Finite Group Databasebeta

← C23×#7554 #19155180

Subgroups — C23×#7554 #19155180

Order 5888.

3158 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C23C211yesmaximal, characteristic
2C22×C23×#95C216yesmaximal
3C24×C4×C23C2214yes—
4C24×C4×C23C2213yes—
5C22×C42×C23—212no—
6C22×C42×C23C414yescomplemented
7C2×C23×#95—212no—
8C2×C23×#95—212no—
9C2×C23×#95C4124yescomplemented
10C25×C23C2311yescharacteristic
11C23×C4×C23—212no—
12C23×C4×C23—212no—
13C23×C4×C23—212no—
14C23×C4×C23—212no—
15C23×C4×C23—224no—
16C23×C4×C23C2×C4124yes—
17C23×C4×C23C2×C4112yes—
18C23×C4×C23C2×C416yes—
19C23×C4×C23D416yes—
20C23×C4×C23D4112yes—
21C23×C4×C23Q816yes—
22C2×C42×C23—232no—
23C2×C42×C23—224no—
24C23×#95—248no—
25C24×C23C22×C411yescharacteristic
26C24×C23C22×C416yes—
27C24×C23C2×D416yes—
28C24×C23C2×D413yes—
29C24×C23C2×Q813yes—
30C24×C23#41112yes—
31C22×C4×C23—212no—
32C22×C4×C23—212no—
33C22×C4×C23—248no—
34C22×C4×C23—224no—
35C22×C4×C23—224no—
36C22×C4×C23—224no—
37C22×C4×C23—224no—
38C22×C4×C23—224no—
39C22×C4×C23—224no—
40C22×C4×C23—248no—
41C22×C4×C23—248no—
42C22×C4×C23—44no—
43C22×C4×C23—424no—
44C22×C4×C23—412no—
45C22×C4×C23—412no—
46C22×C4×C23—48no—
47C22×C4×C23—44no—
48C22×C4×C23C42112yes—
49C22×C4×C23C42116yescomplemented
50C22×C4×C23C22⋊C4112yes—
51C22×C4×C23C22⋊C4124yes—
52C22×C4×C23C4⋊C4112yes—
53C22×C4×C23C4⋊C4124yes—
54C42×C23—232no—
55#7554C2311yesmaximal, characteristic, direct product factor, Sylow
56C23×C23C2×C4213yes—
57C23×C23C2×C4214yes—
58C23×C23C2×C22⋊C413yes—
59C23×C23C2×C22⋊C416yes—
60C23×C23C2×C4⋊C413yes—
61C23×C23C2×C4⋊C416yes—
62C23×C23#11716yes—
63C23×C23#117112yes—
64C23×C23C4×D4124yes—
65C23×C23C4×D4112yes—
66C23×C23C4×Q8112yes—
67C23×C23#12014yes—
68C23×C23#121112yes—
69C23×C23C22⋊Q8112yes—
70C23×C23#123112yes—
71C23×C23#12416yes—
72C23×C23#12516yes—
73C23×C23#12618yes—
74C23×C23#12711yescharacteristic
75C23×C23C4⋊Q813yes—
76C2×C4×C23—224no—
77C2×C4×C23—212no—
78C2×C4×C23—224no—
79C2×C4×C23—212no—
80C2×C4×C23—248no—
81C2×C4×C23—248no—
82C2×C4×C23—248no—
83C2×C4×C23—424no—
84C2×C4×C23—448no—
85C2×C4×C23—424no—
86C2×C4×C23#95124yescomplemented
87C23×C42C2×C2311yescharacteristic
88C22×#95C2×C2316yes—
89C22×C23C4311yescharacteristic
90C22×C23C2×#9513yes—
91C22×C23#37613yes—
92C22×C23C4×C22⋊C416yes—
93C22×C23C4×C22⋊C4112yes—
94C22×C23C4×C4⋊C416yes—
95C22×C23C4×C4⋊C4112yes—
96C22×C23#37911yescharacteristic
97C22×C23#38016yes—
98C22×C23#38113yes—
99C22×C23#38213yes—
100C22×C23#38312yes—
101C22×C23#38411yescharacteristic
102C22×C23#385112yes—
103C22×C23#386112yes—
104C22×C23#387124yes—
105C22×C23#388124yes—
106C22×C23#389112yes—
107C22×C23#39016yes—
108C22×C23#39116yes—
109C4×C23—224no—
110C4×C23—416no—
111C24×C4C22×C2314yes—
112C24×C4C22×C2313yes—
113C22×C42—212no—
114C22×C42C4×C2314yescomplemented
115C2×#95—212no—
116C2×#95—212no—
117C2×#95C4×C23124yescomplemented
118C2×C23C4×#9513yes—
119C2×C23C22⋊#9513yes—
120C2×C23#143416yes—
121C2×C23C4⋊#9513yes—
