Finite Group Databasebeta

← C2×C11×#2023 #14600640

Subgroups — C2×C11×#2023 #14600640

Order 2816.

1734 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C22×C11×#102C212yesmaximal
3C2×C11×#390C211yesmaximal, characteristic
4C11×#2023C218yesmaximal, direct product factor
5C2×C11×#340C212yesmaximal, complemented
6C2×C11×#336C211yesmaximal, characteristic, complemented
7C23×Q8×C11—21no—
8C23×D4×C11C2211yescharacteristic
9C23×C8×C11C2212yes—
10C2×C11×C4⋊Q8—28no—
11C2×C11×C4⋊Q8—22no—
12C2×C11×C4⋊Q8C2214yescomplemented
13C22×C11×C4⋊C4—21no—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4—21no—
17C22×C11×C22⋊C4—21no—
18C22×C42×C11C2211yescharacteristic
19C2×C11×#102—28no—
20C2×C11×#102C2218yes—
21C11×#390—22no—
22C11×#390C2214yes—
23C11×#340C2218yescomplemented
24C11×#336C2214yescomplemented
25C25×C11—21no—
26C22×Q8×C11—28no—
27C22×Q8×C11—24no—
28C22×Q8×C11—44no—
29C22×Q8×C11—44no—
30C22×D4×C11—24no—
31C22×D4×C11—21no—
32C22×D4×C11—24no—
33C22×D4×C11—22no—
34C22×D4×C11Q814yescomplemented
35C22×D4×C11C2312yes—
36C23×C4×C11—22no—
37C23×C4×C11—21no—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C8×C11—24no—
42C22×C8×C11—24no—
43C22×C8×C11—24no—
44C22×C8×C11C2314yes—
45C11×C4⋊Q8—216no—
46C11×C4⋊Q8—216no—
47C2×C11×C4⋊C4—28no—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D418yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—44no—
59C2×C11×C22⋊C4—44no—
60C2×C42×C11—24no—
61C2×C42×C11D412yes—
62C2×C42×C11C2312yes—
63C11×#102—216no—
64C2×#2023C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—24no—
66C24×C11—22no—
67C24×C11—42no—
68C24×C11—42no—
69C24×C11—42no—
70C24×C11—42no—
71C24×C11—42no—
72C24×C11—42no—
73C24×C11C2×D411yescharacteristic
74C2×Q8×C11—216no—
75C2×Q8×C11—48no—
76C2×Q8×C11—432no—
77C2×Q8×C11—48no—
78C2×D4×C11—216no—
79C2×D4×C11—24no—
80C2×D4×C11—24no—
81C2×D4×C11—24no—
82C2×D4×C11—22no—
83C2×D4×C11—42no—
84C2×D4×C11—48no—
85C2×D4×C11—42no—
86C2×D4×C11C2×Q814yescomplemented
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—28no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—44no—
95C22×C4×C11—44no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11D814yes—
100C22×C4×C11SD1614yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D414yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11#4114yes—
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C2×C8×C11—24no—
110C2×C8×C11—24no—
111C2×C8×C11—24no—
112C2×C8×C11—48no—
113C11×C4⋊C4—216no—
114C11×C4⋊C4—28no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4C2×D418yes—
119C11×C22⋊C4—48no—
120C11×C22⋊C4—48no—
121C42×C11—24no—
122C42×C11—24no—
123C22×C4⋊Q8C2×C1111yescharacteristic, complemented
124C22×#102C2×C1112yes—
125C2×#390C2×C1111yescharacteristic
126#2023C2×C1118yesdirect product factor
127C2×#340C2×C1112yescomplemented
128C2×#336C2×C1111yescharacteristic, complemented
129C23×C11—24no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—48no—
137C23×C11—48no—
138C23×C11—48no—
139C23×C11—84no—
140C23×C11—84no—
141C23×C11—84no—
142C23×C11—84no—
143C23×C11#12012yes—
144C23×C11C22⋊Q812yes—
145C23×C11#12412yes—
146C23×C11C2×D812yes—
147C23×C11C2×SD1612yes—
148C23×C11AGL(1,ℤ/8)12yes—
149C23×C11#13712yes—
150C23×C11C22×D411yescharacteristic
151Q8×C11—432no—
152D4×C11—28no—
153D4×C11—44no—
