Group #19157029 — subgroups

Subgroups — C₂₃×#9403 #19157029

Order 5888.

570 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2975	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2542	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1800	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1549	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1303	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
8	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#436	—	2	4	no	—
10	C₂₃×#431	C₂²	1	2	yes	—
11	C₂₃×#423	C₂²	1	2	yes	—
12	C₂×C₂₃×#100	—	2	1	no	—
13	C₂₃×#407	—	2	2	no	—
14	C₂₃×#399	C₄	1	4	yes	—
15	C₂₃×#390	—	2	1	no	—
16	C₂₃×#384	—	2	1	no	—
17	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#343	—	2	1	no	—
19	C₂₃×#332	—	2	4	no	—
20	C₂²×Q₈×C₂₃	—	2	1	no	—
21	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₂₃	D₄	1	2	yes	—
23	C₂×M₁₆×C₂₃	—	2	4	no	—
24	C₂×M₁₆×C₂₃	—	2	2	no	—
25	C₂₃×C₄⋊Q₈	—	2	2	no	—
26	C₂₃×C₄⋊Q₈	—	2	2	no	—
27	C₂₃×C₂²⋊Q₈	—	4	8	no	—
28	C₄×D₄×C₂₃	—	2	2	no	—
29	C₄×D₄×C₂₃	—	2	2	no	—
30	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
31	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
32	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
33	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
36	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₂₃	—	2	1	no	—
38	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
39	C₂₃×C₄⋊C₈	—	2	2	no	—
40	C₂₃×C₄⋊C₈	—	2	2	no	—
41	C₂₃×C₄⋊C₈	D₄	1	4	yes	—
42	C₂₃×#100	—	4	2	no	—
43	C₂₃×C₂²⋊C₈	—	2	4	no	—
44	C₂₃×C₂²⋊C₈	—	2	2	no	—
45	C₄×C₈×C₂₃	—	2	2	no	—
46	C₂₃×#95	C₂×C₄	1	2	yes	—
47	C₂⁴×C₂₃	C₂²⋊C₄	1	2	yes	—
48	C₂×Q₈×C₂₃	—	4	4	no	—
49	C₂×Q₈×C₂₃	—	4	1	no	—
50	C₂×Q₈×C₂₃	—	4	1	no	—
51	C₂×D₄×C₂₃	—	2	2	no	—
52	C₂×D₄×C₂₃	—	2	1	no	—
53	C₂×D₄×C₂₃	—	2	2	no	—
54	C₂×D₄×C₂₃	—	2	1	no	—
55	C₂²×C₄×C₂₃	—	2	2	no	—
56	C₂²×C₄×C₂₃	—	2	2	no	—
57	C₂²×C₄×C₂₃	—	2	2	no	—
58	C₂²×C₄×C₂₃	—	2	2	no	—
59	C₂²×C₄×C₂₃	—	4	4	no	—
60	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
64	M₁₆×C₂₃	—	4	2	no	—
65	M₁₆×C₂₃	—	4	2	no	—
66	M₁₆×C₂₃	—	8	4	no	—
67	C₂×C₈×C₂₃	—	2	4	no	—
68	C₂×C₈×C₂₃	—	4	2	no	—
69	C₄⋊C₄×C₂₃	—	2	4	no	—
70	C₄⋊C₄×C₂₃	—	2	2	no	—
71	C₄⋊C₄×C₂₃	—	2	4	no	—
72	C₄⋊C₄×C₂₃	—	4	8	no	—
73	C₄⋊C₄×C₂₃	—	4	2	no	—
74	C₂²⋊C₄×C₂₃	—	2	4	no	—
75	C₂²⋊C₄×C₂₃	—	4	8	no	—
76	C₄²×C₂₃	—	4	1	no	—
77	C₄²×C₂₃	—	4	1	no	—
78	C₄²×C₂₃	C₂×D₄	1	2	yes	—
79	C₄²×C₂₃	#41	1	2	yes	—
80	#9403	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂³×C₂₃	—	2	2	no	—
