Finite Group Databasebeta

← #19212287

Subgroups — #19212287

Order 5888.

566 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13092315C211yesmaximal, characteristic
2#15673465C211yesmaximal, characteristic
3#15671221C214yesmaximal, complemented
4C23×#1817C211yesmaximal, characteristic
5C22×C4⋊Dic23C411yescharacteristic
6C22×C4⋊Dic23C411yescharacteristic
7C22×Dic23⋊C4—21no—
8C2×C22⋊(C23⋊C8)—21no—
9#13092315—21no—
10#13092315—21no—
11#13092315C412yes—
12#13092315C2212yes—
13C2×C23⋊#95—21no—
14#13092172—21no—
15#13092172C2212yes—
16C22×C42×C23C2211yescharacteristic
17C2×C23×C22⋊C8—21no—
18C23×#336—21no—
19C23×#336C2212yes—
20C23×C4×C23C2×C411yescharacteristic
21C23×C4×C23D411yescharacteristic
22C23×C4×C23D411yescharacteristic
23C23×Dic23—21no—
24C23×Dic23—21no—
25C22×C8×C23—22no—
26C2×C42×C23—42no—
27C2×C42×C23C2×C411yescharacteristic
28C2×C42×C23D411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23C2311yescharacteristic
31C2×C4⋊Dic23—21no—
32C2×C4⋊Dic23—22no—
33C2×C4⋊Dic23—21no—
34C2×C4⋊Dic23—42no—
35C2×C4⋊Dic23C814yescomplemented
36C2×C4⋊Dic23C2×C412yes—
37C2×C4⋊Dic23C2×C412yes—
38C2×Dic23⋊C4—22no—
39C2×Dic23⋊C4—22no—
40C2×Dic23⋊C4—44no—
41C22×C23⋊C8—22no—
42C23×C22⋊C8—42no—
43C23⋊#95—22no—
44C23⋊#95—22no—
45C22⋊(C23⋊C8)—42no—
46C24×C23C22⋊C411yescharacteristic
47C22×C4×C23—22no—
48C22×C4×C23—22no—
49C22×C4×C23—22no—
50C22×C4×C23—22no—
51C22×C4×C23—22no—
52C22×C4×C23—22no—
53C22×C4×C23—41no—
54C22×C4×C23—41no—
55C22×C4×C23C22⋊C411yescharacteristic
56C22×C4×C23C22⋊C411yescharacteristic
57C22×C4×C23C22⋊C411yescharacteristic
58C22×C4×C23C2×C812yes—
59C22×C4×C23M1612yes—
60C22×C4×C23C22×C411yescharacteristic
61C22×C4×C23C2×D411yescharacteristic
62C22×C4×C23C2×D411yescharacteristic
63C22×Dic23—24no—
64C22×Dic23—22no—
65C22×Dic23—22no—
66C22×Dic23—42no—
67C22×Dic23—42no—
68C22×Dic23—42no—
69C22×Dic23—42no—
70C22×Dic23—42no—
71C2×C8×C23—42no—
72C2×C8×C23—42no—
73C2×C8×C23—42no—
74C42×C23—41no—
75C42×C23—41no—
76C42×C23—41no—
77C42×C23—41no—
78C4⋊Dic23—24no—
79C4⋊Dic23—22no—
80C4⋊Dic23—42no—
81C4⋊Dic23—42no—
82C4⋊Dic23C2×C814yes—
83Dic23⋊C4—44no—
84Dic23⋊C4—44no—
85C2×C23⋊C8—42no—
86C2×C23⋊C8—42no—
87C2×C23⋊C8—42no—
88#7593—231nomaximal, Sylow
89C23×C23—21no—
90C23×C23—21no—
91C23×C23—21no—
92C23×C23—21no—
93C23×C23C22⋊C812yes—
94C23×C23#9912yes—
95C23×C23#10112yes—
96C23×C23C2×C22⋊C411yescharacteristic
97C2×C4×C23—24no—
98C2×C4×C23—24no—
99C2×C4×C23—21no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—21no—
105C2×C4×C23—21no—
106C2×C4×C23—21no—
107C2×C4×C23—21no—
108C2×C4×C23—21no—
109C2×C4×C23—21no—
110C2×C4×C23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—44no—
114C2×C4×C23—44no—
115C2×C4×C23C22⋊C812yes—
116C2×C4×C23C22×C811yescharacteristic
117C2×C4×C23C2×M1611yescharacteristic
118C2×C4×C23AGL(1,ℤ/8)12yes—
119C2×C4×C23#13712yes—
120C2×Dic23—24no—
121C2×Dic23—48no—
122C2×Dic23—42no—
123C2×Dic23—42no—
124C2×Dic23—42no—
125C2×Dic23—42no—
126C2×Dic23—42no—
127C2×Dic23—84no—
128C8×C23—82no—
129C23⋊C8—82no—
130C2×#389—231no—
131#1817—231no—
132#1817D2311yescharacteristic
133#1271—234no—
134C22×C23—22no—
135C22×C23—22no—
136C22×C23—22no—
137C22×C23—22no—
138C22×C23—22no—
139C22×C23—22no—
140C22×C23#32414yes—
141C22×C23C2×C22⋊C811yescharacteristic
142C22×C23C2×#9911yescharacteristic
143C22×C23C2×#10111yescharacteristic
144C22×C23#41811yescharacteristic
145C22×C23#41911yescharacteristic
146C22×C23#42111yescharacteristic
147C22×C23#42111yescharacteristic
148C4×C23—22no—
