Finite Group Databasebeta

← #19212186

Subgroups — #19212186

Order 5888.

516 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 143 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
1#15675966C211yesmaximal, characteristic
2#15673245C212yesmaximal
3#15671223C211yesmaximal, characteristic
4#15671222C212yesmaximal
5C23×#1272C211yesmaximal, characteristic
6C2×#10625115C411yescharacteristic
7C2×Q8×Dic23C411yescharacteristic
8C2×#10625058C411yescharacteristic
9C2×Dic23⋊C8—22no—
10C2×C8×Dic23—22no—
11#13092323C2211yescharacteristic
12#13092314—22no—
13#13092286C411yescharacteristic
14#13092268—22no—
15C42×Dic23C2211yescharacteristic
16#13092172C2212yes—
17C23×#391C2211yescharacteristic
18C23×#336C2212yes—
19C22×Q8×C23C2×C411yescharacteristic
20C22×Dic46C2×C411yescharacteristic
21C22×C8×C23—22no—
22C2×C4⋊C4×C23C2×C411yescharacteristic
23C2×C42×C23C2311yescharacteristic
24Q8×Dic23—42no—
25#10625115—22no—
26#10625115C814yescomplemented
27C2×C4⋊Dic23—21no—
28C2×C4⋊Dic23C2×C411yescharacteristic
29C2×Dic23⋊C4—22no—
30C2×Dic23⋊C4—21no—
31C2×Dic23⋊C4—22no—
32C2×C4×Dic23—21no—
33C2×C4×Dic23—21no—
34C2×C4×Dic23C2×C411yescharacteristic
35C2×C4×Dic23C2×C411yescharacteristic
36C2×C4×Dic23D412yes—
37C2×C4×Dic23D412yes—
38C22×C23⋊C8—22no—
39#10625058—42no—
40C23×#95—22no—
41C23⋊#95—22no—
42Dic23⋊C8—28no—
43C8×Dic23—44no—
44C2×Q8×C23—21no—
45C2×Q8×C23—41no—
46C2×Q8×C23—41no—
47C2×Q8×C23C2×C812yes—
48C22×C4×C23—21no—
49C22×C4×C23—21no—
50C22×C4×C23C22×C411yescharacteristic
51C22×C4×C23C2×D412yes—
52C22×Dic23—21no—
53C22×Dic23—21no—
54C22×Dic23C22⋊C411yescharacteristic
55C22×Dic23C22⋊C412yes—
56C22×Dic23C22⋊C411yescharacteristic
57C2×Dic46—21no—
58C2×Dic46—41no—
59C2×Dic46—41no—
60C2×Dic46C2×C812yes—
61C2×C8×C23—24no—
62C2×C8×C23—42no—
63C2×C8×C23—42no—
64C4⋊C4×C23—41no—
65C42×C23—41no—
66C4⋊Dic23—42no—
67C4⋊Dic23—41no—
68Dic23⋊C4—28no—
69Dic23⋊C4—42no—
70Dic23⋊C4—44no—
71C4×Dic23—22no—
72C4×Dic23—24no—
73C4×Dic23—42no—
74C4×Dic23—42no—
75C4×Dic23C2×C812yes—
76C4×Dic23M1612yes—
77C4×Dic23SD1614yes—
78C4×Dic23Q1614yes—
79C2×C23⋊C8—24no—
80C2×C23⋊C8—42no—
81C2×C23⋊C8—42no—
82#7571—231nomaximal, Sylow
83C23×C23C2×C22⋊C411yescharacteristic
84Q8×C23—42no—
85Q8×C23—42no—
86C2×C4×C23—22no—
87C2×C4×C23—21no—
88C2×C4×C23—21no—
89C2×C4×C23—22no—
90C2×C4×C23—22no—
91C2×C4×C23—41no—
92C2×C4×C23—41no—
93C2×C4×C23—41no—
94C2×C4×C23—42no—
95C2×C4×C23C22×C811yescharacteristic
96C2×C4×C23C2×M1611yescharacteristic
97C2×C4×C23C2×SD1612yes—
98C2×C4×C23C2×Q1612yes—
99C2×Dic23—22no—
100C2×Dic23—21no—
101C2×Dic23—22no—
102C2×Dic23—41no—
103C2×Dic23—41no—
104C2×Dic23—41no—
105C2×Dic23—42no—
106C2×Dic23C22⋊C814yes—
107C2×Dic23#10012yes—
108C2×Dic23#10314yes—
109C2×Dic23#10314yes—
110C2×Dic23#10414yes—
111Dic46—42no—
112Dic46—42no—
113C8×C23—44no—
114C23⋊C8—44no—
115C4×C4⋊Q8—231no—
116C4×C4⋊C8—232no—
117#1272—231no—
118#1272—232no—
119#1272D2311yescharacteristic
120C22×C23C2×C22⋊C811yescharacteristic
