Finite Group Databasebeta

← C11×#23457 #14600650

Subgroups — C11×#23457 #14600650

Order 2816.

1202 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
1C2×C11×#544C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic
3C22×C11×#103C211yesmaximal, characteristic
4C11×#2310C211yesmaximal, characteristic
5C11×#2026C214yesmaximal, complemented
6C11×#2024C214yesmaximal, complemented
7C11×#1736C211yesmaximal, characteristic
8C11×#1735C211yesmaximal, characteristic
9C11×#1729C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C11×#544—24no—
14C11×#544—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×#125—21no—
18C2×C11×#125C2212yes—
19C2×C11×C22⋊Q8—22no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#419—24no—
25C2×C11×#103—24no—
26C2×C11×#103C2214yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C11×#391—21no—
30C11×#391—21no—
31C11×#391C2214yes—
32C11×#381—22no—
33C11×#340C2212yes—
34C11×#340C2212yes—
35C11×#340C2214yes—
36C11×#336C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11Q814yescomplemented
45C22×Q8×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C22×C8×C11—22no—
53C22×C8×C11—22no—
54C22×C8×C11—22no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×C4⋊Q8—28no—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—24no—
60C11×#125—28no—
61C11×#125—24no—
62C11×#125—24no—
63C11×C22⋊Q8—216no—
64C11×#117—22no—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117D414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D414yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2312yes—
88C11×#103—28no—
89C11×#103—24no—
90C11×#103—24no—
91C11×#95—24no—
92C11×#95—24no—
93#23457C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11C2×D411yescharacteristic
95C2×Q8×C11—28no—
96C2×Q8×C11—24no—
97C2×Q8×C11—22no—
98C2×Q8×C11—28no—
99C2×Q8×C11—28no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C2×Q8×C11—44no—
107C2×Q8×C11—44no—
108C2×Q8×C11—84no—
109C2×Q8×C11C2×Q814yes—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—82no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×Q812yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C11×M16—44no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—44no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4C2×D414yes—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—42no—
155C42×C11—24no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—42no—
159C2×#544C2×C1111yescharacteristic
160C2×#419C2×C1111yescharacteristic
161C22×#103C2×C1111yescharacteristic
162#2310C2×C1111yescharacteristic
163#2026C2×C1114yescomplemented
164#2024C2×C1114yescomplemented
165#1736C2×C1111yescharacteristic
166#1735C2×C1111yescharacteristic
167#1729C2×C1111yescharacteristic
168C23×C11—22no—
169C23×C11—22no—
170C23×C11#12012yes—
171C23×C11C22⋊Q812yes—
172C23×C11#12412yes—
173C23×C11C22×D411yescharacteristic
174Q8×C11—24no—
175Q8×C11—24no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—48no—
179Q8×C11—88no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—48no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—84no—
198C2×C4×C11#12012yes—
199C2×C4×C11C22⋊Q814yes—
200C2×C4×C11C22⋊Q814yes—
201C2×C4×C11C22⋊Q812yes—
202C2×C4×C11#12414yes—
203C2×C4×C11#12414yes—
204C2×C4×C11#12412yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C8×C11—42no—
212C8×C11—42no—
213C23×Q8C22×C1111yescharacteristic
214C22×M16C22×C1111yescharacteristic
215C23×C8C22×C1111yescharacteristic
216#544—24no—
217#544—24no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C22×C1112yes—
220C2×#125—21no—
221C2×#125C22×C1112yes—
222C2×C22⋊Q8—22no—
223C2×#117C22×C1111yescharacteristic
224C2×#117C22×C1111yescharacteristic
225C2×#117C22×C1111yescharacteristic
226C22×C4⋊C4C22×C1111yescharacteristic
227#419—24no—
228C2×#103—24no—
229C2×#103C22×C1114yes—
230C2×#103C22×C1112yes—
231C2×#103C22×C1112yes—
232#391—21no—
233#391—21no—
234#391C22×C1114yes—
235#381—22no—
236#340C22×C1112yes—
