Finite Group Databasebeta

← C11×#10242 #14587435

Subgroups — C11×#10242 #14587435

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3205C211yesmaximal, characteristic
2C11×#3037C211yesmaximal, characteristic, complemented
3C11×#2548C211yesmaximal, characteristic, complemented
4C11×#1545C211yesmaximal, characteristic, complemented
5C11×#1502C211yesmaximal, characteristic, complemented
6C11×#1479C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—21no—
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#493—21no—
14C11×#486—21no—
15C11×#464—22no—
16C11×#462—21no—
17C11×#460—21no—
18C11×#459—22no—
19C11×#447—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#417—21no—
24C11×#394—22no—
25C11×#390—22no—
26C11×#390—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#331—22no—
29C11×#327—22no—
30C11×Q8⋊C8—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11D412yes—
36C11×#137—42no—
37C11×#137—42no—
38C2×C11×Q16—22no—
39C2×C11×SD16—22no—
40C2×C11×D8—24no—
41C2×C11×M16—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127D411yescharacteristic
48C11×#124—21no—
49C11×#124—42no—
50C11×#124—42no—
51C11×#121—21no—
52C11×#121—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×C4⋊C8D412yes—
71C11×#103—22no—
72C11×#102—22no—
73C11×#102—24no—
74C11×C22⋊C8—21no—
75C11×C22⋊C8—21no—
76C4×C8×C11—21no—
77C4×C8×C11—21no—
78C11×#95D412yes—
79#10242C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—22no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11D812yescomplemented
92C2×D4×C11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—44no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—82no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—41no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C11×Q16—44no—
116C11×SD16—44no—
117C11×D8—84no—
118C11×M16—41no—
119C11×M16—41no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—41no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—48no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—84no—
134C42×C11—41no—
135C42×C11—41no—
136C42×C11—41no—
137C42×C11—41no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142#3205C2×C1111yescharacteristic
143#3037C2×C1111yescharacteristic, complemented
144#2548C2×C1111yescharacteristic, complemented
145#1545C2×C1111yescharacteristic, complemented
146#1502C2×C1111yescharacteristic, complemented
147#1479C2×C1111yescharacteristic, complemented
148#1303C2×C1111yescharacteristic, complemented
149C23×C11—44no—
150C23×C11—44no—
151C23×C11—41no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11#12011yescharacteristic
156Q8×C11—22no—
157Q8×C11—22no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—42no—
165D4×C11—44no—
166D4×C11—81no—
167D4×C11—82no—
168D4×C11—82no—
169D4×C11—82no—
170D4×C11—81no—
171D4×C11—81no—
172D4×C11—81no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12711yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11#13511yescharacteristic
197C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
199C8×C11—42no—
200C8×C11—42no—
201C8×C11—81no—
202C2×#137—21no—
203#532C22×C1111yescharacteristic
204C2×#127C22×C1111yescharacteristic
205C2×#124—21no—
206C2×C4×Q8C22×C1111yescharacteristic
207#493—21no—
208#486—21no—
209#464—22no—
210#462—21no—
211#460—21no—
212#459—22no—
213#447—22no—
214#431C22×C1111yescharacteristic
215#431C22×C1111yescharacteristic
216#423C22×C1111yescharacteristic
217#417—21no—
218#394—22no—
219#390—22no—
220#390—21no—
221C4×C4⋊C4C22×C1111yescharacteristic
222#331—22no—
223#327—22no—
224Q8⋊C8—22no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—84no—
228C22×C11—84no—
229C22×C11—81no—
230C22×C11—82no—
231C22×C11—82no—
232C22×C11—81no—
233C22×C11—82no—
234C22×C11—81no—
235C22×C11#39211yescharacteristic
236C22×C11#44711yescharacteristic
237C22×C11#44911yescharacteristic
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11#44711yescharacteristic
246C4×C11#44911yescharacteristic
247C4×C11#45512yes—
248C4×C11#46611yescharacteristic
249C4×C11#46911yescharacteristic
250C2×#41—21no—
251C22×Q8D4×C1111yescharacteristic
