Finite Group Databasebeta

← C11×#18380 #14595573

Subgroups — C11×#18380 #14595573

Order 2816.

1336 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic, complemented
2C11×#3186C212yesmaximal, complemented
3C11×#2543C211yesmaximal, characteristic, complemented
4C11×#1610C212yesmaximal, complemented
5C11×#1607C212yesmaximal, complemented
6C11×#1598C212yesmaximal, complemented
7C11×#1595C212yesmaximal, complemented
8C2×C11×#327C212yesmaximal, complemented
9C11×#1459C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537C2212yes—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C2×C11×#121—21no—
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C11×#121C2211yescharacteristic, complemented
22C2×C4×D4×C11C2211yescharacteristic
23C11×#480—22no—
24C11×#480C2214yescomplemented
25C11×#466—24no—
26C11×#447—22no—
27C11×#447C2214yescomplemented
28C2×C11×C22⋊C8C2212yescomplemented
29C11×#398C2211yescharacteristic, complemented
30C11×#397C2211yescharacteristic, complemented
31C11×#394C2211yescharacteristic, complemented
32C11×#392C2211yescharacteristic, complemented
33C11×#388—21no—
34C11×#386—21no—
35C11×#386—21no—
36C2×C11×#95C2211yescharacteristic, complemented
37C11×#327C2214yescomplemented
38C11×#327C2214yescomplemented
39C11×#324C2212yescomplemented
40C11×#323C2212yescomplemented
41C11×H(5,𝔽2)—44no—
42C11×H(5,𝔽2)—44no—
43C2×C11×#41—24no—
44C2×C11×#41—22no—
45C22×D4×C11—24no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11D411yescharacteristic
52C22×D4×C11D412yescomplemented
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C2×C11×D8—24no—
58C22×C8×C11—22no—
59C11×C4⋊Q8—21no—
60C11×#127—21no—
61C11×#124—22no—
62C11×#123—24no—
63C11×#123—24no—
64C11×C22⋊Q8—24no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121—24no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—44no—
75C11×#121D414yescomplemented
76C11×#121C2314yes—
77C11×#120—24no—
78C11×#120—24no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D412yescomplemented
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C11×C22⋊C4C2311yescharacteristic
97C2×C42×C11D411yescharacteristic
98C11×#107—24no—
99C11×#102—24no—
100C11×#102—24no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8C2314yes—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95C2311yescharacteristic
107C11×#95C2311yescharacteristic
108#18380C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—21no—
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C11×#41—44no—
115C11×#41—416no—
116C11×#41—44no—
117C2×Q8×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—42no—
129C2×D4×C11—416no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
139C2×D4×C11—82no—
140C2×D4×C11—82no—
141C2×D4×C11—81no—
142C2×D4×C11D814yescomplemented
143C2×D4×C11C2×D414yes—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—81no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2411yescharacteristic
164C11×D8—84no—
165C2×C8×C11—24no—
166C2×C8×C11—82no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4C2×D414yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—81no—
186C42×C11—21no—
187C42×C11—21no—
188#3496C2×C1111yescharacteristic, complemented
189#3186C2×C1112yescomplemented
190#2543C2×C1111yescharacteristic, complemented
191#1610C2×C1112yescomplemented
192#1607C2×C1112yescomplemented
193#1598C2×C1112yescomplemented
194#1595C2×C1112yescomplemented
195C2×#327C2×C1112yescomplemented
196#1459C2×C1111yescharacteristic, complemented
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—24no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—44no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—44no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—82no—
