Finite Group Databasebeta

← C11×#21034 #14598227

Subgroups — C11×#21034 #14598227

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic
2C2×C11×#389C211yesmaximal, characteristic
3C4×C11×#117C211yesmaximal, characteristic
4C11×#1921C212yesmaximal, complemented
5C11×#1920C212yesmaximal, complemented
6C11×#1919C212yesmaximal, complemented
7C11×#1918C212yesmaximal, complemented
8C11×#1736C211yesmaximal, characteristic
9C11×#1736C211yesmaximal, characteristic
10C11×#1736C211yesmaximal, characteristic
11C11×#1728C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#428C418yescomplemented
21C2×C11×#107C2212yes—
22C2×C11×#106C2212yes—
23C11×#389—21no—
24C11×#389—21no—
25C11×#389C2212yes—
26C11×#389C2212yes—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4—21no—
32C4×C11×C22⋊C4—21no—
33C11×#376—21no—
34C2×C11×#95—21no—
35C43×C11—21no—
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16C2×C414yes—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×#117—22no—
58C11×#117—22no—
59C11×#117C2×C414yes—
60C11×#117Q814yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—44no—
69C2×C11×C4⋊C4C2×C414yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—22no—
81C2×C42×C11—22no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C11×#107C2×C418yescomplemented
91C11×#106C2×C418yescomplemented
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98#21034C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C2×D411yescharacteristic
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C11×M16—28no—
131C11×M16—44no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11C22×C414yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4C22×C412yes—
150C11×C4⋊C4C22×C414yes—
151C11×C4⋊C4C22×C412yes—
152C11×C4⋊C4C2×Q812yes—
153C11×C4⋊C4C2×Q812yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C42×C11—24no—
157C42×C11—24no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—42no—
165C42×C11—42no—
166C42×C11—42no—
167C42×C11—42no—
168C2×#428C2×C1111yescharacteristic
169C2×#389C2×C1111yescharacteristic
170C4×#117C2×C1111yescharacteristic
171#1921C2×C1112yescomplemented
172#1920C2×C1112yescomplemented
173#1919C2×C1112yescomplemented
174#1918C2×C1112yescomplemented
175#1736C2×C1111yescharacteristic
176#1736C2×C1111yescharacteristic
177#1736C2×C1111yescharacteristic
178#1728C2×C1111yescharacteristic
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11C4×D412yes—
184C23×C11C22⋊Q812yes—
185C23×C11#12312yes—
186C23×C11C22×D411yescharacteristic
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—44no—
203C2×C4×C11—44no—
204C2×C4×C11—48no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—84no—
219C2×C4×C11#11714yes—
220C2×C4×C11C4×D412yes—
221C2×C4×C11C4×Q814yes—
222C2×C4×C11C22⋊Q812yes—
223C2×C4×C11#12312yes—
224C2×C4×C11#12514yes—
225C2×C4×C11#12614yes—
226C2×C4×C11AGL(1,ℤ/8)12yes—
227C2×C4×C11#13712yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×Q811yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C8×C11—24no—
235C8×C11—42no—
236C22×M16C22×C1111yescharacteristic
237C22×M16C22×C1111yescharacteristic
238C2×#117C22×C1111yescharacteristic
239C2×#117C22×C1111yescharacteristic
240C22×C4⋊C4—21no—
241C22×C4⋊C4C22×C1111yescharacteristic
242C22×C4⋊C4C22×C1111yescharacteristic
243C22×C42C22×C1111yescharacteristic
244#428C4×C1118yescomplemented
245C2×#107C22×C1112yes—
246C2×#106C22×C1112yes—
247#389—21no—
248#389—21no—
249#389C22×C1112yes—
250#389C22×C1112yes—
251C4×C4⋊C4C22×C1111yescharacteristic
252C4×C4⋊C4C22×C1111yescharacteristic
253C4×C4⋊C4C22×C1111yescharacteristic
254C4×C4⋊C4C22×C1111yescharacteristic
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257#376—21no—
258C2×#95—21no—
259C43—21no—
260#340C22×C1112yes—
261#340C22×C1112yes—
262#340C22×C1112yes—
263#340C22×C1112yes—
264#340C22×C1112yes—
265#340C22×C1112yes—
266#336C22×C1112yes—
267#336C22×C1112yes—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11#38714yes—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×C22⋊Q811yescharacteristic
277C22×C11C2×#12311yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11C2×#13711yescharacteristic
280C22×C11#57511yescharacteristic
281C22×C11#57511yescharacteristic
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—42no—
289C4×C11—44no—
290C4×C11—42no—
291C4×C11—82no—
292C4×C11#38714yes—
293C4×C11C2×#11711yescharacteristic
