Finite Group Databasebeta

← C11×#10239 #14587432

Subgroups — C11×#10239 #14587432

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic, complemented
4C11×#1546C211yesmaximal, characteristic, complemented
5C11×#1502C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#124—21no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#500—21no—
14C11×#486—21no—
15C11×#480—22no—
16C11×#474—22no—
17C11×#463—22no—
18C11×#461—21no—
19C11×#459—21no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#417—21no—
24C11×#397—22no—
25C11×#391—21no—
26C11×#380—22no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#332—22no—
29C11×#327—22no—
30C11×D4⋊C8—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D411yescharacteristic
45C11×#127D411yescharacteristic
46C11×#124—21no—
47C11×#124—42no—
48C11×#124—42no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D412yes—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—21no—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C11×#107—24no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8D412yes—
70C11×#103—22no—
71C11×#102—22no—
72C11×#102—24no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77C11×#95—24no—
78C11×#95D412yes—
79#10239C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—21no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C2×D4×C11D812yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C11×SD16—44no—
113C11×D8—44no—
114C11×M16—41no—
115C11×M16—41no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—41no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C22⋊C4—48no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139#3226C2×C1111yescharacteristic, complemented
140#3036C2×C1111yescharacteristic
141#2547C2×C1111yescharacteristic, complemented
142#1546C2×C1111yescharacteristic, complemented
143#1502C2×C1111yescharacteristic, complemented
144#1478C2×C1111yescharacteristic, complemented
145#1303C2×C1111yescharacteristic, complemented
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11#12011yescharacteristic
153Q8×C11—41no—
154Q8×C11—41no—
155Q8×C11—81no—
156Q8×C11—81no—
157Q8×C11—81no—
158Q8×C11—81no—
159D4×C11—22no—
160D4×C11—22no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—42no—
165D4×C11—41no—
166D4×C11—81no—
167D4×C11—81no—
168D4×C11—81no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—82no—
181C2×C4×C11—82no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11#13511yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C8×C11—42no—
195C8×C11—42no—
196C8×C11—81no—
197C2×AGL(1,ℤ/8)—21no—
198#532C22×C1111yescharacteristic
199C2×C4⋊Q8C22×C1111yescharacteristic
200C2×#124—21no—
201C2×C4×D4C22×C1111yescharacteristic
202#500—21no—
203#486—21no—
204#480—22no—
205#474—22no—
206#463—22no—
207#461—21no—
208#459—21no—
209#431C22×C1111yescharacteristic
210#431C22×C1111yescharacteristic
211#423C22×C1111yescharacteristic
212#417—21no—
213#397—22no—
214#391—21no—
215#380—22no—
216C4×C4⋊C4C22×C1111yescharacteristic
217#332—22no—
218#327—22no—
219D4⋊C8—22no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—44no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#39211yescharacteristic
231C22×C11#44711yescharacteristic
232C22×C11#44911yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—82no—
237C4×C11—82no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11#44711yescharacteristic
241C4×C11#44911yescharacteristic
242C4×C11#45412yes—
243C4×C11#46611yescharacteristic
244C4×C11#46911yescharacteristic
245C2×#41—21no—
246C22×Q8—21no—
247C22×D4D4×C1111yescharacteristic
248C23×C4—21no—
249AGL(1,ℤ/8)—42no—
250AGL(1,ℤ/8)—42no—
251C2×SD16—22no—
252C2×D8—22no—
253C2×M16—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8D4×C1111yescharacteristic
259#127D4×C1111yescharacteristic
260#124—21no—
261#124—42no—
262#124—42no—
263#121—21no—
264#121—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C1111yescharacteristic
274C2×C4⋊C4D4×C1112yes—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—21no—
277C2×C42—21no—
278C2×C42C23×C1111yescharacteristic
279#107—24no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8D4×C1112yes—
283C4⋊C8D4×C1112yes—
284#103—22no—
285#102—22no—
286#102—24no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C4×C8—21no—
290C4×C8—21no—
291#95—24no—
292#95D4×C1112yes—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—82no—
296C2×C11—161no—
297C2×C11#199911yescharacteristic
298C2×C11#200311yescharacteristic
299C2×C11#200911yescharacteristic
300C24—21no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305C2×Q8—21no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4C11×D812yes—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—44no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C2×D4×C1111yescharacteristic
330C22×C4C2×D4×C1111yescharacteristic
331C22×C4C2×D4×C1111yescharacteristic
332SD16—44no—
333D8—44no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—42no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C22⋊C4—48no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42—41no—
354C42—41no—
355C42C2×D4×C1111yescharacteristic
356C42C2×D4×C1111yescharacteristic
357C42C2×D4×C1111yescharacteristic
358C42C11×#4111yescharacteristic
359C11#1023911yescharacteristic, direct product factor, Sylow
360C23—22no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23C11×#12011yescharacteristic
367Q8—41no—
368Q8—41no—
369Q8—81no—
370Q8—81no—
371Q8—81no—
372Q8—81no—
373D4—22no—
374D4—22no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—42no—
379D4—41no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C11×#12011yescharacteristic
399C2×C4C11×#12011yescharacteristic
400C2×C4C11×#12111yescharacteristic
401C2×C4C11×#12111yescharacteristic
402C2×C4C11×#12111yescharacteristic
403C2×C4C11×#12711yescharacteristic
404C2×C4C2×C11×D811yescharacteristic
405C2×C4C11×#13511yescharacteristic
406C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
407C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
408C8—42no—
409C8—42no—
410C8—81no—
411C22—21no—
412C22—21no—
413C22—44no—
414C22—42no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22C11×#39211yescharacteristic
422C22C11×#44711yescharacteristic
423C22C11×#44911yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—82no—
429C4—81no—
430C4—81no—
431C4C11×#44711yescharacteristic
432C4C11×#44911yescharacteristic
433C4C11×#45412yes—
434C4C11×#46611yescharacteristic
435C4C11×#46911yescharacteristic
436C2—21no—
437C2—21no—
438C2—82no—
439C2—161no—
440C2C11×#199911yescharacteristic
441C2C11×#200311yescharacteristic
442C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3036C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3226C2semidirect
3. C11×#2547C2semidirect
4. C11×#1546C2semidirect
5. C11×#1502C2semidirect
6. C11×#1478C2semidirect
7. C11×#1303C2semidirect
79. #10239C11direct (N × H)
139. #3226C2×C11semidirect
141. #2547C2×C11semidirect
142. #1546C2×C11semidirect
143. #1502C2×C11semidirect
144. #1478C2×C11semidirect
145. #1303C2×C11semidirect
359. C11#10239direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#30362
C11×#25472
C11×#15462
C11×#15022
C11×#14782
C11×#13032
#1023911