Finite Group Databasebeta

← C11×#10241 #14587434

Subgroups — C11×#10241 #14587434

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic, complemented
4C11×#1549C211yesmaximal, 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×C4×D4×C11C2211yescharacteristic
12C11×#498—21no—
13C11×#486—21no—
14C11×#481—22no—
15C11×#476—22no—
16C11×#463—22no—
17C11×#461—21no—
18C11×#459—21no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C11×#417—21no—
23C11×#393—22no—
24C11×#390—21no—
25C11×#382—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×#121—21no—
48C11×#121—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—24no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×#106—24no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C4⋊C8D412yes—
68C11×#103—22no—
69C11×#102—22no—
70C11×#102—24no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75C11×#95—24no—
76C11×#95D412yes—
77#10241C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—82no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C2×D4×C11SD1612yes—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—44no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C11×SD16—44no—
108C11×D8—44no—
109C11×M16—41no—
110C11×M16—41no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—84no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134#3227C2×C1111yescharacteristic, complemented
135#3036C2×C1111yescharacteristic
136#2563C2×C1111yescharacteristic, complemented
137#1549C2×C1111yescharacteristic, complemented
138#1502C2×C1111yescharacteristic, complemented
139#1478C2×C1111yescharacteristic, complemented
140#1303C2×C1111yescharacteristic, complemented
141C23×C11—22no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11#12011yescharacteristic
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—82no—
151Q8×C11—82no—
152D4×C11—22no—
153D4×C11—22no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—41no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—81no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—44no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11—82no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12711yescharacteristic
182C2×C4×C11C2×SD1611yescharacteristic
183C2×C4×C11#13511yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11#13711yescharacteristic
186C8×C11—42no—
187C8×C11—42no—
188C8×C11—81no—
189C2×AGL(1,ℤ/8)—21no—
190#532C22×C1111yescharacteristic
191C2×C4⋊Q8C22×C1111yescharacteristic
192C2×C4×D4C22×C1111yescharacteristic
193#498—21no—
194#486—21no—
195#481—22no—
196#476—22no—
197#463—22no—
198#461—21no—
199#459—21no—
200#431C22×C1111yescharacteristic
201#431C22×C1111yescharacteristic
202#423C22×C1111yescharacteristic
203#417—21no—
204#393—22no—
205#390—21no—
206#382—21no—
207#380—22no—
208C4×C4⋊C4C22×C1111yescharacteristic
209#332—22no—
210#327—22no—
211D4⋊C8—22no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—44no—
215C22×C11—42no—
216C22×C11—82no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#39211yescharacteristic
223C22×C11#44811yescharacteristic
224C22×C11#44911yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—82no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11—82no—
232C4×C11#45011yescharacteristic
233C4×C11#45211yescharacteristic
234C4×C11#45412yes—
235C4×C11#46511yescharacteristic
236C4×C11#46811yescharacteristic
237C2×#41—21no—
238C22×Q8—21no—
239C22×D4D4×C1111yescharacteristic
240C23×C4—21no—
241AGL(1,ℤ/8)—42no—
242AGL(1,ℤ/8)—42no—
243C2×SD16—22no—
244C2×D8—22no—
245C2×M16—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8D4×C1111yescharacteristic
251#127D4×C1111yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4D4×C1111yescharacteristic
264C2×C4⋊C4D4×C1112yes—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—24no—
267C2×C42—21no—
268C2×C42C23×C1111yescharacteristic
269#106—24no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8D4×C1112yes—
273C4⋊C8D4×C1112yes—
274#103—22no—
275#102—22no—
276#102—24no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C4×C8—21no—
280C4×C8—21no—
281#95—24no—
282#95D4×C1112yes—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—82no—
286C2×C11—161no—
287C2×C11#200011yescharacteristic
288C2×C11#200311yescharacteristic
289C2×C11#200811yescharacteristic
290C24—21no—
291#41—41no—
292#41—41no—
293#41—41no—
294#41—41no—
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—82no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4C11×SD1612yes—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—44no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4C2×D4×C1111yescharacteristic
317C22×C4C2×D4×C1111yescharacteristic
318C22×C4C2×D4×C1111yescharacteristic
319SD16—44no—
320D8—44no—
321M16—41no—
322M16—41no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—84no—
340C42—41no—
341C42—41no—
342C42C2×D4×C1111yescharacteristic
343C42C2×D4×C1111yescharacteristic
344C42C2×D4×C1111yescharacteristic
345C42C11×#4111yescharacteristic
346C11#1024111yescharacteristic, direct product factor, Sylow
347C23—22no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23C11×#12011yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—82no—
357Q8—82no—
358D4—22no—
359D4—22no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—42no—
364D4—41no—
365D4—81no—
366D4—81no—
367D4—81no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4C11×#12011yescharacteristic
383C2×C4C11×#12011yescharacteristic
384C2×C4C11×#12111yescharacteristic
385C2×C4C11×#12111yescharacteristic
386C2×C4C11×#12111yescharacteristic
387C2×C4C11×#12711yescharacteristic
388C2×C4C2×C11×SD1611yescharacteristic
389C2×C4C11×#13511yescharacteristic
390C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
391C2×C4C11×#13711yescharacteristic
392C8—42no—
393C8—42no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22—42no—
399C22—82no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C11×#39211yescharacteristic
406C22C11×#44811yescharacteristic
407C22C11×#44911yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—81no—
413C4—81no—
414C4—82no—
415C4C11×#45011yescharacteristic
416C4C11×#45211yescharacteristic
417C4C11×#45412yes—
418C4C11×#46511yescharacteristic
419C4C11×#46811yescharacteristic
420C2—21no—
421C2—21no—
422C2—82no—
423C2—161no—
424C2C11×#200011yescharacteristic
425C2C11×#200311yescharacteristic
426C2C11×#200811yescharacteristic
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×#3227C2semidirect
3. C11×#2563C2semidirect
4. C11×#1549C2semidirect
5. C11×#1502C2semidirect
6. C11×#1478C2semidirect
7. C11×#1303C2semidirect
77. #10241C11direct (N × H)
134. #3227C2×C11semidirect
136. #2563C2×C11semidirect
137. #1549C2×C11semidirect
138. #1502C2×C11semidirect
139. #1478C2×C11semidirect
140. #1303C2×C11semidirect
346. C11#10241direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C11×#30362
C11×#25632
C11×#15492
C11×#15022
C11×#14782
C11×#13032
#1024111