Finite Group Databasebeta

← C11×#21068 #14598261

Subgroups — C11×#21068 #14598261

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#106C211yesmaximal, characteristic, complemented
2C2×C11×#417C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C11×#2311C211yesmaximal, characteristic
5C11×#2274C211yesmaximal, characteristic, complemented
6C11×#1927C214yesmaximal, complemented
7C11×#1926C214yesmaximal, complemented
8C11×#1736C211yesmaximal, characteristic, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×C11×#106—24no—
18C2×C11×#106C2214yes—
19C11×#417—24no—
20C11×#416C418yescomplemented
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C11×#391C2212yes—
26C11×#390C2212yes—
27C11×#386—22no—
28C11×#380—22no—
29C4×C11×C4⋊C4—22no—
30C4×C11×C4⋊C4C2214yes—
31C4×C11×C22⋊C4—22no—
32C11×#340C2214yes—
33C11×#336C2214yes—
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41C2×C414yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11—21no—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11C2×C414yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×#117—22no—
56C11×#117—22no—
57C11×#117—22no—
58C11×#117C2×C414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4D414yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C2×C42×C11—24no—
74C2×C42×C11C2312yes—
75C11×#106—28no—
76C11×#103—24no—
77C11×#103C2×C418yescomplemented
78C11×#102—24no—
79C11×#102C2×C418yescomplemented
80C11×#95—24no—
81C11×#95—24no—
82#21068C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—21no—
84C24×C11C2×D411yescharacteristic
85C11×#41—28no—
86C11×#41—28no—
87C11×#41—44no—
88C11×#41—44no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11C22×C412yes—
95C2×D4×C11—24no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C2×D4×C11C22×C412yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—82no—
114C22×C4×C11—82no—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C11×M16—44no—
125C2×C8×C11—28no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11C22×C414yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4C22×C414yes—
140C11×C4⋊C4C2×D414yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—84no—
144C42×C11—24no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—84no—
148C22×#106C2×C1111yescharacteristic, complemented
149C2×#417C2×C1111yescharacteristic
150C2×#416C2×C1111yescharacteristic
151#2311C2×C1111yescharacteristic
152#2274C2×C1111yescharacteristic, complemented
153#1927C2×C1114yescomplemented
154#1926C2×C1114yescomplemented
155#1736C2×C1111yescharacteristic, complemented
156#1729C2×C1111yescharacteristic, complemented
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11C4×D412yes—
165C23×C11#12112yes—
166C23×C11#12312yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—22no—
169Q8×C11—22no—
170Q8×C11—41no—
171Q8×C11—41no—
172D4×C11—22no—
173D4×C11—22no—
174D4×C11—48no—
175D4×C11—41no—
176D4×C11—41no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—48no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—84no—
192C2×C4×C11—84no—
193C2×C4×C11#11714yes—
194C2×C4×C11C4×D414yes—
195C2×C4×C11C4×D412yes—
196C2×C4×C11#12112yes—
197C2×C4×C11#12312yes—
198C2×C4×C11#12414yes—
199C2×C4×C11#12614yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C8×C11—24no—
207C8×C11—42no—
208C22×#41C22×C1111yescharacteristic
209C22×M16C22×C1111yescharacteristic
210C23×C8C22×C1111yescharacteristic
211C2×#117C22×C1111yescharacteristic
212C2×#117C22×C1111yescharacteristic
213C22×C4⋊C4C22×C1111yescharacteristic
214C22×C4⋊C4C22×C1111yescharacteristic
215C2×#106—24no—
216C2×#106C22×C1114yes—
217#417—24no—
218#416C4×C1118yescomplemented
219C2×#103C22×C1112yes—
220C2×#103C22×C1112yes—
221C2×#102C22×C1112yes—
222C2×#102C22×C1112yes—
223#391C22×C1112yes—
224#390C22×C1112yes—
225#386—22no—
226#380—22no—
227C4×C4⋊C4—22no—
228C4×C4⋊C4C22×C1114yes—
229C4×C22⋊C4—22no—
230#340C22×C1114yes—
231#336C22×C1114yes—
232C22×C11—24no—
233C22×C11—24no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—44no—
237C22×C11—42no—
238C22×C11—82no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11#38814yes—
242C22×C11C2×C4×D411yescharacteristic
243C22×C11C2×#12111yescharacteristic
244C22×C11C2×#12311yescharacteristic
245C22×C11#57712yes—
246C22×C11#57712yes—
247C4×C11—44no—
248C4×C11—44no—
249C4×C11—44no—
250C4×C11—42no—
251C4×C11—82no—
252C4×C11#38814yes—
