Finite Group Databasebeta

← C11×#18438 #14595631

Subgroups — C11×#18438 #14595631

Order 2816.

908 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3561C211yesmaximal, characteristic
2C11×#3238C211yesmaximal, characteristic, complemented
3C11×#3229C211yesmaximal, characteristic, complemented
4C11×#2640C211yesmaximal, characteristic, complemented
5C11×#1612C214yesmaximal, complemented
6C11×#1608C214yesmaximal, complemented
7C11×#1506C211yesmaximal, characteristic, complemented
8C11×#1500C211yesmaximal, characteristic, complemented
9C11×#1469C211yesmaximal, characteristic, complemented
10C11×#563—21no—
11C11×#562—21no—
12C11×#556—21no—
13C11×#551—22no—
14D4×Q8×C11—21no—
15C11×#548—21no—
16C11×#546—21no—
17C11×#543C2212yes—
18C11×#542—21no—
19C11×#542—22no—
20C11×#538C2212yes—
21C11×#536—21no—
22C11×#533C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#529C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C11×#501—21no—
27C11×#498—21no—
28C11×#489—21no—
29C11×#487—21no—
30C11×#483C2214yes—
31C11×#483C2212yes—
32C11×#480C2212yes—
33C11×#477—21no—
34C11×#476—21no—
35C11×#475—22no—
36C11×#432C2211yescharacteristic
37C11×#431C2211yescharacteristic
38C11×#397C2214yes—
39C11×#393—22no—
40C11×#391—21no—
41C11×#390—21no—
42C11×#376C2211yescharacteristic
43C11×#328C2214yes—
44C11×#328C2212yes—
45C11×#327C2212yes—
46C11×#323C2214yes—
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11D411yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8D411yescharacteristic
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—21no—
64C11×#125—21no—
65C11×#125D411yescharacteristic
66C11×#124—21no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124—21no—
70C11×#124—21no—
71C11×#124—21no—
72C11×#124—21no—
73C11×#124D411yescharacteristic
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—21no—
78C11×#123—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8C2311yescharacteristic
89C11×C22⋊Q8C2312yes—
90C11×#121—21no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#121C2311yescharacteristic
94C11×#120—22no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11D411yescharacteristic
98C4×Q8×C11D412yes—
99C4×D4×C11—21no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—22no—
103C4×D4×C11D411yescharacteristic
104C11×#117—22no—
105C11×#117—21no—
106C11×#117—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4D412yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C11×#107—22no—
116C11×#106—24no—
117C11×#106—22no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×#103—22no—
121C11×#103—24no—
122C11×#102—22no—
123C11×C22⋊C8C2312yes—
124C11×C22⋊C8C2312yes—
125C11×#97—21no—
126C4×C8×C11—21no—
127C11×#95—21no—
128C11×#95—24no—
129C11×#95C2312yes—
130#18438C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11C2×D412yes—
132C11×#41—82no—
133C2×Q8×C11—22no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—42no—
138C2×Q8×C11—41no—
139C2×Q8×C11—41no—
140C2×Q8×C11—82no—
141C2×Q8×C11—82no—
142C2×Q8×C11C2×D411yescharacteristic
143C2×Q8×C11C2×D412yes—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2411yescharacteristic
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—84no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—21no—
202C42×C11—42no—
203C42×C11C2×D411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D411yescharacteristic
207#3561C2×C1111yescharacteristic
208#3238C2×C1111yescharacteristic, complemented
209#3229C2×C1111yescharacteristic, complemented
210#2640C2×C1111yescharacteristic, complemented
211#1612C2×C1114yescomplemented
212#1608C2×C1114yescomplemented
213#1506C2×C1111yescharacteristic, complemented
214#1500C2×C1111yescharacteristic, complemented
215#1469C2×C1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—21no—
218C23×C11—24no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11C22×D411yescharacteristic
222Q8×C11—41no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—81no—
227Q8×C11—82no—
228Q8×C11—82no—
229Q8×C11—82no—
230D4×C11—41no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—81no—
234D4×C11—82no—
235D4×C11—82no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—44no—
252C2×C4×C11—82no—
253C2×C4×C11—82no—
254C2×C4×C11—82no—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C8×C11—42no—
262C8×C11—42no—
263#563—21no—
264#562—21no—
265#556—21no—
266#551—22no—
267D4×Q8—21no—
268#548—21no—
269#546—21no—
270#543C22×C1112yes—
271#542—21no—
272#542—22no—
273#538C22×C1112yes—
274#536—21no—
275#533C22×C1111yescharacteristic
276C2×C4⋊Q8C22×C1111yescharacteristic
277#529C22×C1111yescharacteristic
278C2×#124C22×C1111yescharacteristic
279#501—21no—
280#498—21no—
281#489—21no—
282#487—21no—
283#483C22×C1112yes—
284#483C22×C1114yes—
285#480C22×C1112yes—
286#477—21no—
287#476—21no—
288#475—22no—
289#432C22×C1111yescharacteristic
