Finite Group Databasebeta

← C11×#11139 #14588332

Subgroups — C11×#11139 #14588332

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C22×C11×#100C211yesmaximal, characteristic
3C22×C11×#100C211yesmaximal, characteristic
4C22×C11×#100C211yesmaximal, characteristic
5C11×#1738C211yesmaximal, characteristic, complemented
6C11×#1738C211yesmaximal, characteristic, complemented
7C2×C11×#338C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C11×#430—22no—
16C11×#430—22no—
17C2×C11×#108—22no—
18C2×C11×#100—22no—
19C2×C11×#100—22no—
20C2×C11×#100—22no—
21C2×C11×#100—22no—
22C2×C11×#100—22no—
23C2×C11×#100—22no—
24C2×C11×#100—22no—
25C2×C11×#100—22no—
26C2×C11×#100C414yes—
27C11×#341—22no—
28C11×#341—22no—
29C11×#338—22no—
30C25×C11Q812yes—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11C2×C412yes—
44C22×D4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—21no—
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—21no—
66C2×C11×M16—21no—
67C2×C11×M16—21no—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16C2×C412yes—
75C2×C11×M16C2×C412yes—
76C2×C11×M16D412yes—
77C2×C11×M16D412yes—
78C2×C11×M16D412yes—
79C2×C11×M16D412yes—
80C2×C11×M16D412yes—
81C2×C11×M16D412yes—
82C22×C8×C11—21no—
83C22×C8×C11—21no—
84C22×C8×C11—21no—
85C22×C8×C11—21no—
86C22×C8×C11—21no—
87C22×C8×C11—21no—
88C11×#108—28no—
89C11×#100—28no—
90C11×#100—28no—
91C11×#100—28no—
92#11139C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—84no—
100C24×C11C4⋊C414yes—
101C24×C11C2×Q811yescharacteristic
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11#4111yescharacteristic
139C22×C4×C11#4111yescharacteristic
140C22×C4×C11#4111yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C22×C4×C11#4111yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C11×M16—22no—
145C11×M16—22no—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—41no—
158C11×M16—41no—
159C11×M16—41no—
160C11×M16—41no—
161C11×M16—41no—
162C11×M16—41no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16C22⋊C414yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—41no—
177C2×C8×C11—41no—
178C2×C8×C11—41no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186C2×#430C2×C1111yescharacteristic, complemented
187C22×#100C2×C1111yescharacteristic
188C22×#100C2×C1111yescharacteristic
189C22×#100C2×C1111yescharacteristic
190#1738C2×C1111yescharacteristic, complemented
191#1738C2×C1111yescharacteristic, complemented
192C2×#338C2×C1111yescharacteristic, complemented
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—84no—
202C23×C11—84no—
203C23×C11—84no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11C2×C4⋊C411yescharacteristic
209C23×C11C22⋊Q811yescharacteristic
210C23×C11C22⋊Q811yescharacteristic
211C23×C11C22⋊Q811yescharacteristic
212C23×C11C22⋊Q811yescharacteristic
213C23×C11C22⋊Q811yescharacteristic
214C23×C11C22⋊Q811yescharacteristic
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11#11711yescharacteristic
225C2×C4×C11C4×D411yescharacteristic
226C2×C4×C11C4×D411yescharacteristic
227C2×C4×C11C4×D411yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12311yescharacteristic
241C2×C4×C11#12311yescharacteristic
242C2×C4×C11#12311yescharacteristic
243C2×C4×C11#12311yescharacteristic
244C2×C4×C11#12311yescharacteristic
245C2×C4×C11#12411yescharacteristic
246C2×C4×C11#12411yescharacteristic
247C2×C4×C11#12411yescharacteristic
248C2×C4×C11#12611yescharacteristic
249C2×C4×C11#12611yescharacteristic
250C2×C4×C11#12711yescharacteristic
251C8×C11—24no—
252C8×C11—42no—
253C8×C11—42no—
254C8×C11—42no—
255C8×C11—42no—
256C8×C11—42no—
257C23×D4C22×C1111yescharacteristic
258C22×M16C22×C1111yescharacteristic
259C22×M16C22×C1111yescharacteristic
260C22×M16C22×C1111yescharacteristic
261C22×M16C22×C1111yescharacteristic
262C22×M16C22×C1111yescharacteristic
263C22×M16C22×C1111yescharacteristic
264#430—22no—
265#430—22no—
266C2×#108—22no—
267C2×#100—22no—
268C2×#100—22no—
269C2×#100—22no—
270C2×#100—22no—
271C2×#100—22no—
272C2×#100—22no—
273C2×#100—22no—
274C2×#100—22no—
275C2×#100C4×C1114yes—
276#341—22no—
277#341—22no—
278#338—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—44no—
287C22×C11—84no—
288C22×C11—84no—
289C22×C11—84no—
290C22×C11—84no—
291C22×C11—84no—
292C22×C11—84no—
293C22×C11—84no—
294C22×C11#38011yescharacteristic
295C22×C11#38511yescharacteristic
296C22×C11#38511yescharacteristic
297C22×C11#39311yescharacteristic
298C22×C11#39611yescharacteristic
299C22×C11#39611yescharacteristic
300C22×C11#39911yescharacteristic
301C4×C11#38611yescharacteristic
302C4×C11#38811yescharacteristic
