Subgroups — #41×C₂²⋊D₂₃ #15686882

Order 2944.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093086	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093078	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093074	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093066	C₂	1	3	yes	maximal, complemented
7	#13093061	C₂	1	3	yes	maximal, complemented
8	#13093055	C₂	1	3	yes	maximal, complemented
9	D₄×C₂²⋊D₂₃	C₂	1	3	yes	maximal, complemented
10	#13092963	C₂	1	3	yes	maximal, complemented
11	#13092928	C₂	1	3	yes	maximal, complemented
12	#13092924	C₂	1	3	yes	maximal, complemented
13	#41×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₂²⋊D₂₃	C₂	1	3	yes	maximal, complemented
15	C₂²×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₃	—	2	8	no	—
17	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×#41×C₂₃	C₂²	1	3	yes	complemented
19	C₂×#41×C₂₃	C₂²	1	3	yes	complemented
20	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄×C₂₃	C₂²	1	3	yes	complemented
23	C₂³×C₄×C₂₃	C₂²	1	3	yes	complemented
24	C₂²×C₂²⋊D₂₃	C₂²	1	3	yes	—
25	#41×D₂₃	—	2	8	no	—
26	C₂×#67292	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#67290	C₂²	1	3	yes	complemented
29	C₂×D₄×D₂₃	C₂²	1	3	yes	complemented
30	C₂×#67288	C₂²	1	3	yes	complemented
31	C₂²×C₄×D₂₃	C₂²	1	3	yes	complemented
32	#10625124	C₂²	1	6	yes	complemented
33	C₂×C₂²⋊Dic₂₃	C₂²	1	3	yes	complemented
34	#10625118	C₂²	1	3	yes	complemented
35	#10625117	C₂²	1	3	yes	complemented
36	#10625117	C₂²	1	3	yes	complemented
37	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
38	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
39	#10625115	C₂²	1	3	yes	complemented
40	#10625111	C₂²	1	3	yes	complemented
41	#10625110	C₂²	1	6	yes	complemented
42	#10625110	C₂²	1	6	yes	complemented
43	#10625109	C₂²	1	3	yes	complemented
44	#10625109	C₂²	1	3	yes	complemented
45	#10625108	C₂²	1	6	yes	complemented
46	#10625107	C₂²	1	3	yes	complemented
47	#10625106	C₂²	1	6	yes	complemented
48	D₄×Dic₂₃	C₂²	1	3	yes	complemented
49	D₄×Dic₂₃	C₂²	1	3	yes	complemented
50	#10625101	C₂²	1	3	yes	complemented
51	#10625101	C₂²	1	3	yes	complemented
52	#10625100	C₂²	1	6	yes	complemented
53	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	—
55	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
56	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
57	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
58	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
59	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
60	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
61	C₄×C₂²⋊D₂₃	C₂²	1	6	yes	complemented