214C23×C11—82no—
215C23×C11—82no—
216C23×C11—82no—
217C23×C11#12012yes—
218C23×C11C2×D812yes—
219C23×C11C2×D812yes—
220C23×C11AGL(1,ℤ/8)12yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—44no—
223D4×C11—28no—
224D4×C11—44no—
225D4×C11—44no—
226D4×C11—44no—
227D4×C11—44no—
228D4×C11—48no—
229D4×C11—44no—
230D4×C11—44no—
231D4×C11—48no—
232D4×C11—82no—
233D4×C11—82no—
234D4×C11—84no—
235D4×C11—84no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—48no—
248C2×C4×C11—41no—
249C2×C4×C11—44no—
250C2×C4×C11—41no—
251C2×C4×C11—44no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—81no—
261C2×C4×C11—84no—
262C2×C4×C11#12011yescharacteristic
263C2×C4×C11#12011yescharacteristic
264C2×C4×C11C2×D812yes—
265C2×C4×C11C22×D412yes—
266C8×C11—44no—
267C2×H(5,𝔽2)—21no—
268#547—22no—
269#546—24no—
270D42—22no—
271#537C22×C1112yes—
272#534—21no—
273#534C22×C1112yes—
274#532—21no—
275C2×#121—21no—
276C2×#121—21no—
277C2×#121C22×C1112yes—
278C2×#121C22×C1111yescharacteristic, complemented
279C2×C4×D4C22×C1111yescharacteristic
280#480—22no—
281#480C22×C1114yescomplemented
282#466—24no—
283#447—22no—
284#447C22×C1114yescomplemented
285C2×C22⋊C8C22×C1112yescomplemented
286#398C22×C1111yescharacteristic, complemented
287#397C22×C1111yescharacteristic, complemented
288#394C22×C1111yescharacteristic, complemented
289#392C22×C1111yescharacteristic, complemented
290#388—21no—
291#386—21no—
292#386—21no—
293C2×#95C22×C1111yescharacteristic, complemented
294#327C22×C1114yescomplemented
295#327C22×C1114yescomplemented
296#324C22×C1112yescomplemented
297#323C22×C1112yescomplemented
298C22×C11—21no—
299C22×C11—22no—
300C22×C11—21no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—164no—
320C22×C11—164no—
321C22×C11#44714yes—
322C22×C11C2×#12011yescharacteristic
323C22×C11C22×D811yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C4×C11—22no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—44no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335H(5,𝔽2)—44no—
336H(5,𝔽2)—44no—
337C2×#41—24no—
338C2×#41—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4D4×C1111yescharacteristic
346C22×D4D4×C1112yescomplemented
347C22×D4C23×C1111yescharacteristic
348C23×C4—21no—
349C23×C4D4×C1111yescharacteristic
350C23×C4C23×C1111yescharacteristic
351C2×D8—24no—
352C22×C8—22no—
353C4⋊Q8—21no—
354#127—21no—
355#124—22no—
356#123—24no—
357#123—24no—
358C22⋊Q8—24no—
359#121—22no—
360#121—22no—
361#121—24no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—22no—
366#121—22no—
367#121—22no—
368#121—44no—
369#121D4×C1114yescomplemented
370#121C23×C1114yes—
371#120—24no—
372#120—24no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C1112yescomplemented
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4D4×C1111yescharacteristic
390C2×C22⋊C4C23×C1111yescharacteristic
391C2×C42D4×C1111yescharacteristic
392#107—24no—
393#102—24no—
394#102—24no—
395C22⋊C8—22no—
396C22⋊C8C23×C1114yes—
397#95—21no—
398#95—21no—
399#95—21no—
400#95C23×C1111yescharacteristic
401#95C23×C1111yescharacteristic
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—24no—
405C2×C11—42no—
406C2×C11—84no—
407C2×C11—161no—
408C2×C11C2×#44711yescharacteristic
409C2×C11#301811yescharacteristic
410C2×C11#302611yescharacteristic
411C24—22no—
412C24—22no—
413C24—21no—
414C24C2×D4×C1111yescharacteristic
415C24C2×D4×C1111yescharacteristic
416#41—44no—
417#41—416no—
418#41—44no—
419C2×Q8—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—42no—
431C2×D4—416no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—81no—
441C2×D4—82no—
442C2×D4—82no—
443C2×D4—81no—
444C2×D4C11×D814yescomplemented