82	C₂³×C₂₃	—	2	2	no	—
83	C₂³×C₂₃	—	2	2	no	—
84	C₂³×C₂₃	—	4	2	no	—
85	C₂³×C₂₃	—	4	2	no	—
86	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	Q₈×C₂₃	—	8	2	no	—
88	Q₈×C₂₃	—	8	2	no	—
89	D₄×C₂₃	—	4	2	no	—
90	D₄×C₂₃	—	4	2	no	—
91	C₂×C₄×C₂₃	—	2	2	no	—
92	C₂×C₄×C₂₃	—	2	4	no	—
93	C₂×C₄×C₂₃	—	2	2	no	—
94	C₂×C₄×C₂₃	—	4	1	no	—
95	C₂×C₄×C₂₃	—	4	2	no	—
96	C₂×C₄×C₂₃	—	4	2	no	—
97	C₂×C₄×C₂₃	—	4	4	no	—
98	C₂×C₄×C₂₃	—	4	2	no	—
99	C₂×C₄×C₂₃	—	4	4	no	—
100	C₂×C₄×C₂₃	—	4	2	no	—
101	C₂×C₄×C₂₃	—	8	2	no	—
102	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
104	C₂×C₄×C₂₃	#121	1	2	yes	—
105	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
106	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂×C₄×C₂₃	#137	1	2	yes	—
108	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
109	C₈×C₂₃	—	4	4	no	—
110	C₈×C₂₃	—	8	2	no	—
111	#2975	C₂×C₂₃	1	1	yes	characteristic
112	#2542	C₂×C₂₃	1	1	yes	characteristic
113	#1800	C₂×C₂₃	1	1	yes	characteristic
114	#1549	C₂×C₂₃	1	2	yes	complemented
115	#1303	C₂×C₂₃	1	2	yes	complemented
116	C₂²×C₂₃	—	2	1	no	—
117	C₂²×C₂₃	—	2	1	no	—
118	C₂²×C₂₃	—	4	4	no	—
119	C₂²×C₂₃	—	4	2	no	—
120	C₂²×C₂₃	—	4	2	no	—
121	C₂²×C₂₃	—	4	2	no	—
122	C₂²×C₂₃	—	8	2	no	—
123	C₂²×C₂₃	#386	1	1	yes	characteristic
124	C₂²×C₂₃	#417	1	1	yes	characteristic
125	C₂²×C₂₃	#419	1	1	yes	characteristic
126	C₄×C₂₃	—	2	1	no	—
127	C₄×C₂₃	—	2	2	no	—
128	C₄×C₂₃	—	4	4	no	—
129	C₄×C₂₃	—	4	2	no	—
130	C₄×C₂₃	—	8	2	no	—
131	C₄×C₂₃	#453	1	2	yes	—
132	C₄×C₂₃	#468	1	2	yes	—
133	C₄×C₂₃	#470	1	2	yes	—
134	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
135	C₂×C₂²⋊Q₈	—	2	2	no	—
136	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
137	#436	—	2	4	no	—
138	#431	C₂²×C₂₃	1	2	yes	—
139	#423	C₂²×C₂₃	1	2	yes	—
140	C₂×#100	—	2	1	no	—
141	#407	—	2	2	no	—
142	#399	C₄×C₂₃	1	4	yes	—
143	#390	—	2	1	no	—
144	#384	—	2	1	no	—
145	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
146	#343	—	2	1	no	—
147	#332	—	2	4	no	—
148	C₂×C₂₃	—	2	1	no	—
149	C₂×C₂₃	—	2	1	no	—
150	C₂×C₂₃	—	8	2	no	—
151	C₂×C₂₃	#1887	1	1	yes	characteristic
152	C₂×C₂₃	#1894	1	1	yes	characteristic
153	C₂×C₂₃	#1915	1	1	yes	characteristic
154	C₂²×Q₈	—	2	1	no	—
155	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
156	C₂³×C₄	D₄×C₂₃	1	2	yes	—
157	C₂×M₁₆	—	2	4	no	—
158	C₂×M₁₆	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₂²⋊Q₈	—	4	8	no	—
162	C₄×D₄	—	2	2	no	—
163	C₄×D₄	—	2	2	no	—
164	C₂×C₄⋊C₄	—	2	1	no	—