62	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	3	yes	complemented
63	#10625097	C₂²	1	3	yes	complemented
64	#10625095	C₂²	1	3	yes	complemented
65	#10625095	C₂²	1	3	yes	complemented
66	C₂×Dic₂₃⋊C₄	C₂²	1	3	yes	complemented
67	C₂×C₄×Dic₂₃	C₂²	1	3	yes	complemented
68	C₂⁴×C₂₃	C₂³	1	3	yes	—
69	C₂³×D₂₃	C₂³	1	3	yes	—
70	#41×C₂₃	—	2	4	no	—
71	#41×C₂₃	—	2	12	no	—
72	#41×C₂₃	—	2	12	no	—
73	#41×C₂₃	D₄	1	8	yes	complemented
74	C₂×Q₈×C₂₃	—	2	4	no	—
75	C₂×Q₈×C₂₃	C₂³	1	3	yes	—
76	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₂₃	—	2	12	no	—
78	C₂×D₄×C₂₃	C₂³	1	6	yes	—
79	C₂×D₄×C₂₃	C₂³	1	3	yes	—
80	C₂×D₄×C₂₃	C₂³	1	3	yes	—
81	C₂²×C₄×C₂₃	—	2	12	no	—
82	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
83	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
84	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
85	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
87	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
88	C₂×C₂²⋊D₂₃	—	2	12	no	—
89	C₂×C₂²⋊D₂₃	C₂³	1	3	yes	—
90	C₂×C₂²⋊D₂₃	C₂³	1	3	yes	—
91	C₂×C₂²⋊D₂₃	C₂³	1	3	yes	—
92	C₂×C₂²⋊D₂₃	C₂³	1	6	yes	—
93	C₂×C₂²⋊D₂₃	C₂³	1	6	yes	—
94	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
95	C₂²×Dic₂₃	C₂³	1	3	yes	—
96	C₂²×Dic₂₃	C₂³	1	3	yes	—
97	C₂²×Dic₂₃	C₂³	1	3	yes	—
98	#67292	—	2	4	no	—
99	Q₈×D₂₃	—	2	4	no	—
100	#67290	—	2	12	no	—
101	D₄×D₂₃	—	2	12	no	—
102	#67288	—	2	12	no	—
103	C₂×D₉₂	C₂³	1	3	yes	—
104	C₂×C₄×D₂₃	—	2	12	no	—
105	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₂₃	C₂³	1	3	yes	—
107	C₂×C₄×D₂₃	C₂³	1	3	yes	—
108	C₂×C₄×D₂₃	C₂³	1	3	yes	—
109	C₂×Dic₄₆	C₂³	1	3	yes	—
110	C₂²⋊Dic₂₃	C₂³	1	3	yes	—
111	C₂²⋊Dic₂₃	C₂³	1	6	yes	—
112	C₂²⋊Dic₂₃	C₂³	1	6	yes	—
113	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
114	C₂²⋊Dic₂₃	C₂³	1	3	yes	—
115	C₂²⋊Dic₂₃	C₂³	1	3	yes	—
116	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
117	(C₂×D₂₃)⋊C₄	C₂³	1	3	yes	—
118	(C₂×D₂₃)⋊C₄	C₂³	1	3	yes	—
119	(C₂×D₂₃)⋊C₄	C₂³	1	3	yes	—
120	(C₂×D₂₃)⋊C₄	C₂³	1	6	yes	—
121	C₄⋊Dic₂₃	C₂³	1	3	yes	—
122	C₄⋊Dic₂₃	C₂³	1	3	yes	—
123	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
124	Dic₂₃⋊C₄	C₂³	1	3	yes	—
125	Dic₂₃⋊C₄	C₂³	1	3	yes	—
126	Dic₂₃⋊C₄	C₂³	1	3	yes	—
127	Dic₂₃⋊C₄	C₂³	1	6	yes	—
128	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
129	C₄×Dic₂₃	C₂³	1	3	yes	—
130	C₄×Dic₂₃	C₂³	1	3	yes	—
131	C₄×Dic₂₃	C₂³	1	3	yes	—
132	C₂³×C₂₃	—	2	6	no	—
133	C₂³×C₂₃	—	2	6	no	—
134	C₂³×C₂₃	—	4	3	no	—
135	C₂³×C₂₃	C₂⁴	1	3	yes	—
136	C₂³×C₂₃	C₂⁴	1	3	yes	—
137	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
138	C₂²×D₂₃	—	2	6	no	—
139	C₂²×D₂₃	—	2	6	no	—
140	C₂²×D₂₃	—	4	3	no	—
141	C₂²×D₂₃	C₂⁴	1	3	yes	—
142	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
