Finite Group Databasebeta

← C23×#11883 #19159509

Subgroups — C23×#11883 #19159509

Order 5888.

408 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2546C211yesmaximal, characteristic
2C23×#1801C211yesmaximal, characteristic
3C23×#1461C211yesmaximal, characteristic
4C23×#1346C214yesmaximal
5C2×C23×C4⋊Q8—21no—
6C2×C23×C4⋊Q8C411yescharacteristic
7C2×C4×Q8×C23C2211yescharacteristic
8C23×#431—21no—
9C23×#423—21no—
10C2×C23×#101—21no—
11C23×#398C412yes—
12C23×#398C2212yes—
13C23×#391—21no—
14C23×#389—21no—
15C23×#389—21no—
16C4×C4⋊C4×C23C411yescharacteristic
17C23×#343C2212yes—
18C23×#324—21no—
19C23×#324C2212yes—
20C22×Q8×C23—21no—
21C22×Q8×C23D411yescharacteristic
22C2×M16×C23—22no—
23C23×C4⋊Q8—41no—
24C23×C4⋊Q8—41no—
25C23×C4⋊Q8—42no—
26C23×C4⋊Q8—42no—
27C4×Q8×C23—41no—
28C4×Q8×C23—41no—
29C2×C4⋊C4×C23—21no—
30C2×C4⋊C4×C23—22no—
31C2×C4⋊C4×C23—21no—
32C2×C4⋊C4×C23—22no—
33C2×C4⋊C4×C23C2×C412yes—
34C2×C4⋊C4×C23C2×C411yescharacteristic
35C2×C4⋊C4×C23D411yescharacteristic
36C2×C4⋊C4×C23C2311yescharacteristic
37C2×C42×C23—21no—
38C2×C42×C23C2×C411yescharacteristic
39C2×C42×C23D411yescharacteristic
40C2×C42×C23D411yescharacteristic
41C23×C4⋊C8—41no—
42C23×C4⋊C8—41no—
43C23×C4⋊C8—41no—
44C23×#101—42no—
45C23×C22⋊C8—22no—
46C4×C8×C23—41no—
47C23×#95—22no—
48C23×#95—22no—
49C23×#95C2×C412yes—
50C2×Q8×C23—41no—
51C2×Q8×C23—41no—
52C2×Q8×C23—42no—
53C2×Q8×C23—42no—
54C2×Q8×C23—42no—
55C2×Q8×C23D812yes—
56C2×Q8×C23SD1612yes—
57C22×C4×C23—22no—
58C22×C4×C23—22no—
59C22×C4×C23C22⋊C411yescharacteristic
60C22×C4×C23C22⋊C411yescharacteristic
61C22×C4×C23C22⋊C411yescharacteristic
62C22×C4×C23C22⋊C411yescharacteristic
63C22×C4×C23C22×C411yescharacteristic
64C22×C4×C23C2×D411yescharacteristic
65C22×C4×C23C2×D411yescharacteristic
66M16×C23—42no—
67M16×C23—42no—
68C2×C8×C23—42no—
69C2×C8×C23—42no—
70C4⋊C4×C23—24no—
71C4⋊C4×C23—41no—
72C4⋊C4×C23—41no—
73C4⋊C4×C23—41no—
74C4⋊C4×C23—42no—
75C4⋊C4×C23—41no—
76C4⋊C4×C23—41no—
77C4⋊C4×C23—44no—
78C4⋊C4×C23—42no—
79C4⋊C4×C23—42no—
80C42×C23—21no—
81C42×C23—21no—
82C42×C23—21no—
83C42×C23—21no—
84C42×C23—21no—
85C42×C23—21no—
86C42×C23—42no—
87#11883C2311yesmaximal, characteristic, direct product factor, Sylow
88C23×C23C2×C22⋊C411yescharacteristic
89Q8×C23—42no—
90Q8×C23—42no—
91Q8×C23—84no—
92C2×C4×C23—21no—
93C2×C4×C23—21no—
94C2×C4×C23—21no—
95C2×C4×C23—21no—
96C2×C4×C23—21no—
97C2×C4×C23—21no—
98C2×C4×C23—22no—
99C2×C4×C23—24no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—42no—
104C2×C4×C23—42no—
105C2×C4×C23—41no—
106C2×C4×C23—41no—
107C2×C4×C23—41no—
108C2×C4×C23—42no—
109C2×C4×C23—42no—
110C2×C4×C23—42no—
111C2×C4×C23#9911yescharacteristic
112C2×C4×C23#9911yescharacteristic
113C2×C4×C23#10212yes—
114C2×C4×C23#10212yes—
115C2×C4×C23C2×D811yescharacteristic
116C2×C4×C23C2×SD1611yescharacteristic
117C8×C23—82no—
118C8×C23—82no—
119#2546C2×C2311yescharacteristic
120#1801C2×C2311yescharacteristic
121#1461C2×C2311yescharacteristic
122#1346C2×C2314yes—
123C22×C23—21no—
124C22×C23—21no—
