Finite Group Databasebeta

← C11×#32957 #14610150

Subgroups — C11×#32957 #14610150

Order 2816.

1332 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#477C212yesmaximal, complemented
3C11×#2857C211yesmaximal, characteristic
4C11×#1863C214yesmaximal, complemented
5C11×#1852C212yesmaximal
6C11×#1803C212yesmaximal, complemented
7C11×#1797C211yesmaximal, characteristic
8C11×#1787C212yesmaximal
9C23×Q8×C11C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C22⋊Q8—21no—
12C2×C4×Q8×C11—28no—
13C2×C4×Q8×C11—21no—
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11C2212yes—
16C2×C4×Q8×C11C2212yes—
17C22×C11×C4⋊C4—21no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11—21no—
20C22×C42×C11C2211yescharacteristic
21C11×#477—28no—
22C2×C11×#107C2214yes—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#103C2214yes—
25C2×C11×#103C2214yes—
26C2×C11×C22⋊C8C2212yes—
27C11×#391—21no—
28C11×#389—21no—
29C11×#389C2212yes—
30C11×#384C2211yescharacteristic
31C11×#380—21no—
32C11×#380C2212yes—
33C11×#340C2214yes—
34C11×#336C2212yes—
35C22×Q8×C11—24no—
36C22×Q8×C11—24no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11Q814yescomplemented
41C22×Q8×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C8×C11C2314yes—
48C11×C4⋊Q8—24no—
49C11×C22⋊Q8—44no—
50C4×Q8×C11—28no—
51C4×Q8×C11—28no—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11D418yes—
56C2×C11×C4⋊C4—28no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—28no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11—24no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#107—28no—
78C11×C4⋊C8—24no—
79C11×#103—28no—
80C11×#103—28no—
81C11×C22⋊C8—24no—
82C11×#95—22no—
83C11×#95—22no—
84#32957C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11C2×D411yescharacteristic
86C2×Q8×C11—24no—
87C2×Q8×C11—216no—
88C2×Q8×C11—24no—
89C2×Q8×C11—216no—
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11C2×D414yes—
98C2×Q8×C11C2×Q814yes—
99C2×Q8×C11#4114yes—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—41no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11Q1614yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×Q812yes—
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C2×C8×C11—24no—
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4C2×D414yes—
140C11×C22⋊C4—44no—
141C42×C11—28no—
142C42×C11—28no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11C2×D414yes—
147C22×C4×Q8C2×C1111yescharacteristic
148C2×#477C2×C1112yescomplemented
149#2857C2×C1111yescharacteristic
150#1863C2×C1114yescomplemented
151#1852C2×C1112yes—
152#1803C2×C1112yescomplemented
153#1797C2×C1111yescharacteristic
154#1787C2×C1112yes—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11C22⋊Q812yes—
160C23×C11C2×Q1612yes—
161C23×C11AGL(1,ℤ/8)12yes—
162C23×C11C22×D411yescharacteristic
163Q8×C11—216no—
164Q8×C11—24no—
165Q8×C11—24no—
166Q8×C11—24no—
167Q8×C11—84no—
168Q8×C11C22⋊Q818yescomplemented
169C2×C4×C11—216no—
170C2×C4×C11—21no—
171C2×C4×C11—24no—
172C2×C4×C11—21no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—28no—
182C2×C4×C11—21no—
183C2×C4×C11—24no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—44no—
187C2×C4×C11—48no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11#12012yes—
197C2×C4×C11#12012yes—
198C2×C4×C11C22⋊Q812yes—
199C2×C4×C11C2×Q1612yes—
200C2×C4×C11C2×Q1612yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4112yes—
205C2×C4×C11C2×#4111yescharacteristic
206C8×C11—44no—
207C23×Q8C22×C1111yescharacteristic
208C2×C4⋊Q8C22×C1111yescharacteristic
209C2×C22⋊Q8—21no—
210C2×C4×Q8—28no—
211C2×C4×Q8—21no—
212C2×C4×Q8—21no—
213C2×C4×Q8C22×C1112yes—
214C2×C4×Q8C22×C1112yes—
215C22×C4⋊C4—21no—
216C22×C4⋊C4C22×C1111yescharacteristic
217C22×C42—21no—
218C22×C42C22×C1111yescharacteristic
219#477—28no—
220C2×#107C22×C1114yes—
221C2×C4⋊C8C22×C1112yes—
222C2×#103C22×C1114yes—
223C2×#103C22×C1114yes—
224C2×C22⋊C8C22×C1112yes—
225#391—21no—
226#389—21no—
227#389C22×C1112yes—
228#384C22×C1111yescharacteristic
229#380—21no—
230#380C22×C1112yes—
231#340C22×C1114yes—
232#336C22×C1112yes—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11#47714yescomplemented
240C22×C11C2×#12011yescharacteristic
241C22×C11C2×C22⋊Q811yescharacteristic
242C22×C11#52511yescharacteristic
243C22×C11C22×Q1611yescharacteristic