253C4×C11C2×#11711yescharacteristic
254C4×C11C2×C4×D411yescharacteristic
255C4×C11C2×#12411yescharacteristic
256C4×C11C2×#12611yescharacteristic
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41C2×C4×C1114yes—
263C22×Q8C23×C1111yescharacteristic
264C22×D4—21no—
265C22×D4C23×C1111yescharacteristic
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4C23×C1111yescharacteristic
270C2×M16—22no—
271C2×M16—22no—
272C2×M16—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8C2×C4×C1114yes—
276C22×C8C23×C1112yes—
277C22×C8C23×C1112yes—
278#117—22no—
279#117—22no—
280#117—22no—
281#117C2×C4×C1114yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4D4×C1112yes—
288C2×C4⋊C4D4×C1114yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4D4×C1112yes—
295C2×C42—21no—
296C2×C42—24no—
297C2×C42C23×C1112yes—
298#106—28no—
299#103—24no—
300#103C2×C4×C1118yescomplemented
301#102—24no—
302#102C2×C4×C1118yescomplemented
303#95—24no—
304#95—24no—
305C2×C11—24no—
306C2×C11—82no—
307C2×C11C2×#38811yescharacteristic
308C2×C11#295212yes—
309C2×C11#304211yescharacteristic
310C2×C11#304311yescharacteristic
311C2×C11#309912yes—
312C24—21no—
313C24C2×D4×C1111yescharacteristic
314#41—28no—
315#41—28no—
316#41—44no—
317#41—44no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8C22×C4×C1112yes—
324C2×D4—24no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4C22×C4×C1112yes—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—82no—
343C22×C4—82no—
344C22×C4C22×C4×C1112yes—
345C22×C4C2×D4×C1114yes—
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1112yes—
348C22×C4C11×#4112yes—
349C22×C4C11×#4112yes—
350C22×C4C11×#4112yes—
351C22×C4C11×#4112yes—
352C22×C4C24×C1111yescharacteristic
353M16—44no—
354C2×C8—28no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8C22×C4×C1114yes—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4C22×C4×C1114yes—
369C4⋊C4C2×D4×C1114yes—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—84no—
373C42—24no—
374C42—22no—
375C42—22no—
376C42—84no—
377C11#2106811yescharacteristic, direct product factor, Sylow
378C23—22no—
379C23—22no—
380C23—22no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23C4×D4×C1112yes—
386C23C11×#12112yes—
387C23C11×#12312yes—
388C23C22×D4×C1111yescharacteristic
389Q8—22no—
390Q8—22no—
391Q8—41no—
392Q8—41no—
393D4—22no—
394D4—22no—
395D4—48no—
396D4—41no—
397D4—41no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—48no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—84no—
413C2×C4—84no—
414C2×C4C11×#11714yes—
415C2×C4C4×D4×C1114yes—
416C2×C4C4×D4×C1112yes—
417C2×C4C11×#12112yes—
418C2×C4C11×#12312yes—
419C2×C4C11×#12414yes—
420C2×C4C11×#12614yes—
421C2×C4C23×C4×C1111yescharacteristic
422C2×C4C22×D4×C1111yescharacteristic
423C2×C4C2×C11×#4111yescharacteristic
424C2×C4C2×C11×#4111yescharacteristic
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C2×C11×#4111yescharacteristic
427C8—24no—
428C8—42no—
429C22—24no—
430C22—22no—
431C22—22no—
432C22—24no—
433C22—44no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—82no—
438C22C11×#38814yes—
439C22C2×C4×D4×C1111yescharacteristic
440C22C2×C11×#12111yescharacteristic
441C22C2×C11×#12311yescharacteristic
442C22C11×#57712yes—
443C22C11×#57712yes—
444C4—44no—
445C4—44no—
446C4—42no—
447C4—44no—
448C4—82no—
449C4C11×#38814yes—
450C4C2×C11×#11711yescharacteristic
451C4C2×C4×D4×C1111yescharacteristic
452C4C2×C11×#12411yescharacteristic
453C4C2×C11×#12611yescharacteristic
454C2—24no—
455C2—82no—
456C2C2×C11×#38811yescharacteristic
457C2C11×#295212yes—
458C2C11×#304211yescharacteristic
459C2C11×#304311yescharacteristic
460C2C11×#309912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#106C2semidirect
5. C11×#2274C2semidirect
6. C11×#1927C2semidirect
7. C11×#1926C2semidirect
8. C11×#1736C2semidirect
9. C11×#1729C2semidirect
20. C11×#416C4semidirect
77. C11×#103C2×C4semidirect
79. C11×#102C2×C4semidirect
82. #21068C11direct (N × H)
148. C22×#106C2×C11semidirect
152. #2274C2×C11semidirect
153. #1927C2×C11semidirect
154. #1926C2×C11semidirect
155. #1736C2×C11semidirect
156. #1729C2×C11semidirect
218. #416C4×C11semidirect
300. #103C2×C4×C11semidirect
302. #102C2×C4×C11semidirect
377. C11#21068direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1062
C2×C11×#4172
C2×C11×#4162
C11×#23112
C11×#22742
C11×#19272
C11×#19262
C11×#17362
C11×#17292
#2106811