125C22×C23C2×#9911yescharacteristic
126C22×C23C2×#10211yescharacteristic
127C22×C23#42111yescharacteristic
128C4×C23—21no—
129C4×C23—21no—
130C4×C23—22no—
131C4×C23—22no—
132C4×C23—21no—
133C4×C23—44no—
134C4×C23—41no—
135C4×C23—41no—
136C4×C23—41no—
137C4×C23—82no—
138C4×C23#35612yes—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8C4×C2311yescharacteristic
141C2×C4×Q8C22×C2311yescharacteristic
142#431—21no—
143#423—21no—
144C2×#101—21no—
145#398C4×C2312yes—
146#398C22×C2312yes—
147#391—21no—
148#389—21no—
149#389—21no—
150C4×C4⋊C4C4×C2311yescharacteristic
151#343C22×C2312yes—
152#324—21no—
153#324C22×C2312yes—
154C2×C23—21no—
155C2×C23—21no—
156C2×C23#151911yescharacteristic
157C2×C23#212311yescharacteristic
158C2×C23C2×#35611yescharacteristic
159C22×Q8—21no—
160C22×Q8D4×C2311yescharacteristic
161C2×M16—22no—
162C4⋊Q8—41no—
163C4⋊Q8—41no—
164C4⋊Q8—42no—
165C4⋊Q8—42no—
166C4×Q8—41no—
167C4×Q8—41no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4C2×C4×C2312yes—
173C2×C4⋊C4C2×C4×C2311yescharacteristic
174C2×C4⋊C4D4×C2311yescharacteristic
175C2×C4⋊C4C23×C2311yescharacteristic
176C2×C42—21no—
177C2×C42C2×C4×C2311yescharacteristic
178C2×C42D4×C2311yescharacteristic
179C2×C42D4×C2311yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183#101—42no—
184C22⋊C8—22no—
185C4×C8—41no—
186#95—22no—
187#95—22no—
188#95C2×C4×C2312yes—
189C23#1188311yescharacteristic, direct product factor, Sylow
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8D8×C2312yes—
196C2×Q8SD16×C2312yes—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4C22⋊C4×C2311yescharacteristic
200C22×C4C22⋊C4×C2311yescharacteristic
201C22×C4C22⋊C4×C2311yescharacteristic
202C22×C4C22⋊C4×C2311yescharacteristic
203C22×C4C22×C4×C2311yescharacteristic
204C22×C4C2×D4×C2311yescharacteristic
205C22×C4C2×D4×C2311yescharacteristic
206M16—42no—
207M16—42no—
208C2×C8—42no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C23C2×C22⋊C4×C2311yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4C23×#9911yescharacteristic
251C2×C4C23×#9911yescharacteristic
252C2×C4C23×#10212yes—
253C2×C4C23×#10212yes—
254C2×C4C2×D8×C2311yescharacteristic
255C2×C4C2×SD16×C2311yescharacteristic
256C8—82no—
257C8—82no—
258C22—21no—
259C22—21no—
260C22C2×C23×#9911yescharacteristic
261C22C2×C23×#10211yescharacteristic
262C22C23×#42111yescharacteristic
263C4—21no—
264C4—22no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4C23×#35612yes—
274C2—21no—
275C2—21no—
276C2C23×#151911yescharacteristic
277C2C23×#212311yescharacteristic
278C2C2×C23×#35611yescharacteristic
subgroupG/H
center, socleC22×C23C2×#99
commutatorC22×C4C22×C4×C23
Frattini, cosocleC2×C4⋊C4C23×C23
prime radicalC23×C23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C4×Q8×C23 ◁ G

Complements

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

NH ≅ G/Ntype
87. #11883C23direct (N × H)
189. C23#11883direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#25462
C23×#18012
C23×#14612
C23×#13462
#1188323