165	C₂×C₄⋊C₄	—	2	4	no	—
166	C₂×C₄⋊C₄	—	2	1	no	—
167	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
168	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
169	C₂×C₂²⋊C₄	—	2	4	no	—
170	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
171	C₂×C₄²	—	2	1	no	—
172	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	D₄×C₂₃	1	4	yes	—
176	#100	—	4	2	no	—
177	C₂²⋊C₈	—	2	4	no	—
178	C₂²⋊C₈	—	2	2	no	—
179	C₄×C₈	—	2	2	no	—
180	#95	C₂×C₄×C₂₃	1	2	yes	—
181	C₂₃	#9403	1	1	yes	characteristic, direct product factor, Sylow
182	C₂⁴	C₂²⋊C₄×C₂₃	1	2	yes	—
183	C₂×Q₈	—	4	4	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	2	1	no	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	4	4	no	—
195	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
196	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
197	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
199	M₁₆	—	4	2	no	—
200	M₁₆	—	4	2	no	—
201	M₁₆	—	8	4	no	—
202	C₂×C₈	—	2	4	no	—
203	C₂×C₈	—	4	2	no	—
204	C₄⋊C₄	—	2	4	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	4	no	—
207	C₄⋊C₄	—	4	8	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₂²⋊C₄	—	2	4	no	—
210	C₂²⋊C₄	—	4	8	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	4	1	no	—
213	C₄²	C₂×D₄×C₂₃	1	2	yes	—
214	C₄²	#41×C₂₃	1	2	yes	—
215	C₂³	—	2	2	no	—
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
221	Q₈	—	8	2	no	—
222	Q₈	—	8	2	no	—
223	D₄	—	4	2	no	—
224	D₄	—	4	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
237	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
238	C₂×C₄	C₂₃×#121	1	2	yes	—
239	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
240	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂×C₄	C₂₃×#137	1	2	yes	—
242	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
243	C₈	—	4	4	no	—
244	C₈	—	8	2	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	4	4	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	8	2	no	—
252	C₂²	C₂₃×#386	1	1	yes	characteristic
253	C₂²	C₂₃×#417	1	1	yes	characteristic
254	C₂²	C₂₃×#419	1	1	yes	characteristic
255	C₄	—	2	1	no	—
256	C₄	—	2	2	no	—
257	C₄	—	4	4	no	—
258	C₄	—	4	2	no	—
259	C₄	—	8	2	no	—
260	C₄	C₂₃×#453	1	2	yes	—
261	C₄	C₂₃×#468	1	2	yes	—
262	C₄	C₂₃×#470	1	2	yes	—
263	C₂	—	2	1	no	—
264	C₂	—	2	1	no	—
265	C₂	—	8	2	no	—
266	C₂	C₂₃×#1887	1	1	yes	characteristic
267	C₂	C₂₃×#1894	1	1	yes	characteristic
268	C₂	C₂₃×#1915	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#2975