244C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C22×C11C2×#13711yescharacteristic
246C22×C11#57511yescharacteristic
247C4×C11—28no—
248C4×C11—22no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—41no—
252C4×C11—44no—
253C4×C11—82no—
254C4×C11—82no—
255C4×C11#45114yes—
256C4×C11C2×C22⋊Q812yes—
257C4×C11#52512yes—
258C22×Q8—24no—
259C22×Q8—24no—
260C22×Q8—21no—
261C22×Q8—21no—
262C22×Q8—22no—
263C22×Q8Q8×C1114yescomplemented
264C22×Q8C23×C1112yes—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4D4×C1111yescharacteristic
268C23×C4D4×C1111yescharacteristic
269C23×C4C23×C1111yescharacteristic
270C22×C8C23×C1114yes—
271C4⋊Q8—24no—
272C22⋊Q8—44no—
273C4×Q8—28no—
274C4×Q8—28no—
275C4×Q8—24no—
276C4×Q8—24no—
277C4×Q8—24no—
278C4×Q8D4×C1118yes—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C22⋊C4—22no—
292C2×C42—28no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—24no—
296C2×C42D4×C1111yescharacteristic
297C2×C42D4×C1111yescharacteristic
298C2×C42C23×C1111yescharacteristic
299C2×C42C23×C1111yescharacteristic
300#107—28no—
301C4⋊C8—24no—
302#103—28no—
303#103—28no—
304C22⋊C8—24no—
305#95—22no—
306#95—22no—
307C2×C11—24no—
308C2×C11#284811yescharacteristic
309C2×C11C2×#45111yescharacteristic
310C2×C11#300611yescharacteristic
311C2×C11C2×#47711yescharacteristic
312C2×C11#307811yescharacteristic
313C2×C11#310411yescharacteristic
314C2×C11#311211yescharacteristic
315C24C2×D4×C1111yescharacteristic
316C2×Q8—24no—
317C2×Q8—216no—
318C2×Q8—24no—
319C2×Q8—216no—
320C2×Q8—24no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8C2×D4×C1114yes—
328C2×Q8C2×Q8×C1114yes—
329C2×Q8C11×#4114yes—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—41no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4C11×Q1614yes—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×Q8×C1112yes—
354C22×C4C11×#4112yes—
355C22×C4C24×C1111yescharacteristic
356C2×C8—24no—
357C2×C8—24no—
358C2×C8—24no—
359C4⋊C4—28no—
360C4⋊C4—24no—
361C4⋊C4—28no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—42no—
366C4⋊C4—44no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4C2×D4×C1114yes—
370C22⋊C4—44no—
371C42—28no—
372C42—28no—
373C42—22no—
374C42—22no—
375C42—22no—
376C42C2×D4×C1114yes—
377C11#3295711yescharacteristic, direct product factor, Sylow
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23C11×C22⋊Q812yes—
383C23C2×C11×Q1612yes—
384C23C11×AGL(1,ℤ/8)12yes—
385C23C22×D4×C1111yescharacteristic
386Q8—216no—
387Q8—24no—
388Q8—24no—
389Q8—24no—
390Q8—84no—
391Q8C11×C22⋊Q818yescomplemented
392C2×C4—216no—
393C2×C4—21no—
394C2×C4—24no—
395C2×C4—21no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—44no—
410C2×C4—48no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4C11×#12012yes—
420C2×C4C11×#12012yes—
421C2×C4C11×C22⋊Q812yes—
422C2×C4C2×C11×Q1612yes—
423C2×C4C2×C11×Q1612yes—
424C2×C4C11×#13712yes—
425C2×C4C22×D4×C1112yes—
426C2×C4C22×Q8×C1111yescharacteristic
427C2×C4C2×C11×#4112yes—
428C2×C4C2×C11×#4111yescharacteristic
429C8—44no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22C11×#47714yescomplemented
437C22C2×C11×#12011yescharacteristic
438C22C2×C11×C22⋊Q811yescharacteristic
439C22C11×#52511yescharacteristic
440C22C22×C11×Q1611yescharacteristic
441C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
442C22C2×C11×#13711yescharacteristic
443C22C11×#57511yescharacteristic
444C4—22no—
445C4—22no—
446C4—28no—
447C4—22no—
448C4—41no—
449C4—44no—
450C4—82no—
451C4—82no—
452C4C11×#45114yes—
453C4C2×C11×C22⋊Q812yes—
454C4C11×#52512yes—
455C2—24no—
456C2C11×#284811yescharacteristic
457C2C2×C11×#45111yescharacteristic
458C2C11×#300611yescharacteristic
459C2C2×C11×#47711yescharacteristic
460C2C11×#307811yescharacteristic
461C2C11×#310411yescharacteristic
462C2C11×#311211yescharacteristic
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×#477C2semidirect
4. C11×#1863C2semidirect
6. C11×#1803C2semidirect
40. C22×Q8×C11Q8semidirect
84. #32957C11direct (N × H)
148. C2×#477C2×C11semidirect
150. #1863C2×C11semidirect
152. #1803C2×C11semidirect
168. Q8×C11C22⋊Q8semidirect
239. C22×C11#477semidirect
263. C22×Q8Q8×C11semidirect
377. C11#32957direct (N × H)
391. Q8C11×C22⋊Q8semidirect
436. C22C11×#477semidirect

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×#4772
C11×#28572
C11×#18632
C11×#18522
C11×#18032
C11×#17972
C11×#17872
#3295711