Subgroups — C₂₃×#61435 #19209061

Order 5888.

1852 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3482	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3359	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3342	C₂	1	3	yes	maximal, complemented
6	C₂₃×#3302	C₂	1	6	yes	maximal, complemented
7	C₂₃×#3283	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3170	C₂	1	3	yes	maximal, complemented
9	C₂₃×#3107	C₂	1	6	yes	maximal, complemented
10	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#135	C₂	1	3	yes	maximal, complemented
12	C₂×C₂₃×#135	C₂²	1	3	yes	—
13	C₂₃×#557	C₂²	1	2	yes	—
14	C₂₃×#556	C₂²	1	6	yes	—
15	C₂₃×#552	—	2	6	no	—
16	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
17	C₂₃×#548	—	2	2	no	—
18	C₂₃×#547	C₂²	1	6	yes	—
19	C₂₃×#533	C₂²	1	6	yes	—
20	C₂₃×#529	—	2	6	no	—
21	C₄×#41×C₂₃	C₂²	1	6	yes	—
22	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
24	C₂₃×#500	C₂²	1	3	yes	—
25	C₂₃×#494	C₂²	1	3	yes	—
26	C₂₃×#487	C₂²	1	6	yes	—
27	C₂₃×#485	C₂²	1	12	yes	—
28	C₂₃×#475	C₂²	1	6	yes	—
29	C₂₃×#474	C₂²	1	6	yes	—
30	C₂₃×#467	C₂²	1	6	yes	—
31	C₂₃×#467	C₂²	1	6	yes	—
32	C₂₃×#462	C₂²	1	6	yes	—
33	C₂₃×#461	C₂²	1	6	yes	—
34	C₂₃×#452	C₂²	1	12	yes	—
35	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₂₃	C₂²	1	3	yes	—
38	C₄×Q₁₆×C₂₃	C₂²	1	6	yes	—
39	C₄×Q₁₆×C₂₃	C₂²	1	3	yes	—
40	C₄×SD₁₆×C₂₃	C₂²	1	6	yes	—
41	C₄×SD₁₆×C₂₃	C₂²	1	6	yes	—
42	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₄×D₈×C₂₃	C₂²	1	3	yes	—
44	C₈×D₄×C₂₃	C₂²	1	3	yes	—
45	C₈×D₄×C₂₃	C₂²	1	3	yes	—
46	C₂₃×#431	C₂²	1	3	yes	—
47	C₂₃×#427	C₂²	1	3	yes	—
48	C₂₃×#416	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₂₃	C₂²	1	3	yes	—
50	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
51	C₂×#41×C₂₃	C₂³	1	6	yes	—
52	C₂²×Q₈×C₂₃	—	2	2	no	—
53	C₂₃×#135	—	2	12	no	—
54	C₂×Q₁₆×C₂₃	C₂³	1	3	yes	—
55	C₂×Q₁₆×C₂₃	C₂³	1	6	yes	—
56	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	—
57	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
59	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
60	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
61	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
62	C₂₃×#126	—	2	12	no	—
63	C₂₃×#125	—	2	6	no	—
64	C₂₃×#125	—	2	6	no	—
65	C₂₃×#124	—	2	6	no	—
66	C₂₃×#123	—	2	12	no	—
67	C₂₃×C₂²⋊Q₈	—	2	6	no	—
68	C₂₃×C₂²⋊Q₈	—	2	6	no	—
69	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
70	C₂₃×#121	—	2	6	no	—
71	C₄×Q₈×C₂₃	—	2	2	no	—
72	C₄×Q₈×C₂₃	—	2	6	no	—
73	C₄×Q₈×C₂₃	—	2	6	no	—
74	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
76	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
77	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
78	C₄×D₄×C₂₃	—	2	6	no	—
79	C₄×D₄×C₂₃	—	2	6	no	—
80	C₄×D₄×C₂₃	D₄	1	3	yes	—
81	C₄×D₄×C₂₃	C₂³	1	6	yes	—
82	C₄×D₄×C₂₃	C₂³	1	2	yes	—
83	C₄×D₄×C₂₃	C₂³	1	3	yes	—
84	C₂₃×#117	—	2	6	no	—
85	C₂₃×#117	—	2	6	no	—
86	C₂₃×#117	D₄	1	3	yes	—
87	C₂₃×#117	C₂³	1	6	yes	—
88	C₂×C₄⋊C₄×C₂₃	—	2	6	no	—
