Finite Group Databasebeta

← C11×#11075 #14588268

Subgroups — C11×#11075 #14588268

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#104C212yesmaximal
2C11×#2297C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C11×#339C212yesmaximal, complemented
5C11×#1728C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C22×C11×M16C2212yes—
8C2×C11×#117C2211yescharacteristic
9C22×C11×C4⋊C4—21no—
10C22×C42×C11C2212yes—
11C22×C42×C11C2211yescharacteristic
12C2×C11×#104—24no—
13C2×C11×#104—24no—
14C2×C11×#104—24no—
15C11×#391C412yescomplemented
16C11×#390C412yescomplemented
17C11×#386—21no—
18C11×#386—21no—
19C4×C11×C4⋊C4—24no—
20C4×C11×C22⋊C4—22no—
21C2×C11×#95—21no—
22C11×#339—24no—
23C11×#336—22no—
24C2×C11×#41—21no—
25C2×C11×#41—21no—
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41D412yes—
31C2×C11×#41Q812yes—
32C22×Q8×C11C2×C411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11C2×C411yescharacteristic
35C23×C4×C11—22no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C2×C11×M16—22no—
41C2×C11×M16—22no—
42C2×C11×M16—22no—
43C2×C11×M16—22no—
44C2×C11×M16—22no—
45C2×C11×M16D414yes—
46C22×C8×C11—22no—
47C11×#117—22no—
48C11×#117—22no—
49C2×C11×C4⋊C4—28no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2×C412yes—
64C2×C42×C11D414yes—
65C2×C42×C11D412yes—
66C11×#104—216no—
67C11×#95—24no—
68C11×#95—22no—
69C11×#95—22no—
70#11075C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—21no—
72C24×C11C2×D411yescharacteristic
73C11×#41—24no—
74C11×#41—24no—
75C11×#41—24no—
76C11×#41—24no—
77C11×#41—42no—
78C11×#41—42no—
79C11×#41—42no—
80C11×#41—42no—
81C2×Q8×C11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11C4⋊C412yescomplemented
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11C4⋊C412yescomplemented
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—24no—
98C22×C4×C11—28no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—44no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C22⋊C412yes—
113C22×C4×C11C22⋊C412yes—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×Q811yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C11×M16—24no—
125C11×M16—24no—
126C11×M16—42no—
127C11×M16—42no—
128C2×C8×C11—24no—
129C2×C8×C11—42no—
130C2×C8×C11—42no—
131C11×C4⋊C4—216no—
132C11×C4⋊C4—24no—
133C11×C22⋊C4—44no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—44no—
137C42×C11—24no—
138C42×C11—24no—
139C42×C11—24no—
140C42×C11—24no—
141C42×C11—42no—
142C42×C11—42no—
143C42×C11—42no—
144C22×#104C2×C1112yes—
145#2297C2×C1111yescharacteristic
146C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
147C2×#339C2×C1112yescomplemented
148#1728C2×C1111yescharacteristic, complemented
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11#12011yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11C22⋊Q811yescharacteristic
160C23×C11#12311yescharacteristic
161C23×C11#12411yescharacteristic
162C23×C11#12711yescharacteristic
163Q8×C11—24no—
164Q8×C11—42no—
165D4×C11—24no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—42no—
170D4×C11—42no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—28no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—48no—
181C2×C4×C11—44no—
182C2×C4×C11—48no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—44no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11#10414yescomplemented
194C2×C4×C11C2×C4⋊C411yescharacteristic
195C2×C4×C11#11711yescharacteristic
196C2×C4×C11C4×D412yes—
197C2×C4×C11C4×D412yes—
198C2×C4×C11#12012yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11C22⋊Q812yes—
204C2×C4×C11C22⋊Q812yes—
205C2×C4×C11C22⋊Q811yescharacteristic
206C2×C4×C11#12312yes—
207C2×C4×C11#12312yes—
208C2×C4×C11#12412yes—
209C2×C4×C11#12612yes—
210C8×C11—44no—
211C22×#41C22×C1111yescharacteristic
212C22×M16C22×C1112yes—
213C2×#117C22×C1111yescharacteristic
214C22×C4⋊C4—21no—
215C22×C42C22×C1112yes—
216C22×C42C22×C1111yescharacteristic
217C2×#104—24no—
218C2×#104—24no—
219C2×#104—24no—
220#391C4×C1112yescomplemented
221#390C4×C1112yescomplemented
222#386—21no—
223#386—21no—
224C4×C4⋊C4—24no—
225C4×C22⋊C4—22no—
226C2×#95—21no—
227#339—24no—
228#336—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—44no—
238C22×C11—42no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—82no—
242C22×C11#38011yescharacteristic
243C22×C11#38611yescharacteristic
244C22×C11#39011yescharacteristic
245C22×C11#39211yescharacteristic
246C22×C11#39311yescharacteristic
247C22×C11#39711yescharacteristic
248C22×C11#39911yescharacteristic
249C22×C11C2×#10412yes—
250C22×C11#42112yes—
251C4×C11—24no—
252C4×C11—48no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—82no—
256C4×C11#38512yes—
257C4×C11#38812yes—
258C4×C11#39412yes—
259C4×C11#39612yes—
260C2×#41—21no—
261C2×#41—21no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41D4×C1112yes—
