Group #19158248 — subgroups

Subgroups — C₂₃×#10622 #19158248

Order 5888.

402 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 134 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×#1954	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#1802	C₂	1	2	yes	maximal
4	C₂₃×#1296	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₂₃×#102	—	2	2	no	—
10	C₂×C₂₃×C₂²⋊C₈	—	2	2	no	—
11	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#384	C₂²	1	2	yes	—
13	C₂₃×#340	—	2	2	no	—
14	C₂₃×#340	—	2	2	no	—
15	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₂₃	—	2	1	no	—
17	C₂²×C₈×C₂₃	—	2	2	no	—
18	C₂²×C₈×C₂₃	—	2	1	no	—
19	C₂²×C₈×C₂₃	D₄	1	2	yes	—
20	C₄×D₄×C₂₃	—	2	2	no	—
21	C₄×D₄×C₂₃	—	2	2	no	—
22	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
23	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
24	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
25	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
27	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
28	C₂₃×C₄⋊C₈	—	2	2	no	—
29	C₂₃×C₄⋊C₈	—	2	2	no	—
30	C₂₃×C₄⋊C₈	—	2	2	no	—
31	C₂₃×#102	—	4	4	no	—
32	C₂₃×C₂²⋊C₈	—	4	4	no	—
33	C₄×C₈×C₂₃	—	2	2	no	—
34	C₂⁴×C₂₃	—	2	1	no	—
35	C₂×D₄×C₂₃	—	2	2	no	—
36	C₂×D₄×C₂₃	—	2	1	no	—
37	C₂×D₄×C₂₃	—	2	2	no	—
38	C₂×D₄×C₂₃	Q₁₆	1	2	yes	—
39	C₂²×C₄×C₂₃	—	2	1	no	—
40	C₂²×C₄×C₂₃	—	4	1	no	—
41	C₂²×C₄×C₂₃	—	4	1	no	—
42	C₂²×C₄×C₂₃	—	4	2	no	—
43	C₂²×C₄×C₂₃	—	4	2	no	—
44	C₂²×C₄×C₂₃	—	4	2	no	—
45	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
48	C₂×C₈×C₂₃	—	2	2	no	—
49	C₂×C₈×C₂₃	—	2	2	no	—
50	C₂×C₈×C₂₃	—	2	2	no	—
51	C₂×C₈×C₂₃	—	4	2	no	—
52	C₂×C₈×C₂₃	—	4	1	no	—
53	C₂×C₈×C₂₃	—	4	2	no	—
54	C₂×C₈×C₂₃	—	4	2	no	—
55	C₂×C₈×C₂₃	—	4	2	no	—
56	C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₄⋊C₄×C₂₃	—	4	2	no	—
58	C₄⋊C₄×C₂₃	—	4	2	no	—
59	C₄⋊C₄×C₂₃	—	4	2	no	—
60	C₄⋊C₄×C₂₃	—	4	2	no	—
61	C₄⋊C₄×C₂₃	—	8	2	no	—
62	C₂²⋊C₄×C₂₃	—	4	2	no	—
63	C₄²×C₂₃	#41	1	2	yes	—
64	C₄²×C₂₃	#41	1	2	yes	—
65	#10622	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂³×C₂₃	—	2	2	no	—
67	C₂³×C₂₃	—	4	1	no	—
68	C₂³×C₂₃	—	4	2	no	—
69	C₂³×C₂₃	—	4	1	no	—
70	C₂³×C₂₃	—	4	2	no	—
71	C₂³×C₂₃	#121	1	1	yes	characteristic
72	D₄×C₂₃	—	2	4	no	—
73	D₄×C₂₃	—	4	2	no	—
74	C₂×C₄×C₂₃	—	2	2	no	—
75	C₂×C₄×C₂₃	—	4	1	no	—
76	C₂×C₄×C₂₃	—	4	2	no	—
77	C₂×C₄×C₂₃	—	8	2	no	—
78	C₂×C₄×C₂₃	—	8	1	no	—
79	C₂×C₄×C₂₃	—	8	1	no	—
80	C₂×C₄×C₂₃	—	8	2	no	—
81	C₂×C₄×C₂₃	—	8	2	no	—
82	C₂×C₄×C₂₃	—	8	2	no	—
83	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
84	C₂×C₄×C₂₃	#123	1	2	yes	—
85	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
86	C₂×C₄×C₂₃	#126	1	2	yes	—
87	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
88	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
89	C₂×C₄×C₂₃	#135	1	2	yes	—
90	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
91	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
92	C₈×C₂₃	—	4	2	no	—
93	C₈×C₂₃	—	8	2	no	—
94	C₈×C₂₃	—	8	1	no	—
95	#1954	C₂×C₂₃	1	1	yes	characteristic
96	#1834	C₂×C₂₃	1	1	yes	characteristic, complemented
97	#1802	C₂×C₂₃	1	2	yes	—
98	#1296	C₂×C₂₃	1	2	yes	complemented
99	#1277	C₂×C₂₃	1	1	yes	characteristic, complemented
100	C₂²×C₂₃	—	4	2	no	—
101	C₂²×C₂₃	—	4	4	no	—
102	C₂²×C₂₃	—	8	1	no	—
103	C₂²×C₂₃	—	8	1	no	—