252C22×D4—21no—
253C22×D4—21no—
254C22×D4D4×C1112yes—
255#137—42no—
256#137—42no—
257C2×Q16—22no—
258C2×SD16—22no—
259C2×D8—24no—
260C2×M16—21no—
261C4⋊Q8D4×C1111yescharacteristic
262#127—21no—
263#127—21no—
264#127—21no—
265#127—21no—
266#127D4×C1111yescharacteristic
267#124—21no—
268#124—42no—
269#124—42no—
270#121—21no—
271#121—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—21no—
277C4×D4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4D4×C1111yescharacteristic
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42C23×C1111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8D4×C1112yes—
289C4⋊C8D4×C1112yes—
290#103—22no—
291#102—22no—
292#102—24no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C4×C8—21no—
296C4×C8—21no—
297#95D4×C1112yes—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—161no—
301C2×C11—162no—
302C2×C11#199911yescharacteristic
303C2×C11#200411yescharacteristic
304C2×C11#200811yescharacteristic
305C24—22no—
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8C11×D812yescomplemented
317C2×D4—21no—
318C2×D4—22no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—22no—
322C2×D4—44no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—82no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—41no—
337C22×C4C2×D4×C1111yescharacteristic
338C22×C4C2×D4×C1111yescharacteristic
339C22×C4C2×D4×C1111yescharacteristic
340Q16—44no—
341SD16—44no—
342D8—84no—
343M16—41no—
344M16—41no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—41no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—42no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C22⋊C4—48no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—84no—
359C42—41no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42C2×D4×C1111yescharacteristic
364C42C2×D4×C1111yescharacteristic
365C42C2×D4×C1111yescharacteristic
366C42C11×#4111yescharacteristic
367C11#1024211yescharacteristic, direct product factor, Sylow
368C23—44no—
369C23—44no—
370C23—41no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23C11×#12011yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—41no—
380Q8—41no—
381D4—41no—
382D4—41no—
383D4—42no—
384D4—44no—
385D4—81no—
386D4—82no—
387D4—82no—
388D4—82no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—81no—
393D4—81no—
394D4—81no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C11×#12011yescharacteristic
409C2×C4C11×#12011yescharacteristic
410C2×C4C11×#12111yescharacteristic
411C2×C4C11×#12111yescharacteristic
412C2×C4C11×#12111yescharacteristic
413C2×C4C11×#12711yescharacteristic
414C2×C4C2×C11×D811yescharacteristic
415C2×C4C11×#13511yescharacteristic
416C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
417C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
418C8—42no—
419C8—42no—
420C8—81no—
421C22—21no—
422C22—21no—
423C22—84no—
424C22—84no—
425C22—81no—
426C22—82no—
427C22—82no—
428C22—81no—
429C22—82no—
430C22—81no—
431C22C11×#39211yescharacteristic
432C22C11×#44711yescharacteristic
433C22C11×#44911yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—82no—
439C4—81no—
440C4—81no—
441C4C11×#44711yescharacteristic
442C4C11×#44911yescharacteristic
443C4C11×#45512yes—
444C4C11×#46611yescharacteristic
445C4C11×#46911yescharacteristic
446C2—21no—
447C2—21no—
448C2—162no—
449C2—161no—
450C2C11×#199911yescharacteristic
451C2C11×#200411yescharacteristic
452C2C11×#200811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3205C2
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
2. C11×#3037C2semidirect
3. C11×#2548C2semidirect
4. C11×#1545C2semidirect
5. C11×#1502C2semidirect
6. C11×#1479C2semidirect
7. C11×#1303C2semidirect
79. #10242C11direct (N × H)
91. C2×Q8×C11D8semidirect
143. #3037C2×C11semidirect
144. #2548C2×C11semidirect
145. #1545C2×C11semidirect
146. #1502C2×C11semidirect
147. #1479C2×C11semidirect
148. #1303C2×C11semidirect
316. C2×Q8C11×D8semidirect
367. C11#10242direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#30372
C11×#25482
C11×#15452
C11×#15022
C11×#14792
C11×#13032
#1024211