290#431C22×C1111yescharacteristic
291#397C22×C1114yes—
292#393—22no—
293#391—21no—
294#390—21no—
295#376C22×C1111yescharacteristic
296#328C22×C1112yes—
297#328C22×C1114yes—
298#327C22×C1112yes—
299#323C22×C1114yes—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—41no—
303C22×C11—42no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—41no—
308C22×C11—84no—
309C22×C11C2×#12011yescharacteristic
310C22×C11#57712yes—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—21no—
316C4×C11—41no—
317C4×C11—41no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—41no—
321C4×C11—42no—
322C4×C11—82no—
323C4×C11—82no—
324C4×C11#45512yes—
325C2×#41—21no—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8D4×C1111yescharacteristic
329C22×D4D4×C1111yescharacteristic
330C4⋊Q8—21no—
331C4⋊Q8—22no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8D4×C1111yescharacteristic
337C4⋊Q8D4×C1111yescharacteristic
338#126—22no—
339#126—22no—
340#126—22no—
341#126—21no—
342#125—21no—
343#125D4×C1111yescharacteristic
344#124—21no—
345#124—22no—
346#124—22no—
347#124—21no—
348#124—21no—
349#124—21no—
350#124—21no—
351#124D4×C1111yescharacteristic
352#123—22no—
353#123—22no—
354#123—22no—
355#123—21no—
356#123—22no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8C23×C1111yescharacteristic
367C22⋊Q8C23×C1112yes—
368#121—21no—
369#121—22no—
370#121—22no—
371#121C23×C1111yescharacteristic
372#120—22no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8D4×C1111yescharacteristic
376C4×Q8D4×C1112yes—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4—22no—
381C4×D4D4×C1111yescharacteristic
382#117—22no—
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C23×C1112yes—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4D4×C1112yes—
390C2×C22⋊C4C23×C1112yes—
391C2×C42—21no—
392C2×C42C23×C1111yescharacteristic
393#107—22no—
394#106—24no—
395#106—22no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398#103—24no—
399#103—22no—
400#102—22no—
401C22⋊C8C23×C1112yes—
402C22⋊C8C23×C1112yes—
403#97—21no—
404C4×C8—21no—
405#95—21no—
406#95—24no—
407#95C23×C1112yes—
408C2×C11—22no—
409C2×C11—81no—
410C2×C11—82no—
411C2×C11#301011yescharacteristic
412C2×C11C2×#45511yescharacteristic
413C2×C11#302811yescharacteristic
414C24C2×D4×C1112yes—
415#41—82no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—42no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—82no—
424C2×Q8—82no—
425C2×Q8C2×D4×C1111yescharacteristic
426C2×Q8C2×D4×C1112yes—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4C2×D4×C1111yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1112yes—
443C22×C4C24×C1111yescharacteristic
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C1111yescharacteristic
464C4⋊C4C2×D4×C1112yes—
465C4⋊C4C2×D4×C1111yescharacteristic
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—21no—
481C22⋊C4—84no—
482C42—22no—
483C42—22no—
484C42—21no—
485C42—42no—
486C42C2×D4×C1111yescharacteristic
487C42C2×D4×C1111yescharacteristic
488C42C2×D4×C1111yescharacteristic
489C42C2×D4×C1111yescharacteristic
490C11#1843811yescharacteristic, direct product factor, Sylow
491C23—22no—
492C23—21no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23C22×D4×C1111yescharacteristic
497Q8—41no—
498Q8—42no—
499Q8—42no—
500Q8—42no—
501Q8—81no—
502Q8—82no—
503Q8—82no—
504Q8—82no—
505D4—41no—
506D4—42no—
507D4—42no—
508D4—81no—
509D4—82no—
510D4—82no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4C11×#12011yescharacteristic
531C2×C4C11×#12011yescharacteristic
532C2×C4C11×#12011yescharacteristic
533C2×C4C11×#12011yescharacteristic
534C2×C4C22×D4×C1111yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C8—42no—
537C8—42no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—42no—
545C22—41no—
546C22—84no—
547C22C2×C11×#12011yescharacteristic
548C22C11×#57712yes—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—42no—
560C4—82no—
561C4—82no—
562C4C11×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C11×#301011yescharacteristic
567C2C2×C11×#45511yescharacteristic
568C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3561C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3238C2semidirect
3. C11×#3229C2semidirect
4. C11×#2640C2semidirect
5. C11×#1612C2semidirect
6. C11×#1608C2semidirect
7. C11×#1506C2semidirect
8. C11×#1500C2semidirect
9. C11×#1469C2semidirect
130. #18438C11direct (N × H)
208. #3238C2×C11semidirect
209. #3229C2×C11semidirect
210. #2640C2×C11semidirect
211. #1612C2×C11semidirect
212. #1608C2×C11semidirect
213. #1506C2×C11semidirect
214. #1500C2×C11semidirect
215. #1469C2×C11semidirect
490. C11#18438direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35612
C11×#32382
C11×#32292
C11×#26402
C11×#16122
C11×#16082
C11×#15062
C11×#15002
C11×#14692
#1843811