89	C₂×C₄²×C₂₃	—	2	6	no	—
90	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
91	C₂₃×#107	C₂³	1	1	yes	characteristic
92	C₂₃×#107	C₂³	1	3	yes	—
93	C₂₃×#107	C₂³	1	6	yes	—
94	C₂₃×#106	C₂³	1	6	yes	—
95	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
96	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
97	C₂₃×#103	C₂³	1	6	yes	—
98	C₂₃×#103	C₂³	1	6	yes	—
99	C₂₃×#103	C₂³	1	12	yes	—
100	C₂₃×#102	C₂³	1	2	yes	—
101	C₂₃×#102	C₂³	1	6	yes	—
102	C₂₃×C₂²⋊C₈	C₂³	1	6	yes	—
103	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₄×C₈×C₂₃	C₂³	1	3	yes	—
105	C₄×C₈×C₂₃	C₂³	1	3	yes	—
106	C₄×C₈×C₂₃	C₂³	1	3	yes	—
107	#41×C₂₃	—	2	4	no	—
108	#41×C₂₃	—	2	12	no	—
109	#41×C₂₃	—	4	6	no	—
110	C₂×Q₈×C₂₃	—	2	6	no	—
111	C₂×Q₈×C₂₃	—	4	8	no	—
112	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
114	C₂×D₄×C₂₃	—	2	6	no	—
115	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
116	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₂₃	—	2	6	no	—
118	C₂²×C₄×C₂₃	—	2	6	no	—
119	C₂²×C₄×C₂₃	—	2	2	no	—
120	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
121	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
122	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
123	Q₁₆×C₂₃	—	2	6	no	—
124	Q₁₆×C₂₃	—	4	6	no	—
125	SD₁₆×C₂₃	—	2	12	no	—
126	D₈×C₂₃	#41	1	4	yes	complemented
127	C₂×C₈×C₂₃	—	2	6	no	—
128	C₂×C₈×C₂₃	—	4	3	no	—
129	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
131	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
132	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
133	C₄⋊C₄×C₂₃	—	2	6	no	—
134	C₄⋊C₄×C₂₃	—	2	12	no	—
135	C₄⋊C₄×C₂₃	—	2	6	no	—
136	C₄⋊C₄×C₂₃	—	2	6	no	—
137	C₄⋊C₄×C₂₃	—	2	6	no	—
138	C₄⋊C₄×C₂₃	—	2	6	no	—
139	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
140	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
141	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
142	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
143	C₂²⋊C₄×C₂₃	—	2	12	no	—
144	C₂²⋊C₄×C₂₃	—	2	6	no	—
145	C₂²⋊C₄×C₂₃	—	2	2	no	—
146	C₂²⋊C₄×C₂₃	—	2	6	no	—
147	C₂²⋊C₄×C₂₃	C₂×D₄	1	6	yes	—
148	C₄²×C₂₃	—	2	6	no	—
149	C₄²×C₂₃	—	2	6	no	—
150	C₄²×C₂₃	—	2	6	no	—
151	C₄²×C₂₃	C₂×D₄	1	3	yes	—
152	C₄²×C₂₃	C₂×D₄	1	3	yes	—
153	C₄²×C₂₃	C₂⁴	1	3	yes	—
154	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
155	#61435	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₂₃	—	2	2	no	—
157	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
158	Q₈×C₂₃	—	2	6	no	—
159	Q₈×C₂₃	—	2	6	no	—
160	Q₈×C₂₃	—	4	12	no	—
161	Q₈×C₂₃	#135	1	4	yes	complemented
162	D₄×C₂₃	—	2	6	no	—
163	D₄×C₂₃	—	2	2	no	—
164	D₄×C₂₃	—	4	12	no	—
165	D₄×C₂₃	C₂×#41	1	4	yes	—
166	C₂×C₄×C₂₃	—	2	6	no	—
167	C₂×C₄×C₂₃	—	2	6	no	—
168	C₂×C₄×C₂₃	—	2	3	no	—
169	C₂×C₄×C₂₃	—	2	3	no	—
170	C₂×C₄×C₂₃	—	2	2	no	—
171	C₂×C₄×C₂₃	—	2	6	no	—
172	C₂×C₄×C₂₃	—	2	6	no	—
173	C₂×C₄×C₂₃	—	4	12	no	—
174	C₂×C₄×C₂₃	—	4	12	no	—
175	C₂×C₄×C₂₃	—	4	4	no	—
176	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