C₂

yes

maximal, characteristic

C₂₃×#2542

C₂

yes

maximal, characteristic

C₂₃×#1800

C₂

yes

maximal, characteristic

C₂₃×#1549

C₂

yes

maximal, complemented

C₂₃×#1303

C₂

yes

maximal, complemented

C₂×C₂₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₂₃×C₂²⋊Q₈

—

C₂×C₄×D₄×C₂₃

C₂²

yes

characteristic

C₂₃×#436

—

C₂₃×#431

C₂²

yes

—

C₂₃×#423

C₂²

yes

—

C₂×C₂₃×#100

—

C₂₃×#407

—

C₂₃×#399

C₄

yes

—

C₂₃×#390

—

C₂₃×#384

—

C₄×C₄⋊C₄×C₂₃

C₂²

yes

characteristic

C₂₃×#343

—

C₂₃×#332

—

C₂²×Q₈×C₂₃

—

C₂²×D₄×C₂₃

D₄

yes

characteristic

C₂³×C₄×C₂₃

D₄

yes

—

C₂×M₁₆×C₂₃

—

C₂×M₁₆×C₂₃

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₂²⋊Q₈

—

C₄×D₄×C₂₃

—

C₄×D₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₂₃

—

C₂×C₂²⋊C₄×C₂₃

C₂×C₄

yes

—

C₂×C₄²×C₂₃

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

D₄

yes

—

C₂₃×#100

—

C₂₃×C₂²⋊C₈

—

C₂₃×C₂²⋊C₈

—

C₄×C₈×C₂₃

—

C₂₃×#95

C₂×C₄

yes

—

C₂⁴×C₂₃

C₂²⋊C₄

yes

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₂₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

M₁₆×C₂₃

—

M₁₆×C₂₃

—

M₁₆×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

C₂×D₄

yes

—

C₄²×C₂₃

#41

yes

—

#9403

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₂₃

—

Q₈×C₂₃

—

D₄×C₂₃

—

D₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

100

C₂×C₄×C₂₃

—

101

C₂×C₄×C₂₃

—

102

C₂×C₄×C₂₃

C₄×D₄

yes

—

103

C₂×C₄×C₂₃

#120

yes

characteristic

104

C₂×C₄×C₂₃

#121

yes

—

105

C₂×C₄×C₂₃

#123

yes

characteristic

106

C₂×C₄×C₂₃

AGL(1,ℤ/8)