143	Q₈×C₂₃	—	2	6	no	—
144	Q₈×C₂₃	C₂×D₄	1	4	yes	complemented
145	D₄×C₂₃	—	2	12	no	—
146	D₄×C₂₃	—	2	6	no	—
147	D₄×C₂₃	C₂×D₄	1	12	yes	complemented
148	C₂×C₄×C₂₃	—	2	6	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	6	no	—
151	C₂×C₄×C₂₃	—	2	6	no	—
152	C₂×C₄×C₂₃	—	2	6	no	—
153	C₂×C₄×C₂₃	C₂×D₄	1	12	yes	complemented
154	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₂₃	C₂⁴	1	3	yes	—
156	C₂×C₄×C₂₃	C₂⁴	1	3	yes	—
157	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
158	C₂²⋊D₂₃	—	2	12	no	—
159	C₂²⋊D₂₃	—	2	6	no	—
160	C₂²⋊D₂₃	—	2	6	no	—
161	C₂²⋊D₂₃	—	2	6	no	—
162	C₂²⋊D₂₃	—	4	6	no	—
163	C₂²⋊D₂₃	#41	1	4	yes	direct product factor
164	C₂×Dic₂₃	—	2	6	no	—
165	C₂×Dic₂₃	—	2	6	no	—
166	C₂×Dic₂₃	—	4	3	no	—
167	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₂₃	C₂⁴	1	3	yes	—
169	C₂×Dic₂₃	C₂⁴	1	3	yes	—
170	C₂×Dic₂₃	C₂⁴	1	3	yes	—
171	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
172	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
173	D₉₂	—	2	6	no	—
174	C₄×D₂₃	—	2	2	no	—
175	C₄×D₂₃	—	2	6	no	—
176	C₄×D₂₃	—	2	6	no	—
177	C₄×D₂₃	—	2	6	no	—
178	Dic₄₆	—	2	6	no	—
179	D₄×#41	—	23	1	no	maximal, Sylow
180	C₂²×C₂₃	—	2	1	no	—
181	C₂²×C₂₃	—	2	3	no	—
182	C₂²×C₂₃	—	2	3	no	—
183	C₂²×C₂₃	—	2	1	no	—
184	C₂²×C₂₃	—	2	3	no	—
185	C₂²×C₂₃	—	2	3	no	—
186	C₂²×C₂₃	—	2	3	no	—
187	C₂²×C₂₃	—	4	12	no	—
188	C₂²×C₂₃	C₂²×D₄	1	6	yes	—
189	C₂²×C₂₃	C₂×#41	1	2	yes	complemented
190	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
191	C₂×D₂₃	—	2	1	no	—
192	C₂×D₂₃	—	2	1	no	—
193	C₂×D₂₃	—	2	3	no	—
194	C₂×D₂₃	—	2	3	no	—
195	C₂×D₂₃	—	2	3	no	—
196	C₂×D₂₃	—	4	12	no	—
197	C₂×D₂₃	C₂×#41	1	2	yes	complemented
198	C₄×C₂₃	—	2	1	no	—
199	C₄×C₂₃	—	2	3	no	—
200	C₄×C₂₃	C₂²×D₄	1	6	yes	—
201	C₄×C₂₃	C₂²×D₄	1	2	yes	—
202	Dic₂₃	—	2	3	no	—
203	Dic₂₃	—	2	1	no	—
204	Dic₂₃	—	2	3	no	—
205	Dic₂₃	—	2	1	no	—
206	Dic₂₃	—	2	3	no	—
207	Dic₂₃	C₂×#41	1	2	yes	complemented
208	C₂²×#41	—	23	1	no	—
209	C₂²×#41	D₂₃	1	1	yes	characteristic, complemented
210	#550	—	23	1	no	—
211	D₄×Q₈	—	23	1	no	—
212	#548	—	23	1	no	—
213	#548	—	23	1	no	—
214	#547	—	23	3	no	—
215	#546	—	23	3	no	—
216	#546	—	23	3	no	—
217	D₄²	—	23	3	no	—
218	#532	—	23	3	no	—
219	#525	—	23	3	no	—
220	#525	—	23	3	no	—
221	C₄×#41	—	23	1	no	—
222	C₂×C₄×D₄	—	23	3	no	—
223	C₂×C₂₃	—	2	6	no	—
224	C₂×C₂₃	—	2	2	no	—
225	C₂×C₂₃	—	4	3	no	—
226	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
227	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
228	C₂×C₂₃	#585	1	1	yes	characteristic
229	D₂₃	—	2	2	no	—
230	D₂₃	—	4	3	no	—
231	C₂×#41	—	2	8	no	—
232	C₂×#41	—	23	1	no	—
233	C₂×#41	—	23	3	no	—
234	C₂×#41	—	23	3	no	—
