Finite Group Databasebeta

← C11×#32906 #14610099

Subgroups — C11×#32906 #14610099

Order 2816.

1436 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#462C212yesmaximal, complemented
3C2×C11×#451C212yesmaximal
4C11×#2857C211yesmaximal, characteristic
5C11×#1878C214yesmaximal, complemented
6C11×#1872C212yesmaximal
7C11×#1803C212yesmaximal, complemented
8C11×#1797C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C22×C11×Q16C2214yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11—28no—
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2212yes—
18C22×C11×C4⋊C4—21no—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11—21no—
21C22×C42×C11C2211yescharacteristic
22C11×#462—28no—
23C11×#451—28no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2214yes—
26C2×C11×#103C2214yes—
27C2×C11×C22⋊C8C2212yes—
28C11×#391C2212yes—
29C11×#389—21no—
30C11×#389—21no—
31C11×#384C2211yescharacteristic
32C11×#380—21no—
33C11×#380—21no—
34C11×#340C2214yes—
35C11×#336C2212yes—
36C22×Q8×C11—24no—
37C22×Q8×C11—24no—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11D414yes—
41C22×Q8×C11C2312yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C2×C11×Q16—28no—
49C2×C11×Q16—28no—
50C2×C11×Q16—28no—
51C22×C8×C11C2314yes—
52C11×C4⋊Q8—24no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—24no—
55C4×Q8×C11—28no—
56C4×Q8×C11—28no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11D418yes—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—28no—
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11—24no—
78C2×C42×C11D411yescharacteristic
79C2×C42×C11D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C11×C4⋊C8—24no—
83C11×#103—28no—
84C11×#103—28no—
85C11×C22⋊C8—24no—
86C11×#95—22no—
87C11×#95—22no—
88#32906C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—216no—
92C2×Q8×C11—24no—
93C2×Q8×C11—216no—
94C2×Q8×C11—24no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—24no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—24no—
102C2×Q8×C11C2×D414yes—
103C2×Q8×C11C2×D414yes—
104C2×Q8×C11#4114yes—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—41no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11Q1614yescomplemented
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C11×Q16—416no—
132C2×C8×C11—24no—
133C2×C8×C11—24no—
134C2×C8×C11—24no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—28no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4C2×D414yes—
147C11×C22⋊C4—44no—
148C42×C11—28no—
149C42×C11—28no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11C2×D414yes—
154C22×C4×Q8C2×C1111yescharacteristic
155C2×#462C2×C1112yescomplemented
156C2×#451C2×C1112yes—
157#2857C2×C1111yescharacteristic
158#1878C2×C1114yescomplemented
159#1872C2×C1112yes—
160#1803C2×C1112yescomplemented
161#1797C2×C1111yescharacteristic
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11#12112yes—
167C23×C11C2×Q1612yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170Q8×C11—216no—
171Q8×C11—24no—
172Q8×C11—24no—
173Q8×C11—24no—
174Q8×C11—44no—
175Q8×C11—44no—
176Q8×C11#12118yes—
177C2×C4×C11—216no—
178C2×C4×C11—21no—
179C2×C4×C11—24no—
180C2×C4×C11—21no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—28no—
190C2×C4×C11—21no—
191C2×C4×C11—24no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—44no—
195C2×C4×C11—48no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11#12012yes—
205C2×C4×C11#12012yes—
206C2×C4×C11#12112yes—
207C2×C4×C11C2×Q1612yes—
208C2×C4×C11C2×Q1612yes—
209C2×C4×C11#13712yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D412yes—
212C2×C4×C11C2×#4112yes—
213C2×C4×C11C2×#4111yescharacteristic
214C8×C11—44no—
215C23×Q8C22×C1111yescharacteristic
216C22×Q16C22×C1114yes—
217C2×C4⋊Q8C22×C1111yescharacteristic
218C2×C22⋊Q8C22×C1112yes—
219C2×C4×Q8—28no—
220C2×C4×Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8C22×C1112yes—
223C2×C4×Q8C22×C1112yes—
224C22×C4⋊C4—21no—
225C22×C4⋊C4C22×C1111yescharacteristic
226C22×C42—21no—
227C22×C42C22×C1111yescharacteristic
228#462—28no—
229#451—28no—
230C2×C4⋊C8C22×C1112yes—
231C2×#103C22×C1114yes—
232C2×#103C22×C1114yes—
233C2×C22⋊C8C22×C1112yes—
234#391C22×C1112yes—
235#389—21no—
236#389—21no—
237#384C22×C1111yescharacteristic
238#380—21no—
239#380—21no—
240#340C22×C1114yes—
241#336C22×C1112yes—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11#46214yescomplemented
249C22×C11C2×#12011yescharacteristic
250C22×C11C2×#12111yescharacteristic
251C22×C11#52511yescharacteristic
252C22×C11C22×Q1611yescharacteristic
253C22×C11C2×#13711yescharacteristic