177	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
179	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
180	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
182	C₈×C₂₃	—	2	3	no	—
183	C₈×C₂₃	—	2	1	no	—
184	C₈×C₂₃	—	2	3	no	—
185	C₈×C₂₃	C₂×#41	1	2	yes	—
186	#3482	C₂×C₂₃	1	2	yes	complemented
187	#3395	C₂×C₂₃	1	1	yes	characteristic, complemented
188	Q₈×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
189	#3359	C₂×C₂₃	1	2	yes	complemented
190	#3342	C₂×C₂₃	1	3	yes	complemented
191	#3302	C₂×C₂₃	1	6	yes	complemented
192	#3283	C₂×C₂₃	1	3	yes	complemented
193	#3170	C₂×C₂₃	1	3	yes	complemented
194	#3107	C₂×C₂₃	1	6	yes	complemented
195	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
196	C₄×#135	C₂×C₂₃	1	3	yes	complemented
197	C₂²×C₂₃	—	2	3	no	—
198	C₂²×C₂₃	—	2	4	no	—
199	C₂²×C₂₃	—	2	3	no	—
200	C₂²×C₂₃	—	2	3	no	—
201	C₂²×C₂₃	—	4	2	no	—
202	C₂²×C₂₃	—	4	2	no	—
203	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
204	C₄×C₂₃	—	2	3	no	—
205	C₄×C₂₃	—	2	1	no	—
206	C₄×C₂₃	—	2	3	no	—
207	C₄×C₂₃	—	4	6	no	—
208	C₄×C₂₃	—	4	6	no	—
209	C₄×C₂₃	—	4	2	no	—
210	C₄×C₂₃	C₂×#135	1	6	yes	—
211	C₄×C₂₃	#578	1	2	yes	—
212	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
213	C₄×C₂₃	#585	1	1	yes	characteristic
214	C₂×#135	C₂²×C₂₃	1	3	yes	—
215	#557	C₂²×C₂₃	1	2	yes	—
216	#556	C₂²×C₂₃	1	6	yes	—
217	#552	—	2	6	no	—
218	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
219	#548	—	2	2	no	—
220	#547	C₂²×C₂₃	1	6	yes	—
221	#533	C₂²×C₂₃	1	6	yes	—
222	#529	—	2	6	no	—
223	C₄×#41	C₂²×C₂₃	1	6	yes	—
224	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×C₄×Q₈	—	2	2	no	—
226	#500	C₂²×C₂₃	1	3	yes	—
227	#494	C₂²×C₂₃	1	3	yes	—
228	#487	C₂²×C₂₃	1	6	yes	—
229	#485	C₂²×C₂₃	1	12	yes	—
230	#475	C₂²×C₂₃	1	6	yes	—
231	#474	C₂²×C₂₃	1	6	yes	—
232	#467	C₂²×C₂₃	1	6	yes	—
233	#467	C₂²×C₂₃	1	6	yes	—
234	#462	C₂²×C₂₃	1	6	yes	—
235	#461	C₂²×C₂₃	1	6	yes	—
236	#452	C₂²×C₂₃	1	12	yes	—
237	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
238	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
239	C₄×Q₁₆	C₂²×C₂₃	1	3	yes	—
240	C₄×Q₁₆	C₂²×C₂₃	1	6	yes	—
241	C₄×Q₁₆	C₂²×C₂₃	1	3	yes	—
242	C₄×SD₁₆	C₂²×C₂₃	1	6	yes	—
243	C₄×SD₁₆	C₂²×C₂₃	1	6	yes	—
244	C₄×D₈	C₂²×C₂₃	1	3	yes	—
245	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
246	C₈×D₄	C₂²×C₂₃	1	3	yes	—
247	C₈×D₄	C₂²×C₂₃	1	3	yes	—
248	#431	C₂²×C₂₃	1	3	yes	—
249	#427	C₂²×C₂₃	1	3	yes	—
250	#416	C₂²×C₂₃	1	6	yes	—
251	C₂×C₄×C₈	C₂²×C₂₃	1	3	yes	—
252	C₂×C₂₃	—	4	3	no	—
253	C₂×C₂₃	—	4	4	no	—
254	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
255	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
256	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
257	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
258	C₂×#41	C₂³×C₂₃	1	6	yes	—
259	C₂²×Q₈	—	2	2	no	—
260	#135	—	2	12	no	—
261	C₂×Q₁₆	C₂³×C₂₃	1	3	yes	—
262	C₂×Q₁₆	C₂³×C₂₃	1	6	yes	—
263	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	—