121C22×C23#41011yescharacteristic
122C22×C23C2×#10011yescharacteristic
123C22×C23C2×#10312yes—
124C22×C23C2×#10412yes—
125C4×C23—21no—
126C4×C23—21no—
127C4×C23—22no—
128C4×C23—22no—
129C4×C23—42no—
130C4×C23—81no—
131Dic23—42no—
132Dic23—41no—
133Dic23—81no—
134Dic23Q8⋊C818yes—
135Dic23#33314yes—
136C2×C4⋊Q8—231no—
137C2×C4×Q8—231no—
138C2×C4×Q8—231no—
139C2×C4⋊C8—462no—
140C2×C4×C8—462no—
141#391—231no—
142#391C2×D2311yescharacteristic
143#389—462no—
144#384—231no—
145C4×C4⋊C4—462no—
146C43—231no—
147#336—232no—
148#336C2×D2312yes—
149C2×C23#146011yescharacteristic
150C2×C23C2×Q8⋊C812yes—
151C2×C23#150312yes—
152C2×C23#152511yescharacteristic
153C2×C23C2×#33311yescharacteristic
154C22×Q8—231no—
155C22×Q8C4×D2311yescharacteristic
156C22×C8—22no—
157C22×C8—462no—
158C4⋊Q8—234no—
159C4⋊Q8—462no—
160C4×Q8—922no—
161C4×Q8—922no—
162C2×C4⋊C4—231no—
163C2×C4⋊C4—462no—
164C2×C4⋊C4—461no—
165C2×C4⋊C4—461no—
166C2×C4⋊C4—462no—
167C2×C4⋊C4C4×D2311yescharacteristic
168C2×C42—231no—
169C2×C42—232no—
170C2×C42—231no—
171C2×C42—232no—
172C2×C42—461no—
173C2×C42—461no—
174C2×C42C22×D2311yescharacteristic
175C4⋊C8—468no—
176C4×C8—924no—
177#95—22no—
178#95—462no—
179C23#757111yescharacteristic, complemented, Sylow
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—232no—
184C2×Q8—461no—
185C2×Q8—921no—
186C2×Q8—921no—
187C2×Q8C8×D2312yes—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—231no—
191C22×C4—232no—
192C22×C4—231no—
193C22×C4—461no—
194C22×C4—461no—
195C22×C4C2×C4×D2311yescharacteristic
196C22×C4D4×D2312yes—
197C2×C8—24no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—464no—
201C2×C8—922no—
202C2×C8—922no—
203C4⋊C4—41no—
204C4⋊C4—468no—
205C4⋊C4—921no—
206C4⋊C4—924no—
207C4⋊C4—922no—
208C4⋊C4—922no—
209C42—41no—
210C42—232no—
211C42—232no—
212C42—234no—
213C42—234no—
214C42—464no—
215C42—462no—
216C42—922no—
217C42—922no—
218C23C22⋊C4×D2311yescharacteristic
219Q8—42no—
220Q8—42no—
221Q8—922no—
222Q8—922no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—234no—
233C2×C4—232no—
234C2×C4—234no—
235C2×C4—234no—
236C2×C4—234no—
237C2×C4—462no—
238C2×C4—461no—
239C2×C4—462no—
240C2×C4—921no—
241C2×C4—921no—
242C2×C4—921no—
243C2×C4—922no—
244C2×C4C2×C8×D2311yescharacteristic
245C2×C4M16×D2311yescharacteristic
246C2×C4SD16×D2312yes—
247C2×C4Q16×D2312yes—
248C8—44no—
249C8—924no—
250C22C22⋊C8×D2311yescharacteristic
251C22#1309238911yescharacteristic
252C22#100×D2311yescharacteristic
253C22#103×D2312yes—
254C22#104×D2312yes—
255C4—22no—
256C4—22no—
257C4—21no—
258C4—21no—
259C4—42no—
260C4—81no—
261C4—238no—
262C4—234no—
263C4—922no—
264C4—921no—
265C4—1841no—
266C2#1567171611yescharacteristic
267C2D23×Q8⋊C812yes—
268C2#1567189412yes—
269C2#1567198711yescharacteristic
270C2D23×#33311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7571
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
26. #10625115C8semidirect
179. C23#7571semidirect