154D4×C11—48no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—28no—
160C2×C4×C11—28no—
161C2×C4×C11—28no—
162C2×C4×C11—44no—
163C2×C4×C11—44no—
164C2×C4×C11—416no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—84no—
169C2×C4×C11#12012yes—
170C2×C4×C11C22⋊Q818yes—
171C2×C4×C11C22⋊Q812yes—
172C2×C4×C11#12418yes—
173C2×C4×C11#12412yes—
174C2×C4×C11C2×D814yes—
175C2×C4×C11C2×SD1614yes—
176C2×C4×C11C22×D412yes—
177C2×C4×C11C22×Q811yescharacteristic
178C2×C4×C11C2×#4112yes—
179C2×C4×C11C2×#4111yescharacteristic
180C8×C11—44no—
181C23×Q8—21no—
182C23×D4C22×C1111yescharacteristic
183C23×C8C22×C1112yes—
184C2×C4⋊Q8—28no—
185C2×C4⋊Q8—22no—
186C2×C4⋊Q8C22×C1114yescomplemented
187C22×C4⋊C4—21no—
188C22×C4⋊C4C22×C1111yescharacteristic
189C22×C4⋊C4C22×C1112yes—
190C22×C22⋊C4—21no—
191C22×C22⋊C4—21no—
192C22×C42C22×C1111yescharacteristic
193C2×#102—28no—
194C2×#102C22×C1118yes—
195#390—22no—
196#390C22×C1114yes—
197#340C22×C1118yescomplemented
198#336C22×C1114yescomplemented
199C22×C11—44no—
200C22×C11—44no—
201C22×C11—44no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—816no—
207C22×C11#39314yes—
208C22×C11#44714yes—
209C22×C11#44814yes—
210C22×C11#47414yes—
211C22×C11#47614yes—
212C22×C11#48614yes—
213C22×C11#48914yes—
214C22×C11C2×#12011yescharacteristic
215C22×C11C2×C22⋊Q811yescharacteristic
216C22×C11C2×#12411yescharacteristic
217C22×C11C22×D811yescharacteristic
218C22×C11C22×SD1611yescharacteristic
219C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
220C22×C11C2×#13711yescharacteristic
221C4×C11—24no—
222C4×C11—24no—
223C4×C11—48no—
224C4×C11—82no—
225C4×C11#39314yes—
226C4×C11C2×C22⋊Q812yes—
227C4×C11C2×#12412yes—
228C25—21no—
229C22×Q8—28no—
230C22×Q8—24no—
231C22×Q8—44no—
232C22×Q8—44no—
233C22×D4—24no—
234C22×D4—21no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4Q8×C1114yescomplemented
238C22×D4C23×C1112yes—
239C23×C4—22no—
240C23×C4—21no—
241C23×C4D4×C1111yescharacteristic
242C23×C4D4×C1111yescharacteristic
243C23×C4C23×C1111yescharacteristic
244C22×C8—24no—
245C22×C8—24no—
246C22×C8—24no—
247C22×C8C23×C1114yes—
248C4⋊Q8—216no—
249C4⋊Q8—216no—
250C2×C4⋊C4—28no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C1118yes—
257C2×C4⋊C4C23×C1112yes—
258C2×C4⋊C4C23×C1114yes—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—44no—
262C2×C22⋊C4—44no—
263C2×C42—24no—
264C2×C42D4×C1112yes—
265C2×C42C23×C1112yes—
266#102—216no—
267C2×C11—84no—
268C2×C11#202318yesdirect product factor
269C2×C11C2×#39311yescharacteristic
270C2×C11C2×#44711yescharacteristic
271C2×C11C2×#44811yescharacteristic
272C2×C11C2×#47411yescharacteristic
273C2×C11C2×#47611yescharacteristic
274C2×C11C2×#48611yescharacteristic
275C2×C11C2×#48911yescharacteristic
276C24—24no—
277C24—22no—
278C24—42no—
279C24—42no—
280C24—42no—
281C24—42no—
282C24—42no—
283C24—42no—
284C24C2×D4×C1111yescharacteristic
285C2×Q8—216no—
286C2×Q8—48no—
287C2×Q8—432no—
288C2×Q8—48no—
289C2×D4—216no—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—24no—
293C2×D4—22no—
294C2×D4—42no—
295C2×D4—48no—
296C2×D4—42no—
297C2×D4C2×Q8×C1114yescomplemented
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—28no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—44no—
306C22×C4—44no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4C11×D814yes—
