Finite Group Databasebeta

← C23×#9030 #19156656

Subgroups — C23×#9030 #19156656

Order 5888.

484 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#2983C211yesmaximal, characteristic
2C23×#2399C211yesmaximal, characteristic
3C4×C23×#101C211yesmaximal, characteristic
4C23×#1491C212yesmaximal
5C23×#1300C212yesmaximal
6C2×C4×Q8×C23C2211yescharacteristic
7C2×C4×Q8×C23C2211yescharacteristic
8C23×#446—24no—
9C23×#432—21no—
10C23×#432C2212yes—
11C23×#431—21no—
12C2×C23×#101—21no—
13C4×M16×C23C2212yes—
14C23×#398—21no—
15C23×#398C411yescharacteristic
16C23×#398C411yescharacteristic
17C23×#395—21no—
18C23×#395C411yescharacteristic
19C23×#395C411yescharacteristic
20C4×C4⋊C4×C23—21no—
21C4×C4⋊C4×C23—21no—
22C23×#376C2211yescharacteristic
23C23×#343—21no—
24C23×Q8⋊C8—24no—
25C22×Q8×C23C2×C411yescharacteristic
26C22×Q8×C23D411yescharacteristic
27C2×M16×C23—22no—
28C4×Q8×C23—22no—
29C4×Q8×C23—22no—
30C4×Q8×C23—22no—
31C4×Q8×C23—22no—
32C2×C4⋊C4×C23—21no—
33C2×C4⋊C4×C23—21no—
34C2×C4⋊C4×C23—21no—
35C2×C4⋊C4×C23—21no—
36C2×C4⋊C4×C23—21no—
37C2×C4⋊C4×C23C2×C411yescharacteristic
38C2×C4⋊C4×C23C2×C411yescharacteristic
39C2×C4⋊C4×C23C2×C411yescharacteristic
40C2×C4⋊C4×C23D411yescharacteristic
41C2×C42×C23—21no—
42C2×C42×C23—21no—
43C2×C42×C23D411yescharacteristic
44C2×C42×C23D411yescharacteristic
45C2×C42×C23C2311yescharacteristic
46C23×C4⋊C8—22no—
47C23×C4⋊C8—22no—
48C23×C4⋊C8D414yes—
49C23×#101—24no—
50C23×C22⋊C8—22no—
51C23×#97—22no—
52C23×#97—22no—
53C23×#97—22no—
54C4×C8×C23—22no—
55C4×C8×C23—22no—
56C23×#95—21no—
57C23×#95—21no—
58C23×#95—21no—
59C23×#95—21no—
60C23×#95—21no—
61C23×#95C2×C411yescharacteristic
62C23×#95C2×C411yescharacteristic
63C2×Q8×C23—22no—
64C2×Q8×C23—22no—
65C2×Q8×C23—22no—
66C2×Q8×C23—41no—
67C2×Q8×C23—42no—
68C22×C4×C23—21no—
69C22×C4×C23—21no—
70C22×C4×C23—21no—
71C22×C4×C23—21no—
72C22×C4×C23C22⋊C411yescharacteristic
73C22×C4×C23C22⋊C411yescharacteristic
74C22×C4×C23C22⋊C411yescharacteristic
75C22×C4×C23C22⋊C411yescharacteristic
76C22×C4×C23C22×C411yescharacteristic
77C22×C4×C23C2×D411yescharacteristic
78C22×C4×C23C2×D411yescharacteristic
79M16×C23—24no—
80M16×C23—42no—
81C2×C8×C23—24no—
82C2×C8×C23—42no—
83C4⋊C4×C23—22no—
84C4⋊C4×C23—22no—
85C4⋊C4×C23—22no—
86C4⋊C4×C23—22no—
87C4⋊C4×C23—42no—
88C4⋊C4×C23—42no—
89C4⋊C4×C23—42no—
90C4⋊C4×C23—42no—
91C4⋊C4×C23—42no—
92C42×C23—24no—
93C42×C23—21no—
94C42×C23—21no—
95C42×C23—21no—
96C42×C23—21no—
97C42×C23—41no—
98C42×C23—41no—
99C42×C23C2×D412yes—
100C42×C23#4112yes—
101#9030C2311yesmaximal, characteristic, direct product factor, Sylow
102C23×C23C2×C22⋊C411yescharacteristic
103Q8×C23—24no—
104Q8×C23—44no—
105Q8×C23—42no—
106C2×C4×C23—21no—
107C2×C4×C23—21no—
108C2×C4×C23—21no—
109C2×C4×C23—21no—
110C2×C4×C23—22no—
111C2×C4×C23—22no—
112C2×C4×C23—22no—
113C2×C4×C23—22no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—41no—
120C2×C4×C23—41no—
121C2×C4×C23—41no—
122C2×C4×C23—41no—
123C2×C4×C23—41no—
124C2×C4×C23—41no—
125C2×C4×C23—41no—
126C2×C4×C23—41no—
127C2×C4×C23—41no—
128C2×C4×C23—41no—
129C2×C4×C23—41no—
130C2×C4×C23—41no—
131C2×C4×C23#10412yes—
132C2×C4×C23C4×D412yes—
133C2×C4×C23#12011yescharacteristic
134C2×C4×C23#12112yes—
135C2×C4×C23#12311yescharacteristic
136C8×C23—44no—
137C8×C23—44no—
138#2983C2×C2311yescharacteristic
139#2399C2×C2311yescharacteristic