237#340C22×C1112yes—
238#340C22×C1114yes—
239#336C22×C1114yes—
240C22×C11—24no—
241C22×C11—24no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11#39314yes—
245C22×C11C2×#12011yescharacteristic
246C22×C11C2×C22⋊Q811yescharacteristic
247C22×C11C2×#12411yescharacteristic
248C22×C11#57712yes—
249C22×C11#57812yes—
250C4×C11—44no—
251C4×C11—42no—
252C4×C11—44no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11#39314yes—
258C4×C11C2×C22⋊Q811yescharacteristic
259C4×C11C2×C22⋊Q811yescharacteristic
260C4×C11C2×#12411yescharacteristic
261C4×C11C2×#12411yescharacteristic
262C22×Q8—21no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8Q8×C1114yescomplemented
270C22×Q8C23×C1112yes—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4C23×C1111yescharacteristic
274C2×M16—22no—
275C2×M16—22no—
276C2×M16—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8C23×C1112yes—
281C22×C8C23×C1112yes—
282C4⋊Q8—28no—
283C4⋊Q8—24no—
284C4⋊Q8—24no—
285#125—28no—
286#125—24no—
287#125—24no—
288C22⋊Q8—216no—
289#117—22no—
290#117—22no—
291#117—22no—
292#117—22no—
293#117—22no—
294#117D4×C1114yes—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4D4×C1111yescharacteristic
301C2×C4⋊C4D4×C1111yescharacteristic
302C2×C4⋊C4D4×C1114yes—
303C2×C4⋊C4C23×C1112yes—
304C2×C4⋊C4C23×C1112yes—
305C2×C4⋊C4C23×C1111yescharacteristic
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4D4×C1112yes—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42C23×C1112yes—
313#103—28no—
314#103—24no—
315#103—24no—
316#95—24no—
317#95—24no—
318C2×C11—24no—
319C2×C11C2×#39311yescharacteristic
320C2×C11#300911yescharacteristic
321C2×C11#301111yescharacteristic
322C2×C11#308212yes—
323C2×C11#313712yes—
324C24C2×D4×C1111yescharacteristic
325C2×Q8—28no—
326C2×Q8—24no—
327C2×Q8—22no—
328C2×Q8—28no—
329C2×Q8—28no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×Q8—44no—
337C2×Q8—44no—
338C2×Q8—84no—
339C2×Q8C2×Q8×C1114yes—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—82no—
350C22×C4C2×D4×C1112yes—
351C22×C4C2×D4×C1112yes—
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1112yes—
354C22×C4C2×D4×C1112yes—
355C22×C4C2×Q8×C1112yes—
356C22×C4C11×#4112yes—
357C22×C4C11×#4112yes—
358C22×C4C11×#4112yes—
359C22×C4C24×C1111yescharacteristic
360M16—44no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—44no—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—28no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4C2×D4×C1114yes—
380C4⋊C4C2×D4×C1112yes—
381C4⋊C4C2×D4×C1112yes—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—42no—
385C42—24no—
386C42—22no—
387C42—22no—
388C42—42no—
389C11#2345711yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23—22no—
392C23C11×#12012yes—
393C23C11×C22⋊Q812yes—
394C23C11×#12412yes—
395C23C22×D4×C1111yescharacteristic
396Q8—24no—
397Q8—24no—
398Q8—42no—
399Q8—42no—
400Q8—48no—
401Q8—88no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—48no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—84no—
420C2×C4C11×#12012yes—
421C2×C4C11×C22⋊Q814yes—
422C2×C4C11×C22⋊Q814yes—
423C2×C4C11×C22⋊Q812yes—
424C2×C4C11×#12414yes—
425C2×C4C11×#12414yes—
426C2×C4C11×#12412yes—
427C2×C4C22×D4×C1111yescharacteristic
428C2×C4C22×D4×C1111yescharacteristic
429C2×C4C22×Q8×C1111yescharacteristic
430C2×C4C2×C11×#4111yescharacteristic
431C2×C4C2×C11×#4111yescharacteristic
432C2×C4C2×C11×#4111yescharacteristic
433C8—42no—
434C8—42no—
435C22—22no—
436C22—22no—
437C22—24no—
438C22—24no—
439C22C11×#39314yes—
440C22C2×C11×#12011yescharacteristic
441C22C2×C11×C22⋊Q811yescharacteristic
442C22C2×C11×#12411yescharacteristic
443C22C11×#57712yes—
444C22C11×#57812yes—
445C4—44no—
446C4—42no—
447C4—44no—
448C4—42no—
449C4—42no—
450C4—42no—
451C4—82no—
452C4C11×#39314yes—
453C4C2×C11×C22⋊Q811yescharacteristic
454C4C2×C11×C22⋊Q811yescharacteristic
455C4C2×C11×#12411yescharacteristic
456C4C2×C11×#12411yescharacteristic
457C2—24no—
458C2C2×C11×#39