Finite Group Databasebeta

← C23×#9454 #19157080

Subgroups — C23×#9454 #19157080

Order 5888.

448 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#2983C211yesmaximal, characteristic
2C23×#2567C211yesmaximal, characteristic
3C23×#1556C212yesmaximal
4C23×#1467C211yesmaximal, characteristic
5C23×#1285C212yesmaximal
6C2×C23×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C23C2211yescharacteristic
8C23×#446—24no—
9C23×#432—21no—
10C23×#432C2212yes—
11C23×#432C2212yes—
12C23×#431—21no—
13C23×#395—21no—
14C23×#395—21no—
15C23×#391C412yes—
16C23×#389—21no—
17C23×#389—21no—
18C23×#384C412yes—
19C4×C4⋊C4×C23C2211yescharacteristic
20C23×#332—24no—
21C23×#324—21no—
22C23×#324—21no—
23C22×Q8×C23—21no—
24C22×Q8×C23C2×C411yescharacteristic
25C23×C4⋊Q8—22no—
26C23×C4⋊Q8—22no—
27C4×Q8×C23—22no—
28C4×Q8×C23—22no—
29C2×C4⋊C4×C23—21no—
30C2×C4⋊C4×C23—21no—
31C2×C4⋊C4×C23—22no—
32C2×C4⋊C4×C23—22no—
33C2×C4⋊C4×C23C2×C412yes—
34C2×C4⋊C4×C23C2×C411yescharacteristic
35C2×C4⋊C4×C23D411yescharacteristic
36C2×C4⋊C4×C23D411yescharacteristic
37C2×C42×C23C2×C412yes—
38C2×C42×C23D411yescharacteristic
39C2×C42×C23D411yescharacteristic
40C2×C42×C23C2311yescharacteristic
41C23×C4⋊C8—22no—
42C23×C4⋊C8—22no—
43C23×C4⋊C8—22no—
44C23×C4⋊C8D414yes—
45C23×C22⋊C8—22no—
46C23×C22⋊C8—22no—
47C23×#97—22no—
48C23×#97—22no—
49C23×#97—22no—
50C4×C8×C23—22no—
51C23×#95—22no—
52C23×#95—22no—
53C23×#95—21no—
54C2×Q8×C23—22no—
55C2×Q8×C23—22no—
56C2×Q8×C23—41no—
57C2×Q8×C23—42no—
58C2×Q8×C23—82no—
59C22×C4×C23—22no—
60C22×C4×C23—22no—
61C22×C4×C23C22⋊C411yescharacteristic
62C22×C4×C23C22⋊C411yescharacteristic
63C22×C4×C23C22⋊C411yescharacteristic
64C22×C4×C23C22⋊C411yescharacteristic
65C22×C4×C23C22×C411yescharacteristic
66C22×C4×C23C2×D411yescharacteristic
67C22×C4×C23C2×D411yescharacteristic
68C2×C8×C23—24no—
69C2×C8×C23—42no—
70C4⋊C4×C23—24no—
71C4⋊C4×C23—22no—
72C4⋊C4×C23—22no—
73C4⋊C4×C23—22no—
74C4⋊C4×C23—24no—
75C4⋊C4×C23—41no—
76C4⋊C4×C23—41no—
77C4⋊C4×C23—82no—
78C4⋊C4×C23—82no—
79C42×C23—21no—
80C42×C23—21no—
81C42×C23—21no—
82C42×C23—21no—
83C42×C23—42no—
84C42×C23C2×D412yes—
85C42×C23#4112yes—
86#9454C2311yesmaximal, characteristic, direct product factor, Sylow
87C23×C23C2×C22⋊C411yescharacteristic
88Q8×C23—44no—
89Q8×C23—84no—
90C2×C4×C23—21no—
91C2×C4×C23—21no—
92C2×C4×C23—21no—
93C2×C4×C23—21no—
94C2×C4×C23—22no—
95C2×C4×C23—24no—
96C2×C4×C23—21no—
97C2×C4×C23—21no—
98C2×C4×C23—21no—
99C2×C4×C23—21no—
100C2×C4×C23—21no—
101C2×C4×C23—41no—
102C2×C4×C23—42no—
103C2×C4×C23—42no—
104C2×C4×C23—41no—
105C2×C4×C23—41no—
106C2×C4×C23—42no—
107C2×C4×C23—42no—
108C2×C4×C23—42no—
109C2×C4×C23#10112yes—
110C2×C4×C23C4×D412yes—
111C2×C4×C23#12011yescharacteristic
112C2×C4×C23#12112yes—
113C2×C4×C23#12311yescharacteristic
114C8×C23—44no—
115C8×C23—82no—
116#2983C2×C2311yescharacteristic
117#2567C2×C2311yescharacteristic
118#1556C2×C2312yes—
119#1467C2×C2311yescharacteristic