311C22×C4C11×SD1614yes—
312C22×C4C2×D4×C1112yes—
313C22×C4C2×D4×C1112yes—
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×D4×C1114yes—
316C22×C4C2×Q8×C1112yes—
317C22×C4C11×#4114yes—
318C22×C4C11×#4112yes—
319C22×C4C24×C1111yescharacteristic
320C2×C8—24no—
321C2×C8—24no—
322C2×C8—24no—
323C2×C8—48no—
324C4⋊C4—216no—
325C4⋊C4—28no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—42no—
329C4⋊C4C2×D4×C1118yes—
330C22⋊C4—48no—
331C22⋊C4—48no—
332C42—24no—
333C42—24no—
334C11C2×#202311yescharacteristic, direct product factor, Sylow
335C23—24no—
336C23—42no—
337C23—42no—
338C23—48no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—48no—
344C23—48no—
345C23—84no—
346C23—84no—
347C23—84no—
348C23—84no—
349C23C11×#12012yes—
350C23C11×C22⋊Q812yes—
351C23C11×#12412yes—
352C23C2×C11×D812yes—
353C23C2×C11×SD1612yes—
354C23C11×AGL(1,ℤ/8)12yes—
355C23C11×#13712yes—
356C23C22×D4×C1111yescharacteristic
357Q8—432no—
358D4—28no—
359D4—44no—
360D4—48no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—28no—
366C2×C4—28no—
367C2×C4—28no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—416no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—84no—
375C2×C4C11×#12012yes—
376C2×C4C11×C22⋊Q818yes—
377C2×C4C11×C22⋊Q812yes—
378C2×C4C11×#12418yes—
379C2×C4C11×#12412yes—
380C2×C4C2×C11×D814yes—
381C2×C4C2×C11×SD1614yes—
382C2×C4C22×D4×C1112yes—
383C2×C4C22×Q8×C1111yescharacteristic
384C2×C4C2×C11×#4112yes—
385C2×C4C2×C11×#4111yescharacteristic
386C8—44no—
387C22—44no—
388C22—44no—
389C22—44no—
390C22—82no—
391C22—82no—
392C22—816no—
393C22—82no—
394C22—82no—
395C22C11×#39314yes—
396C22C11×#44714yes—
397C22C11×#44814yes—
398C22C11×#47414yes—
399C22C11×#47614yes—
400C22C11×#48614yes—
401C22C11×#48914yes—
402C22C2×C11×#12011yescharacteristic
403C22C2×C11×C22⋊Q811yescharacteristic
404C22C2×C11×#12411yescharacteristic
405C22C22×C11×D811yescharacteristic
406C22C22×C11×SD1611yescharacteristic
407C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
408C22C2×C11×#13711yescharacteristic
409C4—24no—
410C4—24no—
411C4—48no—
412C4—82no—
413C4C11×#39314yes—
414C4C2×C11×C22⋊Q812yes—
415C4C2×C11×#12412yes—
416C2—84no—
417C2C11×#202318yesdirect product factor
418C2C2×C11×#39311yescharacteristic
419C2C2×C11×#44711yescharacteristic
420C2C2×C11×#44811yescharacteristic
421C2C2×C11×#47411yescharacteristic
422C2C2×C11×#47611yescharacteristic
423C2C2×C11×#48611yescharacteristic
424C2C2×C11×#48911yescharacteristic
subgroupG/H
center, socleC24×C11C2×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊Q8C2semidirect
4. C11×#2023C2direct (N × H)
5. C2×C11×#340C2semidirect
6. C2×C11×#336C2semidirect
12. C2×C11×C4⋊Q8C22semidirect
23. C11×#340C22semidirect
24. C11×#336C22semidirect
34. C22×D4×C11Q8semidirect
64. C2×#2023C11direct (N × H)
86. C2×D4×C11C2×Q8semidirect
123. C22×C4⋊Q8C2×C11semidirect
126. #2023C2×C11direct (N × H)
127. C2×#340C2×C11semidirect
128. C2×#336C2×C11semidirect
186. C2×C4⋊Q8C22×C11semidirect
197. #340C22×C11semidirect
198. #336C22×C11semidirect
237. C22×D4Q8×C11semidirect
268. C2×C11#2023direct (N × H)
297. C2×D4C2×Q8×C11semidirect
334. C11C2×#2023direct (N × H)
417. C2C11×#2023direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C22×C11×#1022
C2×C11×#3902
C11×#20232
C2×C11×#3402
C2×C11×#3362
C2×#202311