Finite Group Databasebeta

← C11×#10571 #14587764

Subgroups — C11×#10571 #14587764

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2646C211yesmaximal, characteristic
2C11×#1853C211yesmaximal, characteristic
3C11×#1852C211yesmaximal, characteristic
4C11×#1442C211yesmaximal, characteristic
5C11×#1294C211yesmaximal, characteristic
6C11×#1294C211yesmaximal, characteristic
7C11×#1280C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×C11×#107—21no—
10C2×C11×#106—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#400—21no—
14C11×#400—21no—
15C11×#398—21no—
16C11×#398—21no—
17C11×#385—21no—
18C11×#385—21no—
19C11×#380C2211yescharacteristic
20C11×#380C2211yescharacteristic
21C2×C11×#95—21no—
22C2×C11×#95—21no—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C11×#340—21no—
26C11×#340—21no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—42no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C11×#107—42no—
48C11×#106—42no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8Q812yes—
52C11×C22⋊C8Q812yes—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—42no—
63C11×#95—42no—
64C11×#95Q812yes—
65#10571C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×Q811yescharacteristic
100C22×C4×C11C2×Q811yescharacteristic
101C22×C4×C11C2×Q811yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—81no—
118C11×C4⋊C4—81no—
119C11×C4⋊C4—81no—
120C11×C4⋊C4—81no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125#2646C2×C1111yescharacteristic
126#1853C2×C1111yescharacteristic
127#1852C2×C1111yescharacteristic
128#1442C2×C1111yescharacteristic
129#1294C2×C1111yescharacteristic
130#1294C2×C1111yescharacteristic
131#1280C2×C1111yescharacteristic
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11#12011yescharacteristic
137C23×C11C22⋊Q811yescharacteristic
138C23×C11C4⋊Q811yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142C23×C11#13711yescharacteristic
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11C22⋊Q811yescharacteristic
188C2×C4×C11C22⋊Q811yescharacteristic
189C2×C4×C11C4⋊Q811yescharacteristic
190C2×C4×C11C4⋊Q811yescharacteristic
191C8×C11—42no—
192C8×C11—42no—
193C22×C4⋊C4C22×C1111yescharacteristic
194C2×#107—21no—
195C2×#106—21no—
196C2×C22⋊C8C22×C1111yescharacteristic
197C2×C22⋊C8C22×C1111yescharacteristic
198#400—21no—
199#400—21no—
200#398—21no—
201#398—21no—
202#385—21no—
203#385—21no—
204#380C22×C1111yescharacteristic
205#380C22×C1111yescharacteristic
206C2×#95—21no—
207C2×#95—21no—
208C2×#95C22×C1111yescharacteristic
209C2×#95C22×C1111yescharacteristic
210#340—21no—
211#340—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11#39511yescharacteristic
225C22×C11#44911yescharacteristic
226C22×C11#45211yescharacteristic
227C22×C11#45411yescharacteristic
228C22×C11#45511yescharacteristic
229C22×C11B(4,𝔽2)11yescharacteristic
230C22×C11#45811yescharacteristic
231C22×C11#47811yescharacteristic
232C22×C11#47911yescharacteristic
233C22×C11#49911yescharacteristic
234C22×C11#50111yescharacteristic
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11—82no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11—81no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4D4×C1111yescharacteristic
250C23×C4D4×C1111yescharacteristic
251C23×C4C23×C1111yescharacteristic
252C22×C8—21no—
253C22×C8—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4D4×C1111yescharacteristic
262C2×C4⋊C4D4×C1111yescharacteristic
263C2×C4⋊C4D4×C1111yescharacteristic
264C2×C4⋊C4D4×C1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267#107—42no—
268#106—42no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8Q8×C1112yes—
272C22⋊C8Q8×C1112yes—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—42no—
283#95—42no—
284#95Q8×C1112yes—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11#159711yescharacteristic
290C2×C11#160611yescharacteristic
291C2×C11#161211yescharacteristic
292C2×C11#161511yescharacteristic
293C2×C11#205911yescharacteristic
294C2×C11#206111yescharacteristic
295C2×C11#206211yescharacteristic
296C24C2×D4×C1111yescharacteristic
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4C2×D4×C1111yescharacteristic
328C22×C4C2×D4×C1111yescharacteristic
329C22×C4C2×Q8×C1111yescharacteristic
330C22×C4C2×Q8×C1111yescharacteristic
331C22×C4C2×Q8×C1111yescharacteristic
332C22×C4C11×#4111yescharacteristic
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—81no—
348C4⋊C4—81no—
349C4⋊C4—81no—
350C4⋊C4—81no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C11#1057111yescharacteristic, direct product factor, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23C11×#12011yescharacteristic
361C23C11×C22⋊Q811yescharacteristic
362C23C11×C4⋊Q811yescharacteristic
363C23C11×#13511yescharacteristic
364C23C11×#13511yescharacteristic
365C23C11×AGL(1,ℤ/8)11yescharacteristic
366C23C11×#13711yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4C11×C22⋊Q811yescharacteristic
412C2×C4C11×C22⋊Q811yescharacteristic
413C2×C4C11×C4⋊Q811yescharacteristic
414C2×C4C11×C4⋊Q811yescharacteristic
415C8—42no—
416C8—42no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22C11×#39511yescharacteristic
430C22C11×#44911yescharacteristic
431C22C11×#45211yescharacteristic
432C22C11×#45411yescharacteristic
433C22C11×#45511yescharacteristic
434C22C11×B(4,𝔽2)11yescharacteristic
435C22C11×#45811yescharacteristic
436C22C11×#47811yescharacteristic
437C22C11×#47911yescharacteristic
438C22C11×#49911yescharacteristic
439C22C11×#50111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—82no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—82no—
449C4—81no—
450C4—81no—
451C4—81no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2C11×#159711yescharacteristic
457C2C11×#160611yescharacteristic
458C2C11×#161211yescharacteristic
459C2C11×#161511yescharacteristic
460C2C11×#205911yescharacteristic
461C2C11×#206111yescharacteristic
462C2C11×#206211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
65. #10571C11direct (N × H)
355. C11#10571direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26462
C11×#18532
C11×#18522
C11×#14422
C11×#12942
C11×#12802
#1057111