Finite Group Databasebeta

← #25003308

Subgroups — #25003308

Order 11008.

2118 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063246C214yesmaximal, complemented
2C2×#14582654C211yesmaximal, characteristic, complemented
3#19132825C211yesmaximal, characteristic, complemented
4C22×#127×C43C211yesmaximal, characteristic
5C23×C43⋊C8C2212yes—
6C22×C4⋊Dic43C2212yes—
7C2×#13063246—28no—
8C2×#13063246—28no—
9C2×#13063246—28no—
10C2×C43⋊#95—22no—
11#14582654—22no—
12C23×D4×C43—22no—
13C23×D4×C43C2212yes—
14C2×#127×C43—28no—
15C2×#127×C43—22no—
16C2×#127×C43C414yescomplemented
17C22×C42×C43C2211yescharacteristic
18C23×Dic43—22no—
19C22×C43⋊C8—24no—
20C22×C43⋊C8—24no—
21C22×C43⋊C8—22no—
22C22×C43⋊C8—22no—
23C22×C43⋊C8D414yescomplemented
24C2×C4⋊Dic43—24no—
25C2×C4⋊Dic43—24no—
26C2×C4⋊Dic43—22no—
27C2×C4⋊Dic43D414yescomplemented
28#13063246—232no—
29C43⋊#95—44no—
30C25×C43—22no—
31C22×D4×C43—216no—
32C22×D4×C43—28no—
33C22×D4×C43—24no—
34C22×D4×C43—24no—
35C22×D4×C43—22no—
36C22×D4×C43—24no—
37C22×D4×C43—24no—
38C22×D4×C43—24no—
39C22×D4×C43—48no—
40C22×D4×C43—44no—
41C22×D4×C43—44no—
42C22×D4×C43C2×C414yes—
43C22×D4×C43D418yes—
44C23×C4×C43D412yes—
45C23×C4×C43C2311yescharacteristic
46#127×C43—216no—
47#127×C43—216no—
48C2×C42×C43—24no—
49C2×C42×C43C2×C412yes—
50C2×C42×C43D412yes—
51C24×C43—24no—
52C24×C43—28no—
53C24×C43—44no—
54C24×C43—42no—
55C24×C43—42no—
56C24×C43—44no—
57C24×C43—44no—
58C24×C43—48no—
59C24×C43C2×D411yescharacteristic
60C2×D4×C43—232no—
61C2×D4×C43—24no—
62C2×D4×C43—28no—
63C2×D4×C43—28no—
64C2×D4×C43—28no—
65C2×D4×C43—28no—
66C2×D4×C43—28no—
67C2×D4×C43—28no—
68C2×D4×C43—28no—
69C2×D4×C43—416no—
70C2×D4×C43—432no—
71C2×D4×C43—432no—
72C2×D4×C43—416no—
73C2×D4×C43—44no—
74C2×D4×C43—44no—
75C2×D4×C43—44no—
76C2×D4×C43—44no—
77C2×D4×C43—44no—
78C2×D4×C43—42no—
79C2×D4×C43—42no—
80C2×D4×C43C22⋊C418yes—
81C22×C4×C43—24no—
82C22×C4×C43—24no—
83C22×C4×C43C22⋊C414yes—
84C22×C4×C43D814yes—
85C22×C4×C43SD1614yes—
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D414yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D412yes—
91C22×C4×C43#4112yes—
92C22×C4×C43#4112yes—
93C22×Dic43—24no—
94C22×Dic43—42no—
95C22×Dic43—42no—
96C22×Dic43—44no—
97C22×Dic43—44no—
98C42×C43—24no—
99C42×C43—24no—
100C4⋊Dic43—28no—
101C4⋊Dic43—44no—
102C2×C43⋊C8—28no—
103C2×C43⋊C8—24no—
104C2×C43⋊C8—42no—
105C2×C43⋊C8—44no—
106C2×C43⋊C8—42no—
107C23×C43—28no—
108C23×C43—44no—
109C23×C43—44no—
110C23×C43—48no—
111C23×C43—48no—
112C23×C43—48no—
113C23×C43—48no—
114C23×C43—416no—
115C23×C43—416no—
116C23×C43—88no—
117C23×C43—88no—
118C23×C43—84no—
119C23×C43—84no—
120C23×C43—82no—
121C23×C43—82no—
122C23×C43—84no—
123C23×C43C2×C22⋊C411yescharacteristic
124C23×C43#12012yes—
125C23×C43#12112yes—
126C23×C43#12411yescharacteristic
127C23×C43#12711yescharacteristic
128C23×C43C2×D812yes—
129C23×C43C2×SD1612yes—
130C23×C43AGL(1,ℤ/8)14yes—
131D4×C43—216no—
132D4×C43—464no—
133D4×C43—48no—
