Finite Group Databasebeta

← C11×#10473 #14587666

Subgroups — C11×#10473 #14587666

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C11×#1957C211yesmaximal, characteristic, complemented
3C11×#1954C211yesmaximal, characteristic, complemented
4C11×#1802C211yesmaximal, characteristic, complemented
5C2×C11×#334C211yesmaximal, characteristic, complemented
6C2×C11×#331C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#459—22no—
12C11×#459—22no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102—21no—
17C2×C11×#102—21no—
18C2×C11×#102—21no—
19C2×C11×#102—21no—
20C2×C11×C22⋊C8—21no—
21C2×C11×C22⋊C8—21no—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C11×#340—21no—
25C11×#334—22no—
26C11×#331—22no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C2×C11×D8—24no—
33C2×C11×D8—42no—
34C2×C11×D8—42no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127D412yes—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×#102—24no—
61C11×#102—42no—
62C11×#102—42no—
63C11×#102—42no—
64C11×C22⋊C8—42no—
65C11×C22⋊C8—42no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68#10473C1111yesmaximal, characteristic, direct product factor, Sylow
69C24×C11—21no—
70C24×C11—41no—
71C2×D4×C11—21no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—81no—
91C2×D4×C11—81no—
92C2×D4×C11SD1612yes—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C11×D8—48no—
105C2×C8×C11—22no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11D812yescomplemented
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—81no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11#4111yescharacteristic
133C2×#459C2×C1111yescharacteristic
134#1957C2×C1111yescharacteristic, complemented
135#1954C2×C1111yescharacteristic, complemented
136#1802C2×C1111yescharacteristic, complemented
137C2×#334C2×C1111yescharacteristic, complemented
138C2×#331C2×C1111yescharacteristic, complemented
139#1296C2×C1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11#12111yescharacteristic
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—41no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—41no—
163D4×C11—82no—
164D4×C11—82no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168D4×C11—81no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12311yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C2×C4×C11#12411yescharacteristic
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11C2×SD1611yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11#13511yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C8×C11—22no—
196C8×C11—42no—
197C8×C11—41no—
198C8×C11—81no—
199C8×C11—81no—
200C22×D8—21no—
201C2×#127C22×C1111yescharacteristic
202C2×C4×D4C22×C1111yescharacteristic
203#459—22no—
204#459—22no—
205C2×C4⋊C8C22×C1111yescharacteristic
206C2×C4⋊C8C22×C1111yescharacteristic
207C2×C4⋊C8C22×C1111yescharacteristic
208C2×#102—21no—
209C2×#102—21no—
210C2×#102—21no—
211C2×#102—21no—
212C2×C22⋊C8—21no—
213C2×C22⋊C8—21no—
214C2×C4×C8C22×C1111yescharacteristic
215#384C22×C1111yescharacteristic
216#340—21no—
217#334—22no—
218#331—22no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—161no—
230C22×C11—161no—
231C22×C11—161no—
232C22×C11—161no—
233C22×C11#39411yescharacteristic
234C22×C11#45911yescharacteristic
235C22×C11#46311yescharacteristic
236C22×C11#46511yescharacteristic
237C22×C11#46911yescharacteristic
238C22×C11#47111yescharacteristic
239C22×C11#47211yescharacteristic
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—81no—
243C4×C11—161no—
244C4×C11#44911yescharacteristic
245C4×C11#45011yescharacteristic
246C4×C11#45911yescharacteristic
247C4×C11#46311yescharacteristic
248C4×C11#46611yescharacteristic
249C4×C11#46911yescharacteristic
250C4×C11#48111yescharacteristic
251C4×C11#48211yescharacteristic
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4D4×C1111yescharacteristic
256C23×C4—21no—
257C2×D8—24no—
258C2×D8—42no—
259C2×D8—42no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8D4×C1111yescharacteristic
264C22×C8D4×C1111yescharacteristic
265#127—21no—
266#127—21no—
267#127—21no—
268#127D4×C1112yes—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4D4×C1111yescharacteristic
277C2×C22⋊C4—21no—
278C2×C42C23×C1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8D4×C1112yes—
285#102—24no—
286#102—42no—
287#102—42no—
288#102—42no—
289C22⋊C8—42no—
290C22⋊C8—42no—
291C4×C8—21no—
292C4×C8—21no—
293C2×C11—82no—
294C2×C11—162no—
295C2×C11#166511yescharacteristic
296C2×C11#167711yescharacteristic
297C2×C11#168711yescharacteristic
298C2×C11#170111yescharacteristic
299C2×C11#203411yescharacteristic
300C2×C11#205111yescharacteristic
301C2×C11#205411yescharacteristic
302C24—21no—
303C24—41no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—81no—
324C2×D4—81no—
325C2×D4C11×SD1612yes—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C11×#4111yescharacteristic
337D8—48no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8C11×D812yescomplemented
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—81no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C42C2×D4×C1111yescharacteristic
363C42C2×D4×C1111yescharacteristic
364C42C11×#4111yescharacteristic
365C42C11×#4111yescharacteristic
366C11#1047311yescharacteristic, direct product factor, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23C11×#12111yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—41no—
390D4—82no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C11×#12011yescharacteristic
409C2×C4C11×#12111yescharacteristic
410C2×C4C11×#12111yescharacteristic
411C2×C4C11×#12311yescharacteristic
412C2×C4C11×#12311yescharacteristic
413C2×C4C11×#12411yescharacteristic
414C2×C4C2×C11×D811yescharacteristic
415C2×C4C2×C11×SD1611yescharacteristic
416C2×C4C11×#13511yescharacteristic
417C2×C4C11×#13511yescharacteristic
418C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
419C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
420C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
421C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
422C8—22no—
423C8—42no—
424C8—41no—
425C8—81no—
426C8—81no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22C11×#39411yescharacteristic
442C22C11×#45911yescharacteristic
443C22C11×#46311yescharacteristic
444C22C11×#46511yescharacteristic
445C22C11×#46911yescharacteristic
446C22C11×#47111yescharacteristic
447C22C11×#47211yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4C11×#44911yescharacteristic
453C4C11×#45011yescharacteristic
454C4C11×#45911yescharacteristic
455C4C11×#46311yescharacteristic
456C4C11×#46611yescharacteristic
457C4C11×#46911yescharacteristic
458C4C11×#48111yescharacteristic
459C4C11×#48211yescharacteristic
460C2—82no—
461C2—162no—
462C2C11×#166511yescharacteristic
463C2C11×#167711yescharacteristic
464C2C11×#168711yescharacteristic
465C2C11×#170111yescharacteristic
466C2C11×#203411yescharacteristic
467C2C11×#205111yescharacteristic
468C2C11×#205411yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1957C2semidirect
3. C11×#1954C2semidirect
4. C11×#1802C2semidirect
5. C2×C11×#334C2semidirect
6. C2×C11×#331C2semidirect
7. C11×#1296C2semidirect
68. #10473C11direct (N × H)
119. C2×C8×C11D8semidirect
134. #1957C2×C11semidirect
135. #1954C2×C11semidirect
136. #1802C2×C11semidirect
137. C2×#334C2×C11semidirect
138. C2×#331C2×C11semidirect
139. #1296C2×C11semidirect
352. C2×C8C11×D8semidirect
366. C11#10473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C11×#19572
C11×#19542
C11×#18022
C2×C11×#3342
C2×C11×#3312
C11×#12962
#1047311