303C4×C11#38811yescharacteristic
304C4×C11#39011yescharacteristic
305C4×C11#39211yescharacteristic
306C4×C11#39411yescharacteristic
307C4×C11#39411yescharacteristic
308C4×C11#39711yescharacteristic
309C25Q8×C1112yes—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4C2×C4×C1112yes—
323C22×D4D4×C1112yes—
324C23×C4C23×C1111yescharacteristic
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16C2×C4×C1112yes—
354C2×M16C2×C4×C1112yes—
355C2×M16D4×C1112yes—
356C2×M16D4×C1112yes—
357C2×M16D4×C1112yes—
358C2×M16D4×C1112yes—
359C2×M16D4×C1112yes—
360C2×M16D4×C1112yes—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367#108—28no—
368#100—28no—
369#100—28no—
370#100—28no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—21no—
374C2×C11—21no—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—84no—
378C2×C11#143911yescharacteristic
379C2×C11#206912yes—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—84no—
387C24C11×C4⋊C414yes—
388C24C2×Q8×C1111yescharacteristic
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C22×C4C22×C4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C11×#4111yescharacteristic
426C22×C4C11×#4111yescharacteristic
427C22×C4C11×#4111yescharacteristic
428C22×C4C11×#4111yescharacteristic
429C22×C4C11×#4111yescharacteristic
430C22×C4C11×#4111yescharacteristic
431M16—22no—
432M16—22no—
433M16—22no—
434M16—22no—
435M16—22no—
436M16—22no—
437M16—22no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—41no—
445M16—41no—
446M16—41no—
447M16—41no—
448M16—41no—
449M16—41no—
450M16—41no—
451M16—41no—
452M16—41no—
453M16—41no—
454M16C11×C22⋊C414yes—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C11#1113911yescharacteristic, direct product factor, Sylow
474C23—24no—
475C23—24no—
476C23—24no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—84no—
483C23—84no—
484C23—84no—
485C23—84no—
486C23—84no—
487C23—84no—
488C23—84no—
489C23C2×C11×C4⋊C411yescharacteristic
490C23C11×C22⋊Q811yescharacteristic
491C23C11×C22⋊Q811yescharacteristic
492C23C11×C22⋊Q811yescharacteristic
493C23C11×C22⋊Q811yescharacteristic
494C23C11×C22⋊Q811yescharacteristic
495C23C11×C22⋊Q811yescharacteristic
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—42no—
504C2×C4C2×C11×C22⋊C411yescharacteristic
505C2×C4C11×#11711yescharacteristic
506C2×C4C4×D4×C1111yescharacteristic
507C2×C4C4×D4×C1111yescharacteristic
508C2×C4C4×D4×C1111yescharacteristic
509C2×C4C4×D4×C1111yescharacteristic
510C2×C4C11×#12011yescharacteristic
511C2×C4C11×#12011yescharacteristic
512C2×C4C11×#12011yescharacteristic
513C2×C4C11×#12111yescharacteristic
514C2×C4C11×#12111yescharacteristic
515C2×C4C11×#12111yescharacteristic
516C2×C4C11×#12111yescharacteristic
517C2×C4C11×#12111yescharacteristic
518C2×C4C11×#12111yescharacteristic
519C2×C4C11×#12111yescharacteristic
520C2×C4C11×#12111yescharacteristic
521C2×C4C11×#12311yescharacteristic
522C2×C4C11×#12311yescharacteristic
523C2×C4C11×#12311yescharacteristic
524C2×C4C11×#12311yescharacteristic
525C2×C4C11×#12311yescharacteristic
526C2×C4C11×#12411yescharacteristic
527C2×C4C11×#12411yescharacteristic
528C2×C4C11×#12411yescharacteristic
529C2×C4C11×#12611yescharacteristic
530C2×C4C11×#12611yescharacteristic
531C2×C4C11×#12711yescharacteristic
532C8—24no—
533C8—42no—
534C8—42no—
535C8—42no—
536C8—42no—
537C8—42no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—44no—
546C22—84no—
547C22—84no—
548C22—84no—
549C22—84no—
550C22—84no—
551C22—84no—
552C22—84no—
553C22C11×#38011yescharacteristic
554C22C11×#38511yescharacteristic
555C22C11×#38511yescharacteristic
556C22C11×#39311yescharacteristic
557C22C11×#39611yescharacteristic
558C22C11×#39611yescharacteristic
559C22C11×#39911yescharacteristic
560C4C11×#38611yescharacteristic
561C4C11×#38811yescharacteristic
562C4C11×#38811yescharacteristic
563C4C11×#39011yescharacteristic
564C4C11×#39211yescharacteristic
565C4C11×#39411yescharacteristic
566C4C11×#39411yescharacteristic
567C4C11×#39711yescharacteristic
568C2—21no—
569C2—21no—
570C2—21no—
571C2—21no—
572C2—21no—
573C2—21no—
574C2—84no—
575C2C11×#143911yescharacteristic
576C2C11×#206912yes—
subgroupG/H
center, socleC22×C11#396
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#430C2semidirect
5. C11×#1738C2semidirect
6. C11×#1738C2semidirect
7. C2×C11×#338C2semidirect
92. #11139C11direct (N × H)
186. C2×#430C2×C11semidirect
190. #1738C2×C11semidirect
191. #1738C2×C11semidirect
192. C2×#338C2×C11semidirect
473. C11#11139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C22×C11×#1002
C11×#17382
C2×C11×#3382
#1113911