134D4×C43—48no—
135D4×C43—48no—
136C2×C4×C43—24no—
137C2×C4×C43—24no—
138C2×C4×C43—28no—
139C2×C4×C43—28no—
140C2×C4×C43#10218yescomplemented
141C2×C4×C43C2×C22⋊C412yes—
142C2×C4×C43C4×D412yes—
143C2×C4×C43C4×D412yes—
144C2×C4×C43#12014yes—
145C2×C4×C43#12012yes—
146C2×C4×C43#12112yes—
147C2×C4×C43#12114yes—
148C2×C4×C43#12114yes—
149C2×C4×C43#12314yes—
150C2×C4×C43#12411yescharacteristic
151C2×C4×C43#12711yescharacteristic
152C2×Dic43—44no—
153C2×Dic43—48no—
154C2×Dic43—84no—
155C2×Dic43—82no—
156C2×Dic43—82no—
157C43⋊C8—44no—
158#11008—431nomaximal, Sylow
159C22×C43—48no—
160C22×C43—416no—
161C22×C43—84no—
162C22×C43—84no—
163C22×C43—88no—
164C22×C43—88no—
165C22×C43—88no—
166C22×C43—816no—
167C22×C43#37911yescharacteristic
168C22×C43#39011yescharacteristic
169C22×C43#39011yescharacteristic
170C22×C43#39212yes—
171C22×C43#39412yes—
172C22×C43C2×#10212yes—
173C22×C43#41812yes—
174C22×C43#44714yes—
175C22×C43#45014yes—
176C22×C43#45914yes—
177C22×C43#46014yes—
178C22×C43#48612yes—
179C22×C43#49012yes—
180C22×C43#49211yescharacteristic
181C22×C43#49311yescharacteristic
182C22×C43#49612yes—
183C4×C43—28no—
184C4×C43#38614yes—
185C4×C43#39212yes—
186C4×C43#39412yes—
187Dic43—84no—
188C22×#127D4311yescharacteristic
189C22×#102—434no—
190C2×#336—431no—
191C4⋊#95—431no—
192C2×C43—88no—
193C2×C43#143811yescharacteristic
194C2×C43#178612yes—
195C2×C43#195711yescharacteristic
196C2×C43#196111yescharacteristic
197C2×C43#198212yes—
198C2×C43#201112yes—
199C2×C43#201412yes—
200C2×C43#204114yes—
201C23×D4—22no—
202C23×D4C2×D4312yes—
203C23×C8—432no—
204C2×#127—28no—
205C2×#127—22no—
206C2×#127Dic4314yescomplemented
207C22×C4⋊C4—432no—
208C22×C42C2×D4311yescharacteristic
209C2×#102—868no—
210C2×#102—868no—
211C2×#102—868no—
212C2×#95—862no—
213#336—862no—
214C43#1100811yescharacteristic, complemented, Sylow
215C25—22no—
216C22×D4—216no—
217C22×D4—28no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—22no—
224C22×D4—48no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4C2×Dic4314yes—
228C22×D4C22⋊D4318yes—
229C23×C4—862no—
230C23×C4C22⋊D4312yes—
231C23×C4C22×D4311yescharacteristic
232C22×C8—434no—
233C22×C8—864no—
234C22×C8—862no—
235C22×C8—862no—
236C22×C8—864no—
237#127—216no—
238#127—216no—
239C2×C4⋊C4—434no—
240C2×C4⋊C4—864no—
241C2×C4⋊C4—864no—
242C2×C4⋊C4—862no—
243C2×C42—24no—
244C2×C42C2×Dic4312yes—
245C2×C42C22⋊D4312yes—
246#102—8632no—
247#95—1724no—
248C24—24no—
249C24—28no—
250C24—44no—
251C24—42no—
252C24—42no—
253C24—44no—
254C24—44no—
255C24—48no—
256C24C2×C22⋊D4311yescharacteristic
257C2×D4—232no—
258C2×D4—24no—
259C2×D4—28no—
260C2×D4—28no—
261C2×D4—28no—
262C2×D4—28no—
263C2×D4—28no—
264C2×D4—28no—
265C2×D4—28no—
266C2×D4—432no—
267C2×D4—416no—
268C2×D4—432no—
269C2×D4—416no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4C22⋊Dic4318yes—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—864no—
281C22×C4—1722no—
282C22×C4—1722no—
283C22×C4—1724no—
