Finite Group Databasebeta

← C23×#11908 #19159534

Subgroups — C23×#11908 #19159534

Order 5888.

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

normal subgroups only

This group has 388 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×#2567C211yesmaximal, characteristic
2C23×#1801C211yesmaximal, characteristic
3C23×#1461C211yesmaximal, characteristic
4C23×#1354C214yesmaximal
5C2×C23×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C23C2211yescharacteristic
7C23×#431—21no—
8C23×#423—21no—
9C2×C23×#101—21no—
10C23×#395C412yes—
11C23×#395C2212yes—
12C23×#391—21no—
13C23×#389—21no—
14C23×#389—21no—
15C23×#384—21no—
16C4×C4⋊C4×C23C411yescharacteristic
17C23×#343C2212yes—
18C23×#324—21no—
19C23×#324C2212yes—
20C22×Q8×C23C2×C412yes—
21C22×Q8×C23D411yescharacteristic
22C2×M16×C23—22no—
23C23×C4⋊Q8—41no—
24C23×C4⋊Q8—41no—
25C4×Q8×C23—41no—
26C4×Q8×C23—41no—
27C2×C4⋊C4×C23—21no—
28C2×C4⋊C4×C23—21no—
29C2×C4⋊C4×C23—21no—
30C2×C4⋊C4×C23—22no—
31C2×C4⋊C4×C23—22no—
32C2×C4⋊C4×C23C2×C411yescharacteristic
33C2×C4⋊C4×C23D411yescharacteristic
34C2×C4⋊C4×C23C2311yescharacteristic
35C2×C42×C23—21no—
36C2×C42×C23C2×C411yescharacteristic
37C2×C42×C23D411yescharacteristic
38C2×C42×C23D411yescharacteristic
39C23×C4⋊C8—41no—
40C23×C4⋊C8—41no—
41C23×C4⋊C8—41no—
42C23×#101—42no—
43C23×C22⋊C8—22no—
44C4×C8×C23—41no—
45C23×#95—22no—
46C23×#95—22no—
47C23×#95C2×C412yes—
48C2×Q8×C23—41no—
49C2×Q8×C23—41no—
50C2×Q8×C23—42no—
51C2×Q8×C23—82no—
52C2×Q8×C23SD1612yes—
53C2×Q8×C23Q1612yes—
54C22×C4×C23—22no—
55C22×C4×C23—22no—
56C22×C4×C23C22⋊C411yescharacteristic
57C22×C4×C23C22⋊C411yescharacteristic
58C22×C4×C23C22⋊C411yescharacteristic
59C22×C4×C23C22⋊C411yescharacteristic
60C22×C4×C23C22×C411yescharacteristic
61C22×C4×C23C2×D411yescharacteristic
62C22×C4×C23C2×D411yescharacteristic
63M16×C23—42no—
64M16×C23—42no—
65C2×C8×C23—42no—
66C2×C8×C23—42no—
67C4⋊C4×C23—24no—
68C4⋊C4×C23—41no—
69C4⋊C4×C23—41no—
70C4⋊C4×C23—41no—
71C4⋊C4×C23—42no—
72C4⋊C4×C23—41no—
73C4⋊C4×C23—41no—
74C4⋊C4×C23—82no—
75C4⋊C4×C23—82no—
76C42×C23—21no—
77C42×C23—21no—
78C42×C23—21no—
79C42×C23—21no—
80C42×C23—21no—
81C42×C23—21no—
82C42×C23—42no—
83#11908C2311yesmaximal, characteristic, direct product factor, Sylow
84C23×C23C2×C22⋊C411yescharacteristic
85Q8×C23—42no—
86Q8×C23—42no—
87Q8×C23—84no—
88C2×C4×C23—21no—
89C2×C4×C23—21no—
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—42no—
100C2×C4×C23—42no—
101C2×C4×C23—41no—
102C2×C4×C23—41no—
103C2×C4×C23—41no—
104C2×C4×C23—42no—
105C2×C4×C23—42no—
106C2×C4×C23—42no—
107C2×C4×C23#9911yescharacteristic
108C2×C4×C23#9911yescharacteristic
109C2×C4×C23#10312yes—
110C2×C4×C23#10312yes—
111C2×C4×C23C2×SD1611yescharacteristic
112C2×C4×C23C2×Q1611yescharacteristic
113C8×C23—82no—
114C8×C23—82no—
115#2567C2×C2311yescharacteristic
116#1801C2×C2311yescharacteristic
117#1461C2×C2311yescharacteristic