254C22×C11C2×#13711yescharacteristic
255C22×C11#57511yescharacteristic
256C4×C11—28no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—41no—
261C4×C11—44no—
262C4×C11—82no—
263C4×C11—82no—
264C4×C11#45114yescomplemented
265C4×C11C2×#12112yes—
266C4×C11#52512yes—
267C22×Q8—24no—
268C22×Q8—24no—
269C22×Q8—21no—
270C22×Q8—22no—
271C22×Q8D4×C1114yes—
272C22×Q8C23×C1112yes—
273C22×Q8C23×C1112yes—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4D4×C1111yescharacteristic
277C23×C4D4×C1111yescharacteristic
278C23×C4C23×C1111yescharacteristic
279C2×Q16—28no—
280C2×Q16—28no—
281C2×Q16—28no—
282C22×C8C23×C1114yes—
283C4⋊Q8—24no—
284C22⋊Q8—24no—
285C22⋊Q8—24no—
286C4×Q8—28no—
287C4×Q8—28no—
288C4×Q8—24no—
289C4×Q8—24no—
290C4×Q8—24no—
291C4×Q8D4×C1118yes—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1112yes—
304C2×C22⋊C4—22no—
305C2×C42—28no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—24no—
309C2×C42D4×C1111yescharacteristic
310C2×C42D4×C1111yescharacteristic
311C2×C42C23×C1111yescharacteristic
312C2×C42C23×C1111yescharacteristic
313C4⋊C8—24no—
314#103—28no—
315#103—28no—
316C22⋊C8—24no—
317#95—22no—
318#95—22no—
319C2×C11—24no—
320C2×C11#284711yescharacteristic
321C2×C11C2×#45111yescharacteristic
322C2×C11#300711yescharacteristic
323C2×C11C2×#46211yescharacteristic
324C2×C11#303711yescharacteristic
325C2×C11#310411yescharacteristic
326C2×C11#311311yescharacteristic
327C24C2×D4×C1111yescharacteristic
328C2×Q8—24no—
329C2×Q8—216no—
330C2×Q8—24no—
331C2×Q8—216no—
332C2×Q8—24no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—24no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—24no—
340C2×Q8C2×D4×C1114yes—
341C2×Q8C2×D4×C1114yes—
342C2×Q8C11×#4114yes—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—41no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4C11×Q1614yescomplemented
361C22×C4C2×D4×C1111yescharacteristic
362C22×C4C2×D4×C1111yescharacteristic
363C22×C4C2×D4×C1111yescharacteristic
364C22×C4C2×D4×C1112yes—
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C11×#4112yes—
368C22×C4C24×C1111yescharacteristic
369Q16—416no—
370C2×C8—24no—
371C2×C8—24no—
372C2×C8—24no—
373C4⋊C4—28no—
374C4⋊C4—24no—
375C4⋊C4—28no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—44no—
383C4⋊C4—42no—
384C4⋊C4C2×D4×C1114yes—
385C22⋊C4—44no—
386C42—28no—
387C42—28no—
388C42—22no—
389C42—22no—
390C42—22no—
391C42C2×D4×C1114yes—
392C11#3290611yescharacteristic, direct product factor, Sylow
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23C11×#12112yes—
398C23C2×C11×Q1612yes—
399C23C11×#13712yes—
400C23C22×D4×C1111yescharacteristic
401Q8—216no—
402Q8—24no—
403Q8—24no—
404Q8—24no—
405Q8—44no—
406Q8—44no—
407Q8C11×#12118yes—
408C2×C4—216no—
409C2×C4—21no—
410C2×C4—24no—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—28no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—44no—
426C2×C4—48no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4C11×#12012yes—
436C2×C4C11×#12012yes—
437C2×C4C11×#12112yes—
438C2×C4C2×C11×Q1612yes—
439C2×C4C2×C11×Q1612yes—
440C2×C4C11×#13712yes—
441C2×C4C22×D4×C1111yescharacteristic
442C2×C4C22×D4×C1112yes—
443C2×C4C2×C11×#4112yes—
444C2×C4C2×C11×#4111yescharacteristic
445C8—44no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22C11×#46214yescomplemented
453C22C2×C11×#12011yescharacteristic
454C22C2×C11×#12111yescharacteristic
455C22C11×#52511yescharacteristic
456C22C22×C11×Q1611yescharacteristic
457C22C2×C11×#13711yescharacteristic
458C22C2×C11×#13711yescharacteristic
459C22C11×#57511yescharacteristic
460C4—22no—
461C4—22no—
462C4—28no—
463C4—22no—
464C4—41no—
465C4—44no—
466C4—82no—
467C4—82no—
468C4C11×#45114yescomplemented
469C4C2×C11×#12112yes—
470C4C11×#52512yes—
471C2—24no—
472C2C11×#284711yescharacteristic
473C2C2×C11×#45111yescharacteristic
474C2C11×#300711yescharacteristic
475C2C2×C11×#46211yescharacteristic
476C2C11×#303711yescharacteristic
477C2C11×#310411yescharacteristic
478C2C11×#311311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#462C2semidirect
5. C11×#1878C2semidirect
7. C11×#1803C2semidirect
88. #32906C11direct (N × H)
122. C22×C4×C11Q16semidirect
155. C2×#462C2×C11semidirect
158. #1878C2×C11semidirect
160. #1803C2×C11semidirect
248. C22×C11#462semidirect
264. C4×C11#451semidirect
360. C22×C4C11×Q16semidirect
392. C11#32906direct (N × H)
452. C22C11×#462semidirect
468. C4C11×#451semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C112
C2×C11×#4622
C2×C11×#4512
C11×#28572
C11×#18782
C11×#18722
C11×#18032
C11×#17972
#3290611