445C2×D4C2×D4×C1114yes—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—81no—
457C22×C4—81no—
458C22×C4—81no—
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1112yes—
464C22×C4C2×D4×C1112yes—
465C22×C4C24×C1111yescharacteristic
466D8—84no—
467C2×C8—24no—
468C2×C8—82no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—42no—
475C4⋊C4C2×D4×C1114yes—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C42—21no—
489C42—21no—
490C11#1838011yescharacteristic, direct product factor, Sylow
491C23—21no—
492C23—21no—
493C23—24no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—44no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23C11×#12012yes—
512C23C2×C11×D812yes—
513C23C2×C11×D812yes—
514C23C11×AGL(1,ℤ/8)12yes—
515C23C22×D4×C1111yescharacteristic
516Q8—44no—
517D4—28no—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—44no—
522D4—48no—
523D4—44no—
524D4—44no—
525D4—48no—
526D4—82no—
527D4—82no—
528D4—84no—
529D4—84no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—24no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—48no—
542C2×C4—41no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—44no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—81no—
555C2×C4—84no—
556C2×C4C11×#12011yescharacteristic
557C2×C4C11×#12011yescharacteristic
558C2×C4C2×C11×D812yes—
559C2×C4C22×D4×C1112yes—
560C8—44no—
561C22—21no—
562C22—22no—
563C22—21no—
564C22—22no—
565C22—22no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—41no—
570C22—41no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—164no—
583C22—164no—
584C22C11×#44714yes—
585C22C2×C11×#12011yescharacteristic
586C22C22×C11×D811yescharacteristic
587C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
588C4—22no—
589C4—22no—
590C4—21no—
591C4—21no—
592C4—42no—
593C4—44no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C2—21no—
599C2—21no—
600C2—24no—
601C2—42no—
602C2—84no—
603C2—161no—
604C2C2×C11×#44711yescharacteristic
605C2C11×#301811yescharacteristic
606C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3496C2semidirect
2. C11×#3186C2semidirect
3. C11×#2543C2semidirect
4. C11×#1610C2semidirect
5. C11×#1607C2semidirect
6. C11×#1598C2semidirect
7. C11×#1595C2semidirect
8. C2×C11×#327C2semidirect
9. C11×#1459C2semidirect
21. C2×C11×#121C22semidirect
24. C11×#480C22semidirect
27. C11×#447C22semidirect
28. C2×C11×C22⋊C8C22semidirect
29. C11×#398C22semidirect
30. C11×#397C22semidirect
31. C11×#394C22semidirect
32. C11×#392C22semidirect
36. C2×C11×#95C22semidirect
37. C11×#327C22semidirect
38. C11×#327C22semidirect
39. C11×#324C22semidirect
40. C11×#323C22semidirect
52. C22×D4×C11D4semidirect
75. C11×#121D4semidirect
85. C2×C11×C4⋊C4D4semidirect
108. #18380C11direct (N × H)
142. C2×D4×C11D8semidirect
188. #3496C2×C11semidirect
189. #3186C2×C11semidirect
190. #2543C2×C11semidirect
191. #1610C2×C11semidirect
192. #1607C2×C11semidirect
193. #1598C2×C11semidirect
194. #1595C2×C11semidirect
195. C2×#327C2×C11semidirect
196. #1459C2×C11semidirect
278. C2×#121C22×C11semidirect
281. #480C22×C11semidirect
284. #447C22×C11semidirect
285. C2×C22⋊C8C22×C11semidirect
286. #398C22×C11semidirect
287. #397C22×C11semidirect
288. #394C22×C11semidirect
289. #392C22×C11semidirect
293. C2×#95C22×C11semidirect
294. #327C22×C11semidirect
295. #327C22×C11semidirect
296. #324C22×C11semidirect
297. #323C22×C11semidirect
346. C22×D4D4×C11semidirect
369. #121D4×C11semidirect
379. C2×C4⋊C4D4×C11semidirect
444. C2×D4C11×D8semidirect
490. C11#18380direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#31862
C11×#25432
C11×#16102
C11×#16072
C11×#15982
C11×#15952
C2×C11×#3272
C11×#14592
#1838011