264	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
266	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
267	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
268	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
269	#126	—	2	12	no	—
270	#125	—	2	6	no	—
271	#125	—	2	6	no	—
272	#124	—	2	6	no	—
273	#123	—	2	12	no	—
274	C₂²⋊Q₈	—	2	6	no	—
275	C₂²⋊Q₈	—	2	6	no	—
276	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
277	#121	—	2	6	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	6	no	—
280	C₄×Q₈	—	2	6	no	—
281	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
282	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
283	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
284	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
285	C₄×D₄	—	2	6	no	—
286	C₄×D₄	—	2	6	no	—
287	C₄×D₄	D₄×C₂₃	1	3	yes	—
288	C₄×D₄	C₂³×C₂₃	1	2	yes	—
289	C₄×D₄	C₂³×C₂₃	1	6	yes	—
290	C₄×D₄	C₂³×C₂₃	1	3	yes	—
291	#117	—	2	6	no	—
292	#117	—	2	6	no	—
293	#117	D₄×C₂₃	1	3	yes	—
294	#117	C₂³×C₂₃	1	6	yes	—
295	C₂×C₄⋊C₄	—	2	6	no	—
296	C₂×C₄²	—	2	6	no	—
297	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
298	#107	C₂³×C₂₃	1	1	yes	characteristic
299	#107	C₂³×C₂₃	1	3	yes	—
300	#107	C₂³×C₂₃	1	6	yes	—
301	#106	C₂³×C₂₃	1	6	yes	—
302	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
303	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
304	#103	C₂³×C₂₃	1	6	yes	—
305	#103	C₂³×C₂₃	1	6	yes	—
306	#103	C₂³×C₂₃	1	12	yes	—
307	#102	C₂³×C₂₃	1	2	yes	—
308	#102	C₂³×C₂₃	1	6	yes	—
309	C₂²⋊C₈	C₂³×C₂₃	1	6	yes	—
310	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₂₃	1	3	yes	—
312	C₄×C₈	C₂³×C₂₃	1	3	yes	—
313	C₄×C₈	C₂³×C₂₃	1	3	yes	—
314	C₂₃	#61435	1	1	yes	characteristic, direct product factor, Sylow
315	#41	—	2	4	no	—
316	#41	—	2	12	no	—
317	#41	—	4	6	no	—
318	C₂×Q₈	—	2	6	no	—
319	C₂×Q₈	—	4	8	no	—
320	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
322	C₂×D₄	—	2	6	no	—
323	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
324	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	6	no	—
327	C₂²×C₄	—	2	6	no	—
328	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
329	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
330	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
331	Q₁₆	—	2	6	no	—
332	Q₁₆	—	4	6	no	—
333	SD₁₆	—	2	12	no	—
334	D₈	#41×C₂₃	1	4	yes	complemented
335	C₂×C₈	—	2	6	no	—
336	C₂×C₈	—	4	3	no	—
337	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
338	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
339	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
340	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
341	C₄⋊C₄	—	2	6	no	—
342	C₄⋊C₄	—	2	12	no	—
343	C₄⋊C₄	—	2	6	no	—
344	C₄⋊C₄	—	2	6	no	—
345	C₄⋊C₄	—	2	6	no	—
346	C₄⋊C₄	—	2	6	no	—
347	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
348	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
349	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