104	C₂²×C₂₃	—	8	2	no	—
105	C₂²×C₂₃	#397	1	1	yes	characteristic
106	C₂²×C₂₃	#463	1	2	yes	—
107	C₂²×C₂₃	#467	1	1	yes	characteristic
108	C₂²×C₂₃	#469	1	1	yes	characteristic
109	C₂²×C₂₃	#471	1	2	yes	—
110	C₄×C₂₃	—	2	2	no	—
111	C₄×C₂₃	—	8	1	no	—
112	C₄×C₂₃	—	16	2	no	—
113	C₄×C₂₃	#482	1	2	yes	—
114	C₄×C₂₃	#482	1	2	yes	—
115	C₄×C₂₃	#484	1	2	yes	—
116	C₄×C₂₃	#488	1	1	yes	characteristic
117	C₄×C₂₃	#490	1	1	yes	characteristic
118	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
119	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
120	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
121	C₂×#102	—	2	2	no	—
122	C₂×C₂²⋊C₈	—	2	2	no	—
123	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
124	#384	C₂²×C₂₃	1	2	yes	—
125	#340	—	2	2	no	—
126	#340	—	2	2	no	—
127	C₂×C₂₃	—	8	2	no	—
128	C₂×C₂₃	#1683	1	2	yes	—
129	C₂×C₂₃	#1701	1	2	yes	—
130	C₂×C₂₃	#2073	1	1	yes	characteristic
131	C₂×C₂₃	#2076	1	1	yes	characteristic
132	C₂×C₂₃	#2079	1	1	yes	characteristic
133	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
134	C₂³×C₄	—	2	1	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	D₄×C₂₃	1	2	yes	—
138	C₄×D₄	—	2	2	no	—
139	C₄×D₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	—	2	1	no	—
145	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	2	2	no	—
149	#102	—	4	4	no	—
150	C₂²⋊C₈	—	4	4	no	—
151	C₄×C₈	—	2	2	no	—
152	C₂₃	#10622	1	1	yes	characteristic, direct product factor, Sylow
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	Q₁₆×C₂₃	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	1	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
166	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	1	no	—
172	C₂×C₈	—	4	2	no	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	8	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#41×C₂₃	1	2	yes	—
183	C₄²	#41×C₂₃	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	C₂₃×#121	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	1	no	—
198	C₂×C₄	—	8	2	no	—
199	C₂×C₄	—	8	2	no	—
200	C₂×C₄	—	8	2	no	—
201	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
202	C₂×C₄	C₂₃×#123	1	2	yes	—
203	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
204	C₂×C₄	C₂₃×#126	1	2	yes	—
205	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
206	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
207	C₂×C₄	C₂₃×#135	1	2	yes	—
208	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
209	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	2	no	—
212	C₈	—	8	1	no	—
213	C₂²	—	4	4	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	1	no	—
218	C₂²	C₂₃×#397	1	1	yes	characteristic
219	C₂²	C₂₃×#463	1	2	yes	—
220	C₂²	C₂₃×#467	1	1	yes	characteristic
221	C₂²	C₂₃×#469	1	1	yes	characteristic
222	C₂²	C₂₃×#471	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	16	2	no	—
226	C₄	C₂₃×#482	1	2	yes	—
227	C₄	C₂₃×#482	1	2	yes	—
228	C₄	C₂₃×#484	1	2	yes	—
229	C₄	C₂₃×#488	1	1	yes	characteristic
230	C₄	C₂₃×#490	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	C₂₃×#1683	1	2	yes	—
233	C₂	C₂₃×#1701	1	2	yes	—
234	C₂	C₂₃×#2073	1	1	yes	characteristic
235	C₂	C₂₃×#2076	1	1	yes	characteristic
236	C₂	C₂₃×#2079	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#1954

