Finite Group Databasebeta

← #19212286

Subgroups — #19212286

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
1#15673465C211yesmaximal, characteristic
2#15673465C211yesmaximal, characteristic
3#15671220C214yesmaximal, complemented
4C2×C23×#389C211yesmaximal, characteristic
5C2×C22⋊(C23⋊C8)—21no—
6C2×C22⋊(C23⋊C8)—21no—
7#13092172—21no—
8#13092172—21no—
9#13092172C2212yes—
10#13092172C2212yes—
11C22×C4⋊C4×C23—21no—
12C22×C4⋊C4×C23C411yescharacteristic
13C22×C4⋊C4×C23C411yescharacteristic
14C22×C42×C23C2211yescharacteristic
15C23×#389—21no—
16C23×#389—21no—
17C23×#389C412yes—
18C23×#389C2212yes—
19C2×C23×#95—21no—
20C23×C4×C23—21no—
21C23×C4×C23—21no—
22C23×C4×C23C2×C411yescharacteristic
23C23×C4×C23D411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C2×C4⋊C4×C23—21no—
26C2×C4⋊C4×C23—22no—
27C2×C4⋊C4×C23—21no—
28C2×C4⋊C4×C23—22no—
29C2×C4⋊C4×C23—22no—
30C2×C4⋊C4×C23—42no—
31C2×C4⋊C4×C23—44no—
32C2×C4⋊C4×C23C814yescomplemented
33C2×C4⋊C4×C23C2×C412yes—
34C2×C4⋊C4×C23C2×C412yes—
35C2×C42×C23—42no—
36C2×C42×C23C2×C411yescharacteristic
37C2×C42×C23D411yescharacteristic
38C2×C42×C23D411yescharacteristic
39C2×C42×C23C2311yescharacteristic
40C22×C23⋊C8—22no—
41C22×C23⋊C8—22no—
42C23×#95—22no—
43C23×#95—22no—
44C22⋊(C23⋊C8)—42no—
45C22⋊(C23⋊C8)—42no—
46C24×C23C22⋊C411yescharacteristic
47C22×C4×C23—22no—
48C22×C4×C23—22no—
49C22×C4×C23—24no—
50C22×C4×C23—22no—
51C22×C4×C23—22no—
52C22×C4×C23—22no—
53C22×C4×C23—22no—
54C22×C4×C23—22no—
55C22×C4×C23—22no—
56C22×C4×C23—41no—
57C22×C4×C23—41no—
58C22×C4×C23—42no—
59C22×C4×C23—42no—
60C22×C4×C23—42no—
61C22×C4×C23—42no—
62C22×C4×C23—42no—
63C22×C4×C23C22⋊C411yescharacteristic
64C22×C4×C23C22⋊C411yescharacteristic
65C22×C4×C23C22⋊C411yescharacteristic
66C22×C4×C23C2×C812yes—
67C22×C4×C23M1612yes—
68C22×C4×C23C22×C411yescharacteristic
69C22×C4×C23C2×D411yescharacteristic
70C22×C4×C23C2×D411yescharacteristic
71C4⋊C4×C23—24no—
72C4⋊C4×C23—22no—
73C4⋊C4×C23—42no—
74C4⋊C4×C23—42no—
75C4⋊C4×C23—44no—
76C4⋊C4×C23—44no—
77C4⋊C4×C23C2×C814yes—
78C42×C23—41no—
79C42×C23—41no—
80C42×C23—41no—
81C42×C23—41no—
82C2×C23⋊C8—42no—
83C2×C23⋊C8—42no—
84C2×C23⋊C8—42no—
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—24no—
108C2×C4×C23—21no—
109C2×C4×C23—21no—
110C2×C4×C23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23—44no—
115C2×C4×C23—44no—
116C2×C4×C23—48no—
117C2×C4×C23—42no—
118C2×C4×C23—42no—
119C2×C4×C23—42no—
120C2×C4×C23—42no—
121C2×C4×C23—42no—
122C2×C4×C23—84no—
123C2×C4×C23C22⋊C812yes—
124C2×C4×C23C22×C811yescharacteristic
125C2×C4×C23C2×M1611yescharacteristic
126C2×C4×C23AGL(1,ℤ/8)12yes—
127C2×C4×C23#13712yes—
128C23⋊C8—82no—
129C23⋊C8—82no—
130C2×#389D2311yescharacteristic
131#1817—231no—
132#1817—231no—
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—44no—
154C4×C23—41no—
155C4×C23—41no—
156C4×C23—82no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4Dic2311yescharacteristic
159C22×C4⋊C4Dic2311yescharacteristic