118#1354C2×C2314yes—
119C22×C23—21no—
120C22×C23—21no—
121C22×C23C2×#9911yescharacteristic
122C22×C23C2×#10311yescharacteristic
123C22×C23#42111yescharacteristic
124C4×C23—21no—
125C4×C23—21no—
126C4×C23—22no—
127C4×C23—22no—
128C4×C23—21no—
129C4×C23—44no—
130C4×C23—41no—
131C4×C23—41no—
132C4×C23—41no—
133C4×C23—82no—
134C4×C23#35612yes—
135C2×C4⋊Q8C4×C2311yescharacteristic
136C2×C4×Q8C22×C2311yescharacteristic
137#431—21no—
138#423—21no—
139C2×#101—21no—
140#395C4×C2312yes—
141#395C22×C2312yes—
142#391—21no—
143#389—21no—
144#389—21no—
145#384—21no—
146C4×C4⋊C4C4×C2311yescharacteristic
147#343C22×C2312yes—
148#324—21no—
149#324C22×C2312yes—
150C2×C23—21no—
151C2×C23—21no—
152C2×C23#152011yescharacteristic
153C2×C23#212211yescharacteristic
154C2×C23C2×#35611yescharacteristic
155C22×Q8C2×C4×C2312yes—
156C22×Q8D4×C2311yescharacteristic
157C2×M16—22no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C2×C4×C2311yescharacteristic
168C2×C4⋊C4D4×C2311yescharacteristic
169C2×C4⋊C4C23×C2311yescharacteristic
170C2×C42—21no—
171C2×C42C2×C4×C2311yescharacteristic
172C2×C42D4×C2311yescharacteristic
173C2×C42D4×C2311yescharacteristic
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177#101—42no—
178C22⋊C8—22no—
179C4×C8—41no—
180#95—22no—
181#95—22no—
182#95C2×C4×C2312yes—
183C23#1190811yescharacteristic, direct product factor, Sylow
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—82no—
188C2×Q8SD16×C2312yes—
189C2×Q8Q16×C2312yes—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4C22⋊C4×C2311yescharacteristic
193C22×C4C22⋊C4×C2311yescharacteristic
194C22×C4C22⋊C4×C2311yescharacteristic
195C22×C4C22⋊C4×C2311yescharacteristic
196C22×C4C22×C4×C2311yescharacteristic
197C22×C4C2×D4×C2311yescharacteristic
198C22×C4C2×D4×C2311yescharacteristic
199M16—42no—
200M16—42no—
201C2×C8—42no—
202C2×C8—42no—
203C4⋊C4—24no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—42no—
219C23C2×C22⋊C4×C2311yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—84no—
223C2×C4—21no—
224C2×C4—21no—
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—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4C23×#9911yescharacteristic
243C2×C4C23×#9911yescharacteristic
244C2×C4C23×#10312yes—
245C2×C4C23×#10312yes—
246C2×C4C2×SD16×C2311yescharacteristic
247C2×C4C2×Q16×C2311yescharacteristic
248C8—82no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22C2×C23×#9911yescharacteristic
253C22C2×C23×#10311yescharacteristic
254C22C23×#42111yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4C23×#35612yes—
266C2—21no—
267C2—21no—
268C2C23×#152011yescharacteristic
269C2C23×#212211yescharacteristic
270C2C2×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
83. #11908C23direct (N × H)
183. C23#11908direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#25672
C23×#18012
C23×#14612
C23×#13542
#1190823