120#1285C2×C2312yes—
121C22×C23—21no—
122C22×C23—21no—
123C22×C23#38611yescharacteristic
124C22×C23C2×#10111yescharacteristic
125C22×C23#41311yescharacteristic
126C4×C23—21no—
127C4×C23—22no—
128C4×C23—22no—
129C4×C23—22no—
130C4×C23—44no—
131C4×C23—41no—
132C4×C23—41no—
133C4×C23—41no—
134C4×C23—82no—
135C4×C23#45612yes—
136C2×C4⋊Q8C22×C2311yescharacteristic
137C2×C4×Q8C22×C2311yescharacteristic
138#446—24no—
139#432—21no—
140#432C22×C2312yes—
141#432C22×C2312yes—
142#431—21no—
143#395—21no—
144#395—21no—
145#391C4×C2312yes—
146#389—21no—
147#389—21no—
148#384C4×C2312yes—
149C4×C4⋊C4C22×C2311yescharacteristic
150#332—24no—
151#324—21no—
152#324—21no—
153C2×C23—21no—
154C2×C23—21no—
155C2×C23#188611yescharacteristic
156C2×C23#190111yescharacteristic
157C2×C23#191011yescharacteristic
158C22×Q8—21no—
159C22×Q8C2×C4×C2311yescharacteristic
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4C2×C4×C2312yes—
169C2×C4⋊C4C2×C4×C2311yescharacteristic
170C2×C4⋊C4D4×C2311yescharacteristic
171C2×C4⋊C4D4×C2311yescharacteristic
172C2×C42C2×C4×C2312yes—
173C2×C42D4×C2311yescharacteristic
174C2×C42D4×C2311yescharacteristic
175C2×C42C23×C2311yescharacteristic
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8D4×C2314yes—
180C22⋊C8—22no—
181C22⋊C8—22no—
182#97—22no—
183#97—22no—
184#97—22no—
185C4×C8—22no—
186#95—22no—
187#95—22no—
188#95—21no—
189C23#945411yescharacteristic, direct product factor, Sylow
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—42no—
194C2×Q8—82no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4C22⋊C4×C2311yescharacteristic
198C22×C4C22⋊C4×C2311yescharacteristic
199C22×C4C22⋊C4×C2311yescharacteristic
200C22×C4C22⋊C4×C2311yescharacteristic
201C22×C4C22×C4×C2311yescharacteristic
202C22×C4C2×D4×C2311yescharacteristic
203C22×C4C2×D4×C2311yescharacteristic
204C2×C8—24no—
205C2×C8—42no—
206C4⋊C4—24no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—42no—
220C42C2×D4×C2312yes—
221C42#41×C2312yes—
222C23C2×C22⋊C4×C2311yescharacteristic
223Q8—44no—
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4C23×#10112yes—
245C2×C4C4×D4×C2312yes—
246C2×C4C23×#12011yescharacteristic
247C2×C4C23×#12112yes—
248C2×C4C23×#12311yescharacteristic
249C8—44no—
250C8—82no—
251C22—21no—
252C22—21no—
253C22C23×#38611yescharacteristic
254C22C2×C23×#10111yescharacteristic
255C22C23×#41311yescharacteristic
256C4—21no—
257C4—22no—
258C4—22no—
259C4—22no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4C23×#45612yes—
266C2—21no—
267C2—21no—
268C2C23×#188611yescharacteristic
269C2C23×#190111yescharacteristic
270C2C23×#191011yescharacteristic
subgroupG/H
center, socleC22×C23#386
commutatorC22×C4C22×C4×C23
Frattini, cosocleC2×C42C23×C23
prime radicalC23×C23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
86. #9454C23direct (N × H)
189. C23#9454direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#29832
C23×#25672
C23×#15562
C23×#14672
C23×#12852
#945423