235	C₂×#41	—	46	8	no	—
236	C₂×#41	C₂×D₂₃	1	1	yes	characteristic
237	C₂×#41	C₂×D₂₃	1	3	yes	complemented
238	C₂×#41	C₂×D₂₃	1	3	yes	complemented
239	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
240	C₂²×Q₈	—	23	1	no	—
241	C₂²×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
242	C₂²×D₄	—	23	3	no	—
243	C₂²×D₄	—	23	3	no	—
244	C₂²×D₄	C₂×D₂₃	1	3	yes	complemented
245	C₂³×C₄	—	23	3	no	—
246	C₂³×C₄	C₂×D₂₃	1	3	yes	complemented
247	C₄⋊Q₈	—	23	3	no	—
248	#127	—	23	3	no	—
249	#124	—	23	3	no	—
250	#124	—	23	3	no	—
251	#123	—	23	6	no	—
252	#123	—	23	6	no	—
253	C₂²⋊Q₈	—	23	3	no	—
254	C₂²⋊Q₈	—	23	3	no	—
255	C₂²⋊Q₈	—	23	3	no	—
256	C₂²⋊Q₈	—	23	3	no	—
257	#121	—	23	3	no	—
258	#121	—	23	3	no	—
259	#121	—	23	6	no	—
260	#121	—	23	6	no	—
261	#121	—	23	3	no	—
262	#121	—	23	3	no	—
263	#120	—	23	6	no	—
264	#120	—	23	6	no	—
265	C₄×Q₈	—	23	1	no	—
266	C₄×Q₈	—	23	1	no	—
267	C₄×D₄	—	23	3	no	—
268	C₄×D₄	—	23	3	no	—
269	C₄×D₄	—	23	1	no	—
270	C₄×D₄	—	23	3	no	—
271	C₄×D₄	—	23	3	no	—
272	C₄×D₄	—	23	3	no	—
273	C₄×D₄	—	23	3	no	—
274	C₄×D₄	—	23	3	no	—
275	C₄×D₄	—	23	3	no	—
276	C₄×D₄	—	23	3	no	—
277	C₄×D₄	—	23	6	no	—
278	#117	—	23	3	no	—
279	C₂×C₄⋊C₄	—	23	3	no	—
280	C₂×C₂²⋊C₄	—	23	3	no	—
281	C₂×C₂²⋊C₄	—	23	3	no	—
282	C₂×C₄²	—	23	3	no	—
283	C₂₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
284	C₂⁴	—	23	3	no	—
285	C₂⁴	C₂²×D₂₃	1	3	yes	—
286	#41	—	2	4	no	—
287	#41	—	2	12	no	—
288	#41	—	2	12	no	—
289	#41	—	46	4	no	—
290	#41	—	46	12	no	—
291	#41	—	46	12	no	—
292	#41	C₂²⋊D₂₃	1	8	yes	direct product factor
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	23	3	no	—
295	C₂×Q₈	—	46	4	no	—
296	C₂×Q₈	C₂²×D₂₃	1	3	yes	—
297	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
298	C₂×D₄	—	2	12	no	—
299	C₂×D₄	—	23	1	no	—
300	C₂×D₄	—	23	3	no	—
301	C₂×D₄	—	23	3	no	—
302	C₂×D₄	—	23	3	no	—
303	C₂×D₄	—	23	6	no	—
304	C₂×D₄	—	23	6	no	—
305	C₂×D₄	—	23	3	no	—
306	C₂×D₄	—	46	12	no	—
307	C₂×D₄	—	46	12	no	—
308	C₂×D₄	C₂²×D₂₃	1	6	yes	—
309	C₂×D₄	C₂²×D₂₃	1	3	yes	—
310	C₂×D₄	C₂²×D₂₃	1	3	yes	—
311	C₂²×C₄	—	2	12	no	—
312	C₂²×C₄	—	23	3	no	—
313	C₂²×C₄	—	23	3	no	—
314	C₂²×C₄	—	23	3	no	—
315	C₂²×C₄	—	23	3	no	—
316	C₂²×C₄	—	23	3	no	—
317	C₂²×C₄	—	23	1	no	—
318	C₂²×C₄	—	23	3	no	—
319	C₂²×C₄	—	46	12	no	—
320	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
321	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
322	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
323	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
325	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
326	C₄⋊C₄	—	23	1	no	—
327	C₄⋊C₄	—	23	3	no	—
328	C₄⋊C₄	—	23	3	no	—
329	C₄⋊C₄	—	23	3	no	—
330	C₄⋊C₄	—	23	3	no	—