294C4×C11C2×C4×Q811yescharacteristic
295C4×C11C2×#12511yescharacteristic
296C4×C11C2×#12611yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C23×C4D4×C1111yescharacteristic
300C23×C4D4×C1111yescharacteristic
301C23×C4C23×C1111yescharacteristic
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16C2×C4×C1114yes—
308C22×C8C23×C1112yes—
309C22×C8C23×C1112yes—
310#117—22no—
311#117—22no—
312#117C2×C4×C1114yes—
313#117Q8×C1114yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4C2×C4×C1114yes—
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1111yescharacteristic
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42D4×C1111yescharacteristic
340C2×C42D4×C1111yescharacteristic
341C2×C42C23×C1111yescharacteristic
342C2×C42C23×C1111yescharacteristic
343#107C2×C4×C1118yescomplemented
344#106C2×C4×C1118yescomplemented
345#95—22no—
346#95—22no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351C2×C11—24no—
352C2×C11C2×#38711yescharacteristic
353C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
354C2×C11C4×#13711yescharacteristic
355C2×C11#307911yescharacteristic
356C2×C11#308011yescharacteristic
357C2×C11#309411yescharacteristic
358C2×C11#309511yescharacteristic
359C24C2×D4×C1111yescharacteristic
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4C22×C4×C1112yes—
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×Q8×C1112yes—
385C22×C4C11×#4112yes—
386C22×C4C11×#4112yes—
387C22×C4C11×#4112yes—
388C22×C4C11×#4112yes—
389C22×C4C24×C1111yescharacteristic
390M16—28no—
391M16—44no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8C22×C4×C1114yes—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—44no—
407C4⋊C4—42no—
408C4⋊C4—44no—
409C4⋊C4C22×C4×C1112yes—
410C4⋊C4C22×C4×C1114yes—
411C4⋊C4C22×C4×C1112yes—
412C4⋊C4C2×Q8×C1112yes—
413C4⋊C4C2×Q8×C1112yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C42—24no—
417C42—24no—
418C42—22no—
419C42—22no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—42no—
425C42—42no—
426C42—42no—
427C42—42no—
428C11#2103411yescharacteristic, direct product factor, Sylow
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23C4×D4×C1112yes—
434C23C11×C22⋊Q812yes—
435C23C11×#12312yes—
436C23C22×D4×C1111yescharacteristic
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—48no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—84no—
469C2×C4C11×#11714yes—
470C2×C4C4×D4×C1112yes—
471C2×C4C4×Q8×C1114yes—
472C2×C4C11×C22⋊Q812yes—
473C2×C4C11×#12312yes—
474C2×C4C11×#12514yes—
475C2×C4C11×#12614yes—
476C2×C4C11×AGL(1,ℤ/8)12yes—
477C2×C4C11×#13712yes—
478C2×C4C23×C4×C1111yescharacteristic
479C2×C4C22×Q8×C1111yescharacteristic
480C2×C4C2×C11×#4111yescharacteristic
481C2×C4C2×C11×#4111yescharacteristic
482C2×C4C2×C11×#4111yescharacteristic
483C2×C4C2×C11×#4111yescharacteristic
484C8—24no—
485C8—42no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22C11×#38714yes—
493C22C2×C4×D4×C1111yescharacteristic
494C22C2×C11×C22⋊Q811yescharacteristic
495C22C2×C11×#12311yescharacteristic
496C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
497C22C2×C11×#13711yescharacteristic
498C22C11×#57511yescharacteristic
499C22C11×#57511yescharacteristic
500C4—22no—
501C4—22no—
502C4—44no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—41no—
508C4—41no—
509C4—82no—
510C4C11×#38714yes—
511C4C2×C11×#11711yescharacteristic
512C4C2×C4×Q8×C1111yescharacteristic
513C4C2×C11×#12511yescharacteristic
514C4C2×C11×#12611yescharacteristic
515C2—24no—
516C2C2×C11×#38711yescharacteristic
517C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
518C2C4×C11×#13711yescharacteristic
519C2C11×#307911yescharacteristic
520C2C11×#308011yescharacteristic
521C2C11×#309411yescharacteristic
522C2C11×#309511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1921C2semidirect
5. C11×#1920C2semidirect
6. C11×#1919C2semidirect
7. C11×#1918C2semidirect
20. C11×#428C4semidirect
90. C11×#107C2×C4semidirect
91. C11×#106C2×C4semidirect
98. #21034C11direct (N × H)
171. #1921C2×C11semidirect
172. #1920C2×C11semidirect
173. #1919C2×C11semidirect
174. #1918C2×C11semidirect
244. #428C4×C11semidirect
343. #107C2×C4×C11semidirect
344. #106C2×C4×C11semidirect
428. C11#21034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#3892
C4×C11×#1172
C11×#19212
C11×#19202
C11×#19192
C11×#19182
C11×#17362
C11×#17282
#2103411