267C2×#41Q8×C1112yes—
268C22×Q8C2×C4×C1111yescharacteristic
269C22×D4—21no—
270C22×D4C2×C4×C1111yescharacteristic
271C23×C4—22no—
272C23×C4—21no—
273C23×C4D4×C1111yescharacteristic
274C23×C4D4×C1111yescharacteristic
275C23×C4C23×C1111yescharacteristic
276C2×M16—22no—
277C2×M16—22no—
278C2×M16—22no—
279C2×M16—22no—
280C2×M16—22no—
281C2×M16D4×C1114yes—
282C22×C8—22no—
283#117—22no—
284#117—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4C2×C4×C1112yes—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—21no—
298C2×C42—22no—
299C2×C42C2×C4×C1112yes—
300C2×C42D4×C1114yes—
301C2×C42D4×C1112yes—
302#104—216no—
303#95—24no—
304#95—22no—
305#95—22no—
306C2×C11—21no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—82no—
311C2×C11#143911yescharacteristic
312C2×C11#180612yes—
313C2×C11#189611yescharacteristic
314C2×C11#189711yescharacteristic
315C2×C11#198012yes—
316C24—21no—
317C24C2×D4×C1111yescharacteristic
318#41—24no—
319#41—24no—
320#41—24no—
321#41—24no—
322#41—42no—
323#41—42no—
324#41—42no—
325#41—42no—
326C2×Q8—21no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8C11×C4⋊C412yescomplemented
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4C11×C4⋊C412yescomplemented
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—24no—
343C22×C4—28no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—24no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—42no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4C11×C22⋊C412yes—
358C22×C4C11×C22⋊C412yes—
359C22×C4C22×C4×C1111yescharacteristic
360C22×C4C2×D4×C1111yescharacteristic
361C22×C4C2×D4×C1112yes—
362C22×C4C2×D4×C1112yes—
363C22×C4C2×D4×C1111yescharacteristic
364C22×C4C2×Q8×C1111yescharacteristic
365C22×C4C11×#4111yescharacteristic
366C22×C4C11×#4111yescharacteristic
367C22×C4C11×#4112yes—
368C22×C4C11×#4112yes—
369M16—24no—
370M16—24no—
371M16—42no—
372M16—42no—
373C2×C8—24no—
374C2×C8—42no—
375C2×C8—42no—
376C4⋊C4—216no—
377C4⋊C4—24no—
378C22⋊C4—44no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—44no—
382C42—24no—
383C42—24no—
384C42—24no—
385C42—24no—
386C42—42no—
387C42—42no—
388C42—42no—
389C11#1107511yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23—22no—
392C23—22no—
393C23—41no—
394C23—41no—
395C23—42no—
396C23—42no—
397C23C2×C11×C22⋊C411yescharacteristic
398C23C11×#12011yescharacteristic
399C23C11×#12111yescharacteristic
400C23C11×C22⋊Q811yescharacteristic
401C23C11×#12311yescharacteristic
402C23C11×#12411yescharacteristic
403C23C11×#12711yescharacteristic
404Q8—24no—
405Q8—42no—
406D4—24no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—42no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—28no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—44no—
422C2×C4—48no—
423C2×C4—48no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4C11×#10414yescomplemented
435C2×C4C2×C11×C4⋊C411yescharacteristic
436C2×C4C11×#11711yescharacteristic
437C2×C4C4×D4×C1112yes—
438C2×C4C4×D4×C1112yes—
439C2×C4C11×#12012yes—
440C2×C4C11×#12112yes—
441C2×C4C11×#12111yescharacteristic
442C2×C4C11×#12112yes—
443C2×C4C11×#12112yes—
444C2×C4C11×C22⋊Q812yes—
445C2×C4C11×C22⋊Q812yes—
446C2×C4C11×C22⋊Q811yescharacteristic
447C2×C4C11×#12312yes—
448C2×C4C11×#12312yes—
449C2×C4C11×#12412yes—
450C2×C4C11×#12612yes—
451C8—44no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—42no—
461C22—44no—
462C22—81no—
463C22—81no—
464C22—82no—
465C22C11×#38011yescharacteristic
466C22C11×#38611yescharacteristic
467C22C11×#39011yescharacteristic
468C22C11×#39211yescharacteristic
469C22C11×#39311yescharacteristic
470C22C11×#39711yescharacteristic
471C22C11×#39911yescharacteristic
472C22C2×C11×#10412yes—
473C22C11×#42112yes—
474C4—24no—
475C4—48no—
476C4—42no—
477C4—42no—
478C4—82no—
479C4C11×#38512yes—
480C4C11×#38812yes—
481C4C11×#39412yes—
482C4C11×#39612yes—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—82no—
488C2C11×#143911yescharacteristic
489C2C11×#180612yes—
490C2C11×#189611yescharacteristic
491C2C11×#189711yescharacteristic
492C2C11×#198012yes—
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC23×C11C2×C22⋊C4
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C11×C4⋊C4C2semidirect
4. C2×C11×#339C2semidirect
5. C11×#1728C2semidirect
15. C11×#391C4semidirect
16. C11×#390C4semidirect
70. #11075C11direct (N × H)
84. C2×Q8×C11C4⋊C4semidirect
94. C2×D4×C11C4⋊C4semidirect
146. C2×C4×C4⋊C4C2×C11semidirect
147. C2×#339C2×C11semidirect
148. #1728C2×C11semidirect
193. C2×C4×C11#104semidirect
220. #391C4×C11semidirect
221. #390C4×C11semidirect
329. C2×Q8C11×C4⋊C4semidirect
339. C2×D4C11×C4⋊C4semidirect
389. C11#11075direct (N × H)
434. C2×C4C11×#104semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1042
C11×#22972
C2×C4×C11×C4⋊C42
C2×C11×#3392
C11×#17282
#1107511