350	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
351	C₂²⋊C₄	—	2	12	no	—
352	C₂²⋊C₄	—	2	6	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	6	no	—
355	C₂²⋊C₄	C₂×D₄×C₂₃	1	6	yes	—
356	C₄²	—	2	6	no	—
357	C₄²	—	2	6	no	—
358	C₄²	—	2	6	no	—
359	C₄²	C₂×D₄×C₂₃	1	3	yes	—
360	C₄²	C₂×D₄×C₂₃	1	3	yes	—
361	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
362	C₄²	C₂⁴×C₂₃	1	3	yes	—
363	C₂³	—	2	2	no	—
364	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
365	Q₈	—	2	6	no	—
366	Q₈	—	2	6	no	—
367	Q₈	—	4	12	no	—
368	Q₈	C₂₃×#135	1	4	yes	complemented
369	D₄	—	2	6	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	12	no	—
372	D₄	C₂×#41×C₂₃	1	4	yes	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	3	no	—
376	C₂×C₄	—	2	3	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	6	no	—
379	C₂×C₄	—	2	6	no	—
380	C₂×C₄	—	4	12	no	—
381	C₂×C₄	—	4	12	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
384	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
386	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
387	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
388	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
389	C₈	—	2	3	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	3	no	—
392	C₈	C₂×#41×C₂₃	1	2	yes	—
393	C₂²	—	2	3	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
400	C₄	—	2	3	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	3	no	—
403	C₄	—	4	6	no	—
404	C₄	—	4	6	no	—
405	C₄	—	4	2	no	—
406	C₄	C₂×C₂₃×#135	1	6	yes	—
407	C₄	C₂₃×#578	1	2	yes	—
408	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
409	C₄	C₂₃×#585	1	1	yes	characteristic
410	C₂	—	4	3	no	—
411	C₂	—	4	4	no	—
412	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
413	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
414	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3482	C₂	semidirect
2. C₂₃×#3395	C₂	semidirect
3. Q₈×D₈×C₂₃	C₂	semidirect
4. C₂₃×#3359	C₂	semidirect
5. C₂₃×#3342	C₂	semidirect
6. C₂₃×#3302	C₂	semidirect
7. C₂₃×#3283	C₂	semidirect
8. C₂₃×#3170	C₂	semidirect
9. C₂₃×#3107	C₂	semidirect
10. C₈×#41×C₂₃	C₂	semidirect
11. C₄×C₂₃×#135	C₂	semidirect
126. D₈×C₂₃	#41	semidirect
155. #61435	C₂₃	direct (N × H)
161. Q₈×C₂₃	#135	semidirect
186. #3482	C₂×C₂₃	semidirect
187. #3395	C₂×C₂₃	semidirect
188. Q₈×D₈	C₂×C₂₃	semidirect
189. #3359	C₂×C₂₃	semidirect
190. #3342	C₂×C₂₃	semidirect
191. #3302	C₂×C₂₃	semidirect
192. #3283	C₂×C₂₃	semidirect
193. #3170	C₂×C₂₃	semidirect
194. #3107	C₂×C₂₃	semidirect
195. C₈×#41	C₂×C₂₃	semidirect
196. C₄×#135	C₂×C₂₃	semidirect
314. C₂₃	#61435	direct (N × H)
334. D₈	#41×C₂₃	semidirect
368. Q₈	C₂₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3482	2
C₂₃×#3395	2
Q₈×D₈×C₂₃	2
C₂₃×#3359	2
C₂₃×#3342	2
C₂₃×#3302	2
C₂₃×#3283	2
C₂₃×#3170	2
C₂₃×#3107	2
C₈×#41×C₂₃	2
C₄×C₂₃×#135	2
#61435	23

Subgroups — C23×#61435 #19209061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61435 #19209061