C₂

yes

maximal, characteristic

C₂₃×#1834

C₂

yes

maximal, characteristic, complemented

C₂₃×#1802

C₂

yes

maximal

C₂₃×#1296

C₂

yes

maximal, complemented

C₂₃×#1277

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₄×C₂₃

C₂²

yes

characteristic

C₂×C₂₃×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₂₃×C₄⋊C₈

C₂²

yes

—

C₂×C₂₃×#102

—

C₂×C₂₃×C₂²⋊C₈

—

C₂×C₄×C₈×C₂₃

C₂²

yes

characteristic

C₂₃×#384

C₂²

yes

—

C₂₃×#340

—

C₂₃×#340

—

C₂²×D₄×C₂₃

D₄

yes

characteristic

C₂³×C₄×C₂₃

—

C₂²×C₈×C₂₃

—

C₂²×C₈×C₂₃

—

C₂²×C₈×C₂₃

D₄

yes

—

C₄×D₄×C₂₃

—

C₄×D₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₂₃

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

—

C₂₃×#102

—

C₂₃×C₂²⋊C₈

—

C₄×C₈×C₂₃

—

C₂⁴×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

Q₁₆

yes

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₃

#41

yes

characteristic

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₄²×C₂₃

#41

yes

—

C₄²×C₂₃

#41

yes

—

#10622

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

#121

yes

characteristic

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

—

C₂×C₄×C₂₃

#123

yes

characteristic

C₂×C₄×C₂₃

#123

yes

—

C₂×C₄×C₂₃

#124

yes

characteristic

C₂×C₄×C₂₃

#126

yes

—

C₂×C₄×C₂₃

C₂×Q₁₆

yes

C₂×C₄×C₂₃

yes

C₂×C₄×C₂₃

yes

—

C₂×C₄×C₂₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₂₃

AGL(1,ℤ/8)