331	C₄⋊C₄	—	23	3	no	—
332	C₄⋊C₄	—	23	6	no	—
333	C₂²⋊C₄	—	23	1	no	—
334	C₂²⋊C₄	—	23	3	no	—
335	C₂²⋊C₄	—	23	3	no	—
336	C₂²⋊C₄	—	23	3	no	—
337	C₂²⋊C₄	—	23	6	no	—
338	C₂²⋊C₄	—	23	6	no	—
339	C₂²⋊C₄	—	23	1	no	—
340	C₂²⋊C₄	—	23	3	no	—
341	C₂²⋊C₄	—	23	3	no	—
342	C₂²⋊C₄	—	23	3	no	—
343	C₂²⋊C₄	—	23	6	no	—
344	C₄²	—	23	3	no	—
345	C₄²	—	23	3	no	—
346	C₄²	—	23	1	no	—
347	C₄²	—	23	3	no	—
348	C₂³	—	2	6	no	—
349	C₂³	—	2	6	no	—
350	C₂³	—	4	3	no	—
351	C₂³	—	23	1	no	—
352	C₂³	—	23	3	no	—
353	C₂³	—	46	6	no	—
354	C₂³	—	46	6	no	—
355	C₂³	—	92	3	no	—
356	C₂³	C₂³×D₂₃	1	3	yes	—
357	C₂³	C₂³×D₂₃	1	1	yes	characteristic
358	C₂³	C₂³×D₂₃	1	3	yes	—
359	Q₈	—	2	6	no	—
360	Q₈	—	46	6	no	—
361	Q₈	C₂×C₂²⋊D₂₃	1	4	yes	complemented
362	D₄	—	2	12	no	—
363	D₄	—	2	6	no	—
364	D₄	—	23	4	no	—
365	D₄	—	46	6	no	—
366	D₄	—	46	6	no	—
367	D₄	—	46	6	no	—
368	D₄	—	46	12	no	—
369	D₄	—	46	6	no	—
370	D₄	—	92	6	no	—
371	D₄	C₂×C₂²⋊D₂₃	1	12	yes	complemented
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	23	1	no	—
378	C₂×C₄	—	23	1	no	—
379	C₂×C₄	—	23	3	no	—
380	C₂×C₄	—	23	3	no	—
381	C₂×C₄	—	23	1	no	—
382	C₂×C₄	—	23	3	no	—
383	C₂×C₄	—	46	6	no	—
384	C₂×C₄	—	46	6	no	—
385	C₂×C₄	—	46	2	no	—
386	C₂×C₄	—	46	6	no	—
387	C₂×C₄	—	46	6	no	—
388	C₂×C₄	—	46	6	no	—
389	C₂×C₄	—	92	3	no	—
390	C₂×C₄	C₂×C₂²⋊D₂₃	1	12	yes	complemented
391	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₂₃	1	3	yes	—
393	C₂×C₄	C₂³×D₂₃	1	3	yes	—
394	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
395	C₂²	—	2	1	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	2	3	no	—
402	C₂²	—	4	12	no	—
403	C₂²	—	23	2	no	—
404	C₂²	—	46	1	no	—
405	C₂²	—	46	1	no	—
406	C₂²	—	46	3	no	—
407	C₂²	—	46	3	no	—
408	C₂²	—	46	3	no	—
409	C₂²	—	92	12	no	—
410	C₂²	#41×D₂₃	1	2	yes	complemented
411	C₂²	C₂²×C₂²⋊D₂₃	1	6	yes	—
412	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	3	no	—
415	C₄	—	23	2	no	—
416	C₄	—	46	1	no	—
417	C₄	—	46	3	no	—
418	C₄	—	46	3	no	—
419	C₄	—	46	1	no	—
420	C₄	—	46	3	no	—
421	C₄	C₂²×C₂²⋊D₂₃	1	2	yes	—
422	C₄	C₂²×C₂²⋊D₂₃	1	6	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	2	6	no	—
425	C₂	—	4	3	no	—
426	C₂	—	46	2	no	—
427	C₂	—	92	3	no	—
428	C₂	C₂³×C₂²⋊D₂₃	1	1	yes	characteristic
429	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
430	C₂	#13093253	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂²×#41×C₂₃	C₂
hypercenter	C₂²×#41	D₂₃
hypocenter	C₂₃	D₄×#41
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₂₃	C₂	semidirect
2. #13093086	C₂	semidirect
3. Q₈×C₂²⋊D₂₃	C₂	semidirect
4. #13093078	C₂	semidirect
5. #13093074	C₂	semidirect
6. #13093066	C₂	semidirect
7. #13093061	C₂	semidirect
8. #13093055	C₂	semidirect