122C2×C23#1436112yes—
123C2×C23#143714yes—
124C25C23×C2311yescharacteristic
125C23×C4—212no—
126C23×C4—212no—
127C23×C4—212no—
128C23×C4—212no—
129C23×C4—224no—
130C23×C4C2×C4×C23124yes—
131C23×C4C2×C4×C23112yes—
132C23×C4C2×C4×C2316yes—
133C23×C4D4×C2316yes—
134C23×C4D4×C23112yes—
135C23×C4Q8×C2316yes—
136C2×C42—232no—
137C2×C42—224no—
138#95—248no—
139C23#755411yescharacteristic, direct product factor, Sylow
140C24C22×C4×C2311yescharacteristic
141C24C22×C4×C2316yes—
142C24C2×D4×C2316yes—
143C24C2×D4×C2313yes—
144C24C2×Q8×C2313yes—
145C24#41×C23112yes—
146C22×C4—212no—
147C22×C4—212no—
148C22×C4—248no—
149C22×C4—224no—
150C22×C4—224no—
151C22×C4—224no—
152C22×C4—224no—
153C22×C4—224no—
154C22×C4—224no—
155C22×C4—248no—
156C22×C4—248no—
157C22×C4—44no—
158C22×C4—424no—
159C22×C4—412no—
160C22×C4—412no—
161C22×C4—48no—
162C22×C4—44no—
163C22×C4C42×C23112yes—
164C22×C4C42×C23116yescomplemented
165C22×C4C22⋊C4×C23124yes—
166C22×C4C22⋊C4×C23112yes—
167C22×C4C4⋊C4×C23112yes—
168C22×C4C4⋊C4×C23124yes—
169C42—232no—
170C23C2×C42×C2313yes—
171C23C2×C42×C2314yes—
172C23C2×C22⋊C4×C2313yes—
173C23C2×C22⋊C4×C2316yes—
174C23C2×C4⋊C4×C2313yes—
175C23C2×C4⋊C4×C2316yes—
176C23C23×#11716yes—
177C23C23×#117112yes—
178C23C4×D4×C23124yes—
179C23C4×D4×C23112yes—
180C23C4×Q8×C23112yes—
181C23C23×#12014yes—
182C23C23×#121112yes—
183C23C23×C22⋊Q8112yes—
184C23C23×#123112yes—
185C23C23×#12416yes—
186C23C23×#12516yes—
187C23C23×#12618yes—
188C23C23×#12711yescharacteristic
189C23C23×C4⋊Q813yes—
190C2×C4—224no—
191C2×C4—212no—
192C2×C4—224no—
193C2×C4—212no—
194C2×C4—248no—
195C2×C4—248no—
196C2×C4—248no—
197C2×C4—424no—
198C2×C4—448no—
199C2×C4—424no—
200C2×C4C23×#95124yescomplemented
201C22C43×C2311yescharacteristic
202C22C2×C23×#9513yes—
203C22C23×#37613yes—
204C22C4×C22⋊C4×C2316yes—
205C22C4×C22⋊C4×C23112yes—
206C22C4×C4⋊C4×C2316yes—
207C22C4×C4⋊C4×C23112yes—
208C22C23×#37911yescharacteristic
209C22C23×#38016yes—
210C22C23×#38113yes—
211C22C23×#38213yes—
212C22C23×#38312yes—
213C22C23×#38411yescharacteristic
214C22C23×#385112yes—
215C22C23×#386112yes—
216C22C23×#387124yes—
217C22C23×#388124yes—
218C22C23×#389112yes—
219C22C23×#39016yes—
220C22C23×#39116yes—
221C4—224no—
222C4—416no—
223C2C4×C23×#9513yes—
224C2C23×C22⋊#9513yes—
225C2C23×#143416yes—
226C2C23×C4⋊#9513yes—
227C2C23×#1436112yes—
228C2C23×#143714yes—
subgroupG/H
center, socle, prime radicalC25×C23C23
commutatorC22C43×C23
Frattini, cosocleC25C23×C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C23 ◁ G

Complements

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

NH ≅ G/Ntype
6. C22×C42×C23C4semidirect
9. C2×C23×#95C4semidirect
49. C22×C4×C23C42semidirect
55. #7554C23direct (N × H)
86. C2×C4×C23#95semidirect
114. C22×C42C4×C23semidirect
117. C2×#95C4×C23semidirect
139. C23#7554direct (N × H)
164. C22×C4C42×C23semidirect
200. C2×C4C23×#95semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C232
C22×C23×#952
#755423