Finite Group Databasebeta

← C23×#9452 #19157078

Subgroups — C23×#9452 #19157078

Order 5888.

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

normal subgroups only

This group has 468 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×#2546C211yesmaximal, characteristic
3C23×#1558C212yesmaximal
4C23×#1467C211yesmaximal, characteristic
5C23×#1285C212yesmaximal
6C2×C23×C4⋊Q8C412yes—
7C2×C23×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C23C2211yescharacteristic
9C23×#446—24no—
10C23×#432—21no—
11C23×#432C2212yes—
12C23×#432C2212yes—
13C23×#431—21no—
14C23×#398—21no—
15C23×#398—21no—
16C23×#391C412yes—
17C23×#389—21no—
18C23×#389—21no—
19C4×C4⋊C4×C23C2211yescharacteristic
20C23×#333—24no—
21C23×#324—21no—
22C23×#324—21no—
23C22×Q8×C23C2×C412yes—
24C22×Q8×C23C2×C411yescharacteristic
25C23×C4⋊Q8—22no—
26C23×C4⋊Q8—22no—
27C23×C4⋊Q8—44no—
28C4×Q8×C23—22no—
29C4×Q8×C23—22no—
30C2×C4⋊C4×C23—21no—
31C2×C4⋊C4×C23—22no—
32C2×C4⋊C4×C23—22no—
33C2×C4⋊C4×C23—21no—
34C2×C4⋊C4×C23—21no—
35C2×C4⋊C4×C23C2×C411yescharacteristic
36C2×C4⋊C4×C23D411yescharacteristic
37C2×C4⋊C4×C23D411yescharacteristic
38C2×C42×C23C2×C412yes—
39C2×C42×C23D411yescharacteristic
40C2×C42×C23D411yescharacteristic
41C2×C42×C23C2311yescharacteristic
42C23×C4⋊C8—22no—
43C23×C4⋊C8—22no—
44C23×C4⋊C8—22no—
45C23×C4⋊C8D414yes—
46C23×C22⋊C8—22no—
47C23×C22⋊C8—22no—
48C23×#97—22no—
49C23×#97—22no—
50C23×#97—22no—
51C4×C8×C23—22no—
52C23×#95—22no—
53C23×#95—22no—
54C23×#95—21no—
55C2×Q8×C23—22no—
56C2×Q8×C23—22no—
57C2×Q8×C23—24no—
58C2×Q8×C23—41no—
59C2×Q8×C23—42no—
60C2×Q8×C23—42no—
61C22×C4×C23—22no—
62C22×C4×C23—22no—
63C22×C4×C23C22⋊C411yescharacteristic
64C22×C4×C23C22⋊C411yescharacteristic
65C22×C4×C23C22⋊C411yescharacteristic
66C22×C4×C23C22⋊C411yescharacteristic
67C22×C4×C23C22×C411yescharacteristic
68C22×C4×C23C2×D411yescharacteristic
69C22×C4×C23C2×D411yescharacteristic
70C2×C8×C23—24no—
71C2×C8×C23—42no—
72C4⋊C4×C23—24no—
73C4⋊C4×C23—22no—
74C4⋊C4×C23—22no—
75C4⋊C4×C23—22no—
76C4⋊C4×C23—44no—
77C4⋊C4×C23—44no—
78C4⋊C4×C23—41no—
79C4⋊C4×C23—42no—
80C4⋊C4×C23—41no—
81C42×C23—21no—
82C42×C23—21no—
83C42×C23—21no—
84C42×C23—21no—
85C42×C23—42no—
86C42×C23C2×D412yes—
87C42×C23#4112yes—
88#9452C2311yesmaximal, characteristic, direct product factor, Sylow
89C23×C23C2×C22⋊C411yescharacteristic
90Q8×C23—44no—
91Q8×C23—84no—
92C2×C4×C23—21no—
93C2×C4×C23—21no—
94C2×C4×C23—21no—
95C2×C4×C23—21no—
96C2×C4×C23—22no—
97C2×C4×C23—24no—
98C2×C4×C23—21no—
99C2×C4×C23—21no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—41no—
104C2×C4×C23—42no—
105C2×C4×C23—42no—
106C2×C4×C23—41no—
107C2×C4×C23—41no—
108C2×C4×C23—42no—
109C2×C4×C23—42no—
110C2×C4×C23—42no—
111C2×C4×C23#10012yes—
112C2×C4×C23C4×D412yes—
113C2×C4×C23#12011yescharacteristic
114C2×C4×C23#12112yes—
115C2×C4×C23#12311yescharacteristic
116C8×C23—44no—
117C8×C23—82no—