149C4×C23—21no—
150C4×C23—21no—
151C4×C23—22no—
152C4×C23—22no—
153C4×C23—41no—
154C4×C23—41no—
155Dic23—44no—
156Dic23—82no—
157C22×C4⋊C4—231no—
158C22×C4⋊C4—231no—
159C22×C4⋊C4—461no—
160C22×C42C2×D2311yescharacteristic
161C2×C22⋊C8—21no—
162C2×C22⋊C8—461no—
163#389—232no—
164#389—232no—
165#389—461no—
166#389—461no—
167C2×#95—461no—
168#336—21no—
169#336—232no—
170#336—461no—
171#336C2×D2312yes—
172C2×C23—24no—
173C2×C23C2×#32411yescharacteristic
174C2×C23#147811yescharacteristic
175C2×C23#147911yescharacteristic
176C2×C23#151011yescharacteristic
177C2×C23#151111yescharacteristic
178C2×C23#153411yescharacteristic
179C2×C23#155611yescharacteristic
180C23×C4—461no—
181C23×C4—461no—
182C23×C4C4×D2311yescharacteristic
183C23×C4D9211yescharacteristic
184C23×C4C22⋊D2311yescharacteristic
185C22×C8—22no—
186C22×C8—462no—
187C2×C4⋊C4—234no—
188C2×C4⋊C4—232no—
189C2×C4⋊C4—232no—
190C2×C4⋊C4—462no—
191C2×C4⋊C4—461no—
192C2×C4⋊C4—461no—
193C2×C4⋊C4—462no—
194C2×C4⋊C4—462no—
195C2×C4⋊C4—922no—
196C2×C4⋊C4—924no—
197C2×C42—42no—
198C2×C42C4×D2311yescharacteristic
199C2×C42D9211yescharacteristic
200C2×C42C22⋊D2311yescharacteristic
201C2×C42C22×D2311yescharacteristic
202C22⋊C8—42no—
203C22⋊C8—922no—
204#95—462no—
205#95—462no—
206C23#759311yescharacteristic, complemented, Sylow
207C24(C2×D23)⋊C411yescharacteristic
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—462no—
217C22×C4—464no—
218C22×C4—462no—
219C22×C4—922no—
220C22×C4—922no—
221C22×C4—922no—
222C22×C4—922no—
223C22×C4—922no—
224C22×C4C8×D2312yes—
225C22×C4#6726212yes—
226C22×C4(C2×D23)⋊C411yescharacteristic
227C22×C4(C2×D23)⋊C411yescharacteristic
228C22×C4(C2×D23)⋊C411yescharacteristic
229C22×C4C2×C4×D2311yescharacteristic
230C22×C4C2×D9211yescharacteristic
231C22×C4C2×C22⋊D2311yescharacteristic
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—922no—
236C2×C8—922no—
237C2×C8—922no—
238C4⋊C4—234no—
239C4⋊C4—462no—
240C4⋊C4—464no—
241C4⋊C4—922no—
242C4⋊C4—924no—
243C4⋊C4—922no—
244C4⋊C4—924no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—41no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23#1062498812yes—
254C23(C2×D23)⋊C812yes—
255C23#1062500612yes—
256C23C2×(C2×D23)⋊C411yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—464no—
276C2×C4—928no—
277C2×C4—922no—
278C2×C4—922no—
279C2×C4—922no—
280C2×C4—922no—
281C2×C4—922no—
282C2×C4—1844no—
283C2×C4(C2×D23)⋊C812yes—
284C2×C4C2×C8×D2311yescharacteristic
285C2×C4C2×#6726211yescharacteristic
286C2×C4#1062508012yes—
287C2×C4#1062512012yes—
288C8—82no—
289C8—1842no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22#1309214214yes—
297C22C2×(C2×D23)⋊C811yescharacteristic
298C22C2×#1062498811yescharacteristic
299C22C2×#1062500611yescharacteristic
300C22#1309242111yescharacteristic
301C22#1309242711yescharacteristic
302C22#1309243311yescharacteristic
303C22#1309243511yescharacteristic
304C4—22no—
305C4—22no—
306C4—21no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—924no—
312C4—1842no—
313C2—24no—
314C2C2×#1309214211yescharacteristic
315C2#1567178711yescharacteristic
316C2#1567179311yescharacteristic
317C2#1567192511yescharacteristic
318C2#1567193111yescharacteristic
319C2#1567202311yescharacteristic
320C2#1567211511yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1817C2
socleC23×C23C2×C22⋊C4
hypercenter#1817D23
hypocenterC23#7593
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #15671221C2semidirect
35. C2×C4⋊Dic23C8semidirect
206. C23#7593semidirect