yes

characteristic

107

C₂×C₄×C₂₃

#137

yes

—

108

C₂×C₄×C₂₃

#137

yes

characteristic

109

C₈×C₂₃

—

110

C₈×C₂₃

—

111

#2975

C₂×C₂₃

yes

characteristic

112

#2542

C₂×C₂₃

yes

characteristic

113

#1800

C₂×C₂₃

yes

characteristic

114

#1549

C₂×C₂₃

yes

complemented

115

#1303

C₂×C₂₃

yes

complemented

116

C₂²×C₂₃

—

117

C₂²×C₂₃

—

118

C₂²×C₂₃

—

119

C₂²×C₂₃

—

120

C₂²×C₂₃

—

121

C₂²×C₂₃

—

122

C₂²×C₂₃

—

123

C₂²×C₂₃

#386

yes

characteristic

124

C₂²×C₂₃

#417

yes

characteristic

125

C₂²×C₂₃

#419

yes

characteristic

126

C₄×C₂₃

—

127

C₄×C₂₃

—

128

C₄×C₂₃

—

129

C₄×C₂₃

—

130

C₄×C₂₃

—

131

C₄×C₂₃

#453

yes

—

132

C₄×C₂₃

#468

yes

—

133

C₄×C₂₃

#470

yes

—

134

C₂×C₄⋊Q₈

C₂²×C₂₃

yes

characteristic

135

C₂×C₂²⋊Q₈

—

136

C₂×C₄×D₄

C₂²×C₂₃

yes

characteristic

137

#436

—

138

#431

C₂²×C₂₃

yes

—

139

#423

C₂²×C₂₃

yes

—

140

C₂×#100

—

141

#407

—

142

#399

C₄×C₂₃

yes

—

143

#390

—

144

#384

—

145

C₄×C₄⋊C₄

C₂²×C₂₃

yes

characteristic

146

#343

—

147

#332

—

148

C₂×C₂₃

—

149

C₂×C₂₃

—

150

C₂×C₂₃

—

151

C₂×C₂₃

#1887

yes

characteristic

152

C₂×C₂₃

#1894

yes

characteristic

153

C₂×C₂₃

#1915

yes

characteristic

154

C₂²×Q₈

—

155

C₂²×D₄

D₄×C₂₃

yes

characteristic

156

C₂³×C₄

D₄×C₂₃

yes

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₂²⋊Q₈

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

C₂×C₄×C₂₃

yes

—

168

C₂×C₄⋊C₄

D₄×C₂₃

yes

characteristic

169

C₂×C₂²⋊C₄

—

170

C₂×C₂²⋊C₄

C₂×C₄×C₂₃

yes

—

171

C₂×C₄²

—

172

C₂×C₄²

C₂³×C₂₃

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

D₄×C₂₃

yes

—

176

#100

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₄×C₈

—

180

#95

C₂×C₄×C₂₃

yes

—

181

C₂₃

#9403

yes

characteristic, direct product factor, Sylow

182

C₂⁴

C₂²⋊C₄×C₂₃

yes

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

C₂²⋊C₄×C₂₃

yes

—

196

C₂²×C₄

C₂²×C₄×C₂₃

yes

characteristic

197

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

198

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

213

C₄²

C₂×D₄×C₂₃

yes

—

214

C₄²

#41×C₂₃

yes

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

C₂×C₂²⋊C₄×C₂₃

yes

characteristic

221

Q₈

—

222

Q₈

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

C₄×D₄×C₂₃

yes

—

237

C₂×C₄

C₂₃×#120

yes

characteristic

238

C₂×C₄

C₂₃×#121

yes

—

239

C₂×C₄

C₂₃×#123

yes

characteristic

240

C₂×C₄

C₂₃×AGL(1,ℤ/8)

yes

characteristic

241

C₂×C₄

C₂₃×#137

yes

—

242

C₂×C₄

C₂₃×#137

yes

characteristic

243

C₈

—

244

C₈

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

C₂₃×#386

yes

characteristic

253

C₂²

C₂₃×#417

yes

characteristic

254

C₂²

C₂₃×#419

yes

characteristic

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

C₂₃×#453

yes

—

261

C₄

C₂₃×#468

yes

—

262

C₄

C₂₃×#470

yes

—

263

C₂

—

264

C₂

—

265

C₂

—

266

C₂

C₂₃×#1887

yes

characteristic

267

C₂

C₂₃×#1894

yes

characteristic

268

C₂

C₂₃×#1915

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₃

#386

commutator

C₂²×C₄

C₂²×C₄×C₂₃

Frattini, cosocle

C₂×C₄²

C₂³×C₂₃

prime radical

C₂²×D₄×C₂₃

D₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

N	H ≅ G/N	type
4. C₂₃×#1549	C₂	semidirect
5. C₂₃×#1303	C₂	semidirect
80. #9403	C₂₃	direct (N × H)
114. #1549	C₂×C₂₃	semidirect
115. #1303	C₂×C₂₃	semidirect
181. C₂₃	#9403	direct (N × H)

H ≅ G/N

type

4. C₂₃×#1549

C₂

semidirect

5. C₂₃×#1303

C₂

semidirect

80. #9403

C₂₃

direct (N × H)

114. #1549

C₂×C₂₃

semidirect

115. #1303

C₂×C₂₃

semidirect

181. C₂₃

#9403

direct (N × H)

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

subgroup	index
C₂₃×#2975	2
C₂₃×#2542	2
C₂₃×#1800	2
C₂₃×#1549	2
C₂₃×#1303	2
#9403	23

subgroup

index

C₂₃×#2975

C₂₃×#2542

C₂₃×#1800

C₂₃×#1549

C₂₃×#1303

#9403

Subgroups — C₂₃×#9403 #19157029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#9403 #19157029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#9403 #19157029