9. D₄×C₂²⋊D₂₃	C₂	semidirect
10. #13092963	C₂	semidirect
11. #13092928	C₂	semidirect
12. #13092924	C₂	semidirect
13. #41×Dic₂₃	C₂	semidirect
14. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
15. C₂²×#41×C₂₃	C₂	semidirect
18. C₂×#41×C₂₃	C₂²	semidirect
19. C₂×#41×C₂₃	C₂²	semidirect
20. C₂×#41×C₂₃	C₂²	semidirect
21. C₂²×Q₈×C₂₃	C₂²	semidirect
22. C₂²×D₄×C₂₃	C₂²	semidirect
23. C₂³×C₄×C₂₃	C₂²	semidirect
26. C₂×#67292	C₂²	semidirect
27. C₂×Q₈×D₂₃	C₂²	semidirect
28. C₂×#67290	C₂²	semidirect
29. C₂×D₄×D₂₃	C₂²	semidirect
30. C₂×#67288	C₂²	semidirect
31. C₂²×C₄×D₂₃	C₂²	semidirect
32. #10625124	C₂²	semidirect
33. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
34. #10625118	C₂²	semidirect
35. #10625117	C₂²	semidirect
36. #10625117	C₂²	semidirect
37. Q₈×Dic₂₃	C₂²	semidirect
38. Q₈×Dic₂₃	C₂²	semidirect
39. #10625115	C₂²	semidirect
40. #10625111	C₂²	semidirect
41. #10625110	C₂²	semidirect
42. #10625110	C₂²	semidirect
43. #10625109	C₂²	semidirect
44. #10625109	C₂²	semidirect
45. #10625108	C₂²	semidirect
46. #10625107	C₂²	semidirect
47. #10625106	C₂²	semidirect
48. D₄×Dic₂₃	C₂²	semidirect
49. D₄×Dic₂₃	C₂²	semidirect
50. #10625101	C₂²	semidirect
51. #10625101	C₂²	semidirect
52. #10625100	C₂²	semidirect
55. C₄×C₂²⋊D₂₃	C₂²	semidirect
56. C₄×C₂²⋊D₂₃	C₂²	semidirect
57. C₄×C₂²⋊D₂₃	C₂²	semidirect
58. C₄×C₂²⋊D₂₃	C₂²	semidirect
59. C₄×C₂²⋊D₂₃	C₂²	semidirect
60. C₄×C₂²⋊D₂₃	C₂²	semidirect
61. C₄×C₂²⋊D₂₃	C₂²	semidirect
62. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
63. #10625097	C₂²	semidirect
64. #10625095	C₂²	semidirect
65. #10625095	C₂²	semidirect
66. C₂×Dic₂₃⋊C₄	C₂²	semidirect
67. C₂×C₄×Dic₂₃	C₂²	semidirect
73. #41×C₂₃	D₄	semidirect
144. Q₈×C₂₃	C₂×D₄	semidirect
147. D₄×C₂₃	C₂×D₄	semidirect
153. C₂×C₄×C₂₃	C₂×D₄	semidirect
163. C₂²⋊D₂₃	#41	direct (N × H)
189. C₂²×C₂₃	C₂×#41	semidirect
197. C₂×D₂₃	C₂×#41	semidirect
207. Dic₂₃	C₂×#41	semidirect
209. C₂²×#41	D₂₃	semidirect
237. C₂×#41	C₂×D₂₃	semidirect
238. C₂×#41	C₂×D₂₃	semidirect
239. C₂×#41	C₂×D₂₃	semidirect
241. C₂²×Q₈	C₂×D₂₃	semidirect
244. C₂²×D₄	C₂×D₂₃	semidirect
246. C₂³×C₄	C₂×D₂₃	semidirect
283. C₂₃	D₄×#41	semidirect
292. #41	C₂²⋊D₂₃	direct (N × H)
361. Q₈	C₂×C₂²⋊D₂₃	semidirect
371. D₄	C₂×C₂²⋊D₂₃	semidirect
390. C₂×C₄	C₂×C₂²⋊D₂₃	semidirect
410. C₂²	#41×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₂₃	2
#13093086	2
Q₈×C₂²⋊D₂₃	2
#13093078	2
#13093074	2
#13093066	2
#13093061	2
#13093055	2
D₄×C₂²⋊D₂₃	2
#13092963	2
#13092928	2
#13092924	2
#41×Dic₂₃	2
C₂×C₄×C₂²⋊D₂₃	2
C₂²×#41×C₂₃	2
D₄×#41	23

Subgroups — #41×C22⋊D23 #15686882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×C₂²⋊D₂₃ #15686882