140C4×#101C2×C2311yescharacteristic
141#1491C2×C2312yes—
142#1300C2×C2312yes—
143C22×C23—21no—
144C22×C23—21no—
145C22×C23#38611yescharacteristic
146C22×C23C2×#10411yescharacteristic
147C22×C23#42111yescharacteristic
148C4×C23—22no—
149C4×C23—22no—
150C4×C23—21no—
151C4×C23—22no—
152C4×C23—42no—
153C4×C23—42no—
154C4×C23—41no—
155C4×C23—41no—
156C4×C23—41no—
157C4×C23—42no—
158C4×C23—81no—
159C4×C23#45612yes—
160C2×C4×Q8C22×C2311yescharacteristic
161C2×C4×Q8C22×C2311yescharacteristic
162#446—24no—
163#432—21no—
164#432C22×C2312yes—
165#431—21no—
166C2×#101—21no—
167C4×M16C22×C2312yes—
168#398—21no—
169#398C4×C2311yescharacteristic
170#398C4×C2311yescharacteristic
171#395—21no—
172#395C4×C2311yescharacteristic
173#395C4×C2311yescharacteristic
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176#376C22×C2311yescharacteristic
177#343—21no—
178Q8⋊C8—24no—
179C2×C23—21no—
180C2×C23—21no—
181C2×C23#187111yescharacteristic
182C2×C23#188611yescharacteristic
183C2×C23#189111yescharacteristic
184C22×Q8C2×C4×C2311yescharacteristic
185C22×Q8D4×C2311yescharacteristic
186C2×M16—22no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C2×C4×C2311yescharacteristic
197C2×C4⋊C4C2×C4×C2311yescharacteristic
198C2×C4⋊C4C2×C4×C2311yescharacteristic
199C2×C4⋊C4D4×C2311yescharacteristic
200C2×C42—21no—
201C2×C42—21no—
202C2×C42D4×C2311yescharacteristic
203C2×C42D4×C2311yescharacteristic
204C2×C42C23×C2311yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8D4×C2314yes—
208#101—24no—
209C22⋊C8—22no—
210#97—22no—
211#97—22no—
212#97—22no—
213C4×C8—22no—
214C4×C8—22no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×C4×C2311yescharacteristic
221#95C2×C4×C2311yescharacteristic
222C23#903011yescharacteristic, direct product factor, Sylow
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—42no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4C22⋊C4×C2311yescharacteristic
233C22×C4C22⋊C4×C2311yescharacteristic
234C22×C4C22⋊C4×C2311yescharacteristic
235C22×C4C22⋊C4×C2311yescharacteristic
236C22×C4C22×C4×C2311yescharacteristic
237C22×C4C2×D4×C2311yescharacteristic
238C22×C4C2×D4×C2311yescharacteristic
239M16—24no—
240M16—42no—
241C2×C8—24no—
242C2×C8—42no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C42—24no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—41no—
258C42—41no—
259C42C2×D4×C2312yes—
260C42#41×C2312yes—
261C23C2×C22⋊C4×C2311yescharacteristic
262Q8—24no—
263Q8—44no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4C23×#10412yes—
291C2×C4C4×D4×C2312yes—
292C2×C4C23×#12011yescharacteristic
293C2×C4C23×#12112yes—
294C2×C4C23×#12311yescharacteristic
295C8—44no—
296C8—44no—
297C22—21no—
298C22—21no—
299C22C23×#38611yescharacteristic
300C22C2×C23×#10411yescharacteristic
301C22C23×#42111yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4C23×#45612yes—
314C2—21no—
315C2—21no—
316C2C23×#187111yescharacteristic
317C2C23×#188611yescharacteristic
318C2C23×#189111yescharacteristic
subgroupG/H
centerC2×C4×C23#120
commutatorC22×C4C22×C4×C23
Frattini, cosocleC2×C42C23×C23
socleC22×C23#386
prime radicalC23×C23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
101. #9030C23direct (N × H)
222. C23#9030direct (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×#23992
C4×C23×#1012
C23×#14912
C23×#13002
#903023