160C22×C42C2×D2311yescharacteristic
161C2×C22⋊C8—461no—
162C2×C22⋊C8—461no—
163#389—21no—
164#389—21no—
165#389Dic2312yes—
166#389C2×D2312yes—
167C2×#95—21no—
168#336—232no—
169#336—232no—
170#336—461no—
171#336—461no—
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—21no—
181C23×C4—21no—
182C23×C4C2×Dic2311yescharacteristic
183C23×C4C22⋊D2311yescharacteristic
184C23×C4C22⋊D2311yescharacteristic
185C22×C8—462no—
186C22×C8—462no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4C23⋊C814yescomplemented
195C2×C4⋊C4C2×Dic2312yes—
196C2×C4⋊C4C2×Dic2312yes—
197C2×C42—42no—
198C2×C42C2×Dic2311yescharacteristic
199C2×C42C22⋊D2311yescharacteristic
200C2×C42C22⋊D2311yescharacteristic
201C2×C42C22×D2311yescharacteristic
202C22⋊C8—922no—
203C22⋊C8—922no—
204#95—22no—
205#95—22no—
206C23#759311yescharacteristic, complemented, Sylow
207C24C22⋊Dic2311yescharacteristic
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4C2×C23⋊C812yes—
225C22×C4#6726712yes—
226C22×C4C22⋊Dic2311yescharacteristic
227C22×C4C22⋊Dic2311yescharacteristic
228C22×C4C22⋊Dic2311yescharacteristic
229C22×C4C22×Dic2311yescharacteristic
230C22×C4C2×C22⋊D2311yescharacteristic
231C22×C4C2×C22⋊D2311yescharacteristic
232C2×C8—922no—
233C2×C8—922no—
234C2×C8—922no—
235C2×C8—922no—
236C2×C8—922no—
237C2×C8—922no—
238C4⋊C4—22no—
239C4⋊C4—24no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4C2×C23⋊C814yes—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—41no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23C22⋊(C23⋊C8)12yes—
254C23#1062501612yes—
255C23#1062501812yes—
256C23C2×C22⋊Dic2311yescharacteristic
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—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—48no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—84no—
283C2×C4C22⋊(C23⋊C8)12yes—
284C2×C4C22×C23⋊C811yescharacteristic
285C2×C4C2×#6726711yescharacteristic
286C2×C4#1062510312yes—
287C2×C4#1062511312yes—
288C8—1842no—
289C8—1842no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22#1309214314yes—
297C22C2×C22⋊(C23⋊C8)11yescharacteristic
298C22C2×#1062501611yescharacteristic
299C22C2×#1062501811yescharacteristic
300C22#1309242211yescharacteristic
301C22#1309242611yescharacteristic
302C22#1309243411yescharacteristic
303C22#1309243411yescharacteristic
304C4—22no—
305C4—22no—
306C4—21no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—44no—
312C4—82no—
313C2—24no—
314C2C2×#1309214311yescharacteristic
315C2#1567178811yescharacteristic
316C2#1567179211yescharacteristic
317C2#1567192611yescharacteristic
318C2#1567193011yescharacteristic
319C2#1567202411yescharacteristic
320C2#1567211411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC2×C23×#389C2
socleC23×C23C2×C22⋊C4
hypercenterC2×#389D23
hypocenterC23#7593
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #15671220C2semidirect
32. C2×C4⋊C4×C23C8semidirect
194. C2×C4⋊C4C23⋊C8semidirect
206. C23#7593semidirect