	C₄	—	46	2	no	—
446	C₄	—	46	2	no	—
447	C₄	—	46	4	no	—
448	C₄	—	46	1	no	—
449	C₄	C₂×Q₈×D₂₃	1	2	yes	—
450	C₄	#41×D₂₃	1	2	yes	—
451	C₂	—	2	4	no	—
452	C₂	—	23	4	no	—
453	C₂	—	46	4	no	—
454	C₂	C₂²×Q₈×D₂₃	1	1	yes	characteristic
455	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
456	C₂	H(5,𝔽₂)×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#554	C₂
prime radical	C₂×D₄×D₂₃	C₂²
hypercenter	#554	D₂₃
hypocenter	C₂₃	C₂×#554
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #13093128	C₂	semidirect
2. #13093127	C₂	semidirect
3. #13093126	C₂	semidirect
4. #13093125	C₂	semidirect
5. #13093124	C₂	semidirect
6. #13093123	C₂	semidirect
7. #13093122	C₂	semidirect
8. #13093121	C₂	semidirect
9. C₄⋊Q₈×D₂₃	C₂	semidirect
10. #125×D₂₃	C₂	semidirect
11. C₂²⋊Q₈×D₂₃	C₂	semidirect
12. C₂²⋊Q₈×D₂₃	C₂	semidirect
13. C₄×Q₈×D₂₃	C₂	semidirect
16. C₂×C₄⋊C₄×D₂₃	C₂	semidirect
17. C₂₃×#554	C₂	semidirect
23. C₂₃×C₄⋊Q₈	C₂²	semidirect
24. C₂₃×#125	C₂²	semidirect
25. C₂₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂₃×C₂²⋊Q₈	C₂²	semidirect
27. C₄×Q₈×C₂₃	C₂²	semidirect
30. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
31. #10625117	C₂²	semidirect
32. #10625117	C₂²	semidirect
33. Q₈×Dic₂₃	C₂²	semidirect
34. #10625115	C₂²	semidirect
39. C₂×C₄⋊Dic₂₃	C₂²	semidirect
40. #10625095	C₂²	semidirect
41. #10625095	C₂²	semidirect
42. C₂×Dic₂₃⋊C₄	C₂²	semidirect
43. #10625068	C₂²	semidirect
44. #10625068	C₂²	semidirect
45. #10625067	C₂²	semidirect
46. #10625067	C₂²	semidirect
47. #10625067	C₂²	semidirect
57. C₄⋊C₄×D₂₃	C₂²	semidirect
58. C₄⋊C₄×D₂₃	C₂²	semidirect
59. C₄⋊C₄×D₂₃	C₂²	semidirect
60. #10625061	C₂²	semidirect
61. #10625061	C₂²	semidirect
62. #10625060	C₂²	semidirect
63. #10625060	C₂²	semidirect
64. #10625059	C₂²	semidirect
65. #10625059	C₂²	semidirect
66. #10625058	C₂²	semidirect
67. #10625058	C₂²	semidirect
72. #10625049	C₂²	semidirect
73. #10625049	C₂²	semidirect
74. #10625049	C₂²	semidirect
79. #10625041	C₂²	semidirect
80. #10625040	C₂²	semidirect
81. C₄×Dic₄₆	C₂²	semidirect
82. C₄×Dic₄₆	C₂²	semidirect
94. D₄×D₂₃	Q₈	semidirect
161. D₄×C₂₃	C₂×Q₈	semidirect
171. C₂²⋊D₂₃	C₂×Q₈	semidirect
181. D₉₂	C₂×Q₈	semidirect
231. #554	D₂₃	direct (N × H)
245. D₂₃	#554	direct (N × H)
255. C₄⋊Q₈	C₂×D₂₃	semidirect
261. #125	C₂×D₂₃	semidirect
274. C₂²⋊Q₈	C₂×D₂₃	semidirect
275. C₂²⋊Q₈	C₂×D₂₃	semidirect
281. C₄×Q₈	C₂×D₂₃	semidirect
306. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
311. C₂₃	C₂×#554	semidirect
396. D₄	Q₈×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
#13093128	2
#13093127	2
#13093126	2
#13093125	2
#13093124	2
#13093123	2
#13093122	2
#13093121	2
C₄⋊Q₈×D₂₃	2
#125×D₂₃	2
C₂²⋊Q₈×D₂₃	2
C₄×Q₈×D₂₃	2
C₄×D₄×D₂₃	2
C₂×C₄⋊C₄×D₂₃	2
C₂₃×#554	2
C₂×#554	23

Subgroups — D23×#554 #15686924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#554 #15686924