Finite Group Databasebeta

← #19212332

Subgroups — #19212332

Order 5888.

440 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 111 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#15673539C212yesmaximal
3#15671223C211yesmaximal, characteristic
4#15671222C212yesmaximal
5C23×#1272C211yesmaximal, characteristic
6C2×#10625115C411yescharacteristic
7C2×Q8×Dic23C411yescharacteristic
8C2×#10625058C411yescharacteristic
9#13092323C2211yescharacteristic
10#13092314—22no—
11#13092286C411yescharacteristic
12#13092268—22no—
13C42×Dic23C2211yescharacteristic
14#13092172C2212yes—
15#13092171—22no—
16#13092171—22no—
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—
42C2×Q8×C23—21no—
43C2×Q8×C23—41no—
44C2×Q8×C23—41no—
45C2×Q8×C23C2×C812yes—
46C22×C4×C23—21no—
47C22×C4×C23—21no—
48C22×C4×C23C22×C411yescharacteristic
49C22×C4×C23C2×D412yes—
50C22×Dic23—21no—
51C22×Dic23—21no—
52C22×Dic23C22⋊C411yescharacteristic
53C22×Dic23C22⋊C412yes—
54C22×Dic23C22⋊C411yescharacteristic
55C2×Dic46—21no—
56C2×Dic46—41no—
57C2×Dic46—41no—
58C2×Dic46C2×C812yes—
59C2×C8×C23—42no—
60C2×C8×C23—42no—
61C2×C8×C23—42no—
62C4⋊C4×C23—41no—
63C42×C23—41no—
64C4⋊Dic23—42no—
65C4⋊Dic23—41no—
66Dic23⋊C4—28no—
67Dic23⋊C4—42no—
68Dic23⋊C4—44no—
69C4×Dic23—22no—
70C4×Dic23—22no—
71C4×Dic23—22no—
72C4×Dic23—42no—
73C4×Dic23—42no—
74C4×Dic23—42no—
75C4×Dic23C2×C812yes—
76C4×Dic23M1612yes—
77C2×C23⋊C8—42no—
78C2×C23⋊C8—42no—
79C2×C23⋊C8—42no—
80#7605—231nomaximal, Sylow
81C23×C23C2×C22⋊C411yescharacteristic
82Q8×C23—42no—
83Q8×C23—42no—
84C2×C4×C23—22no—
85C2×C4×C23—21no—
86C2×C4×C23—21no—
87C2×C4×C23—22no—
88C2×C4×C23—22no—
89C2×C4×C23—41no—
90C2×C4×C23—41no—
91C2×C4×C23—41no—
92C2×C4×C23—42no—
93C2×C4×C23C22×C811yescharacteristic
94C2×C4×C23C2×M1611yescharacteristic
95C2×C4×C23#13712yes—
96C2×C4×C23#13712yes—
97C2×Dic23—22no—
98C2×Dic23—22no—
99C2×Dic23—22no—
100C2×Dic23—22no—
101C2×Dic23—21no—
102C2×Dic23—22no—
103C2×Dic23—41no—
104C2×Dic23—41no—
105C2×Dic23—41no—
106C2×Dic23—42no—
107C2×Dic23C22⋊C814yes—
108C2×Dic23#10012yes—
109Dic46—42no—
110Dic46—42no—
111C8×C23—82no—
112C23⋊C8—82no—
113C4×C4⋊Q8—231no—
114#1839—232no—
115#1272—231no—
116#1272—232no—
117#1272D2311yescharacteristic
118C22×C23C2×C22⋊C811yescharacteristic
119C22×C23#41011yescharacteristic
120C22×C23C2×#10011yescharacteristic
121C22×C23#41912yes—
122C22×C23#42112yes—
123C4×C23—21no—
124C4×C23—21no—
125C4×C23—22no—
126C4×C23—22no—
127C4×C23—42no—
128C4×C23—81no—
129Dic23—22no—
130Dic23—24no—
131Dic23—41no—
132Dic23—42no—
133Dic23—81no—
134C2×C4⋊Q8—231no—
135C2×C4×Q8—231no—
136C2×C4×Q8—231no—
137#391—231no—
138#391C2×D2311yescharacteristic
139#389—462no—
140#384—231no—
141C4×C4⋊C4—462no—
142C43—231no—
143#336—232no—
144#336—462no—
145#336—462no—
146#336C2×D2312yes—
147C2×C23#146011yescharacteristic
148C2×C23#147912yes—
149C2×C23#151512yes—
150C2×C23#153611yescharacteristic
151C2×C23#155811yescharacteristic
152C22×Q8—231no—
153C22×Q8C4×D2311yescharacteristic
154C22×C8—22no—
155C22×C8—462no—
156C4⋊Q8—234no—
157C4⋊Q8—462no—
158C4×Q8—922no—
159C4×Q8—922no—
160C2×C4⋊C4—231no—
161C2×C4⋊C4—462no—
162C2×C4⋊C4—461no—
163C2×C4⋊C4—461no—
164C2×C4⋊C4—462no—
165C2×C4⋊C4C4×D2311yescharacteristic
166C2×C42—231no—
167C2×C42—231no—
168C2×C42—232no—
169C2×C42—232no—
170C2×C42—461no—
171C2×C42—461no—
172C2×C42C22×D2311yescharacteristic
173#95—22no—
174#95—462no—
175C23#760511yescharacteristic, complemented, Sylow
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—232no—
180C2×Q8—461no—
181C2×Q8—921no—
182C2×Q8—921no—
183C2×Q8C8×D2312yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—231no—
187C22×C4—232no—
188C22×C4—231no—
189C22×C4—461no—
190C22×C4—461no—
191C22×C4C2×C4×D2311yescharacteristic
192C22×C4D4×D2312yes—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—922no—
197C2×C8—922no—
198C2×C8—922no—
199C4⋊C4—41no—
200C4⋊C4—468no—
201C4⋊C4—921no—
202C4⋊C4—922no—
203C4⋊C4—922no—
204C4⋊C4—924no—
205C42—41no—
206C42—232no—
207C42—232no—
208C42—462no—
209C42—462no—
210C42—462no—
211C42—922no—
212C42—922no—
213C42—922no—
214C23C22⋊C4×D2311yescharacteristic
215Q8—42no—
216Q8—42no—
217Q8—922no—
218Q8—922no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—234no—
229C2×C4—232no—
230C2×C4—462no—
231C2×C4—462no—
232C2×C4—462no—
233C2×C4—462no—
234C2×C4—461no—
235C2×C4—462no—
236C2×C4—921no—
237C2×C4—921no—
238C2×C4—921no—
239C2×C4—922no—
240C2×C4C2×C8×D2311yescharacteristic
241C2×C4M16×D2311yescharacteristic
242C2×C4#1062508612yes—
243C2×C4#1062508912yes—
244C8—82no—
245C8—1842no—
246C22C22⋊C8×D2311yescharacteristic
247C22#1309238911yescharacteristic
248C22#100×D2311yescharacteristic
249C22#1309242412yes—
250C22#1309243212yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—42no—
256C4—81no—
257C4—462no—
258C4—464no—
259C4—922no—
260C4—921no—
261C4—1841no—
262C2#1567171611yescharacteristic
263C2#1567179012yes—
264C2#1567194612yes—
265C2#1567203011yescharacteristic
266C2#1567212111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7605
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
175. C23#7605semidirect