284C22×C4—1724no—
285C22×C4#1062188214yes—
286C22×C4#1062188314yes—
287C22×C4C22⋊Dic4314yes—
288C22×C4D4×D4312yes—
289C22×C4D4×D4312yes—
290C22×C4#1062190012yes—
291C22×C4#1062190012yes—
292C22×C4C22×Dic4311yescharacteristic
293C22×C4C2×C22⋊D4314yes—
294C22×C4C2×C22⋊D4311yescharacteristic
295C2×C8—868no—
296C2×C8—864no—
297C2×C8—1722no—
298C2×C8—1724no—
299C2×C8—1722no—
300C4⋊C4—868no—
301C4⋊C4—1724no—
302C42—24no—
303C42—24no—
304C23—28no—
305C23—416no—
306C23—44no—
307C23—44no—
308C23—48no—
309C23—48no—
310C23—48no—
311C23—48no—
312C23—416no—
313C23—88no—
314C23—88no—
315C23—84no—
316C23—84no—
317C23—82no—
318C23—82no—
319C23—84no—
320C23C2×C22⋊Dic4311yescharacteristic
321C23#1306329412yes—
322C23#1306329612yes—
323C23#1306331211yescharacteristic
324C23#1306332111yescharacteristic
325C23C2×#1062188212yes—
326C23C2×#1062188312yes—
327C23#1306335114yes—
328D4—216no—
329D4—464no—
330D4—48no—
331D4—48no—
332D4—48no—
333C2×C4—28no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—3442no—
338C2×C4—3442no—
339C2×C4—3444no—
340C2×C4—1724no—
341C2×C4—1728no—
342C2×C4#1306324618yescomplemented
343C2×C4C2×C22⋊Dic4312yes—
344C2×C4D4×Dic4312yes—
345C2×C4D4×Dic4312yes—
346C2×C4#1306329314yes—
347C2×C4#1306329412yes—
348C2×C4#1306329612yes—
349C2×C4#1306329714yes—
350C2×C4#1306329714yes—
351C2×C4#1306330614yes—
352C2×C4#1306331211yescharacteristic
353C2×C4#1306332111yescharacteristic
354C8—1724no—
355C22—416no—
356C22—48no—
357C22—88no—
358C22—816no—
359C22—84no—
360C22—88no—
361C22—84no—
362C22—88no—
363C22#1458275511yescharacteristic
364C22#1458280211yescharacteristic
365C22#1458280211yescharacteristic
366C22#1458280712yes—
367C22#1458281312yes—
368C22C2×#1306324612yes—
369C22#1458290412yes—
370C22#1458303314yes—
371C22#1458305014yes—
372C22#1458309114yes—
373C22#1458309614yes—
374C22#1458324512yes—
375C22#1458326312yes—
376C22#1458327111yescharacteristic
377C22#1458327511yescharacteristic
378C22#1458328612yes—
379C4—28no—
380C4—3444no—
381C4#1458277914yes—
382C4#1458280712yes—
383C4#1458281312yes—
384C2—88no—
385C2#1913283611yescharacteristic
386C2#1913452612yes—
387C2#1913540211yescharacteristic
388C2#1913542011yescharacteristic
389C2#1913552312yes—
390C2#1913566612yes—
391C2#1913568312yes—
392C2#1913582614yes—
subgroupG/H
centerC24C2×C22⋊D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC22×#127×C43C2
socleC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC22×#127D43
hypocenterC43#11008
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C22×#13063246C2semidirect
2. C2×#14582654C2semidirect
3. #19132825C2semidirect
16. C2×#127×C43C4semidirect
23. C22×C43⋊C8D4semidirect
27. C2×C4⋊Dic43D4semidirect
140. C2×C4×C43#102semidirect
206. C2×#127Dic43semidirect
214. C43#11008semidirect
342. C2×C4#13063246semidirect

Maximal subgroups

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

subgroupindex
C22×#130632462
C2×#145826542
#191328252
C22×#127×C432
#1100843