yes

—

C₈×C₂₃

—

C₈×C₂₃

—

C₈×C₂₃

—

#1954

C₂×C₂₃

yes

characteristic

#1834

C₂×C₂₃

yes

characteristic, complemented

#1802

C₂×C₂₃

yes

—

#1296

C₂×C₂₃

yes

complemented

#1277

C₂×C₂₃

yes

characteristic, complemented

100

C₂²×C₂₃

—

101

C₂²×C₂₃

—

102

C₂²×C₂₃

—

103

C₂²×C₂₃

—

104

C₂²×C₂₃

—

105

C₂²×C₂₃

#397

yes

characteristic

106

C₂²×C₂₃

#463

yes

—

107

C₂²×C₂₃

#467

yes

characteristic

108

C₂²×C₂₃

#469

yes

characteristic

109

C₂²×C₂₃

#471

yes

—

110

C₄×C₂₃

—

111

C₄×C₂₃

—

112

C₄×C₂₃

—

113

C₄×C₂₃

#482

yes

—

114

C₄×C₂₃

#482

yes

—

115

C₄×C₂₃

#484

yes

—

116

C₄×C₂₃

#488

yes

characteristic

117

C₄×C₂₃

#490

yes

characteristic

118

C₂×C₄×D₄

C₂²×C₂₃

yes

characteristic

119

C₂×C₄⋊C₈

C₂²×C₂₃

yes

—

120

C₂×C₄⋊C₈

C₂²×C₂₃

yes

characteristic

121

C₂×#102

—

122

C₂×C₂²⋊C₈

—

123

C₂×C₄×C₈

C₂²×C₂₃

yes

characteristic

124

#384

C₂²×C₂₃

yes

—

125

#340

—

126

#340

—

127

C₂×C₂₃

—

128

C₂×C₂₃

#1683

yes

—

129

C₂×C₂₃

#1701

yes

—

130

C₂×C₂₃

#2073

yes

characteristic

131

C₂×C₂₃

#2076

yes

characteristic

132

C₂×C₂₃

#2079

yes

characteristic

133

C₂²×D₄

D₄×C₂₃

yes

characteristic

134

C₂³×C₄

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

D₄×C₂₃

yes

—

138

C₄×D₄

—

139

C₄×D₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

D₄×C₂₃

yes

characteristic

144

C₂×C₂²⋊C₄

—

145

C₂×C₄²

C₂³×C₂₃

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

#102

—

150

C₂²⋊C₈

—

151

C₄×C₈

—

152

C₂₃

#10622

yes

characteristic, direct product factor, Sylow

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

Q₁₆×C₂₃

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

165

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

166

C₂²×C₄

#41×C₂₃

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

#41×C₂₃

yes

—

183

C₄²

#41×C₂₃

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

C₂₃×#121

yes

characteristic

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

C₂₃×#123

yes

characteristic

202

C₂×C₄

C₂₃×#123

yes

—

203

C₂×C₄

C₂₃×#124

yes

characteristic

204

C₂×C₄

C₂₃×#126

yes

—

205

C₂×C₄

C₂×Q₁₆×C₂₃

yes

characteristic

206

C₂×C₄

C₂₃×#135

yes

characteristic

207

C₂×C₄

C₂₃×#135

yes

—

208

C₂×C₄

C₂₃×AGL(1,ℤ/8)

yes

—

209

C₂×C₄

C₂₃×AGL(1,ℤ/8)

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

C₂₃×#397

yes

characteristic

219

C₂²

C₂₃×#463

yes

—

220

C₂²

C₂₃×#467

yes

characteristic

221

C₂²

C₂₃×#469

yes

characteristic

222

C₂²

C₂₃×#471

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

C₂₃×#482

yes

—

227

C₄

C₂₃×#482

yes

—

228

C₄

C₂₃×#484

yes

—

229

C₄

C₂₃×#488

yes

characteristic

230

C₄

C₂₃×#490

yes

characteristic

231

C₂

—

232

C₂

C₂₃×#1683

yes

—

233

C₂

C₂₃×#1701

yes

—

234

C₂

C₂₃×#2073

yes

characteristic

235

C₂

C₂₃×#2076

yes

characteristic

236

C₂

C₂₃×#2079

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₂₃

#121

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₂₃

prime radical

C₂²×D₄×C₂₃

D₄

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

N	H ≅ G/N	type
2. C₂₃×#1834	C₂	semidirect
4. C₂₃×#1296	C₂	semidirect
5. C₂₃×#1277	C₂	semidirect
65. #10622	C₂₃	direct (N × H)
96. #1834	C₂×C₂₃	semidirect
98. #1296	C₂×C₂₃	semidirect
99. #1277	C₂×C₂₃	semidirect
152. C₂₃	#10622	direct (N × H)

H ≅ G/N

type

2. C₂₃×#1834

C₂

semidirect

4. C₂₃×#1296

C₂

semidirect

5. C₂₃×#1277

C₂

semidirect

65. #10622

C₂₃

direct (N × H)

96. #1834

C₂×C₂₃

semidirect

98. #1296

C₂×C₂₃

semidirect

99. #1277

C₂×C₂₃

semidirect

152. C₂₃

#10622

direct (N × H)

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

subgroup	index
C₂₃×#1954	2
C₂₃×#1834	2
C₂₃×#1802	2
C₂₃×#1296	2
C₂₃×#1277	2
#10622	23

subgroup

index

C₂₃×#1954

C₂₃×#1834

C₂₃×#1802

C₂₃×#1296

C₂₃×#1277

#10622

Subgroups — C₂₃×#10622 #19158248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#10622 #19158248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10622 #19158248