118#2983C2×C2311yescharacteristic
119#2546C2×C2311yescharacteristic
120#1558C2×C2312yes—
121#1467C2×C2311yescharacteristic
122#1285C2×C2312yes—
123C22×C23—21no—
124C22×C23—21no—
125C22×C23#38611yescharacteristic
126C22×C23C2×#10011yescharacteristic
127C22×C23#41311yescharacteristic
128C4×C23—21no—
129C4×C23—22no—
130C4×C23—22no—
131C4×C23—22no—
132C4×C23—44no—
133C4×C23—41no—
134C4×C23—41no—
135C4×C23—41no—
136C4×C23—82no—
137C4×C23#45612yes—
138C2×C4⋊Q8C4×C2312yes—
139C2×C4⋊Q8C22×C2311yescharacteristic
140C2×C4×Q8C22×C2311yescharacteristic
141#446—24no—
142#432—21no—
143#432C22×C2312yes—
144#432C22×C2312yes—
145#431—21no—
146#398—21no—
147#398—21no—
148#391C4×C2312yes—
149#389—21no—
150#389—21no—
151C4×C4⋊C4C22×C2311yescharacteristic
152#333—24no—
153#324—21no—
154#324—21no—
155C2×C23—21no—
156C2×C23—21no—
157C2×C23#188611yescharacteristic
158C2×C23#190011yescharacteristic
159C2×C23#190911yescharacteristic
160C22×Q8C2×C4×C2312yes—
161C22×Q8C2×C4×C2311yescharacteristic
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—44no—
165C4×Q8—22no—
166C4×Q8—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C2×C4×C2311yescharacteristic
173C2×C4⋊C4D4×C2311yescharacteristic
174C2×C4⋊C4D4×C2311yescharacteristic
175C2×C42C2×C4×C2312yes—
176C2×C42D4×C2311yescharacteristic
177C2×C42D4×C2311yescharacteristic
178C2×C42C23×C2311yescharacteristic
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8D4×C2314yes—
183C22⋊C8—22no—
184C22⋊C8—22no—
185#97—22no—
186#97—22no—
187#97—22no—
188C4×C8—22no—
189#95—22no—
190#95—22no—
191#95—21no—
192C23#945211yescharacteristic, direct product factor, Sylow
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C22⋊C4×C2311yescharacteristic
202C22×C4C22⋊C4×C2311yescharacteristic
203C22×C4C22⋊C4×C2311yescharacteristic
204C22×C4C22⋊C4×C2311yescharacteristic
205C22×C4C22×C4×C2311yescharacteristic
206C22×C4C2×D4×C2311yescharacteristic
207C22×C4C2×D4×C2311yescharacteristic
208C2×C8—24no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—44no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—42no—
224C42C2×D4×C2312yes—
225C42#41×C2312yes—
226C23C2×C22⋊C4×C2311yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4C23×#10012yes—
249C2×C4C4×D4×C2312yes—
250C2×C4C23×#12011yescharacteristic
251C2×C4C23×#12112yes—
252C2×C4C23×#12311yescharacteristic
253C8—44no—
254C8—82no—
255C22—21no—
256C22—21no—
257C22C23×#38611yescharacteristic
258C22C2×C23×#10011yescharacteristic
259C22C23×#41311yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4C23×#45612yes—
270C2—21no—
271C2—21no—
272C2C23×#188611yescharacteristic
273C2C23×#190011yescharacteristic
274C2C23×#190911yescharacteristic
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
88. #9452C23direct (N × H)
192. C23#9452direct (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×#25462
C23×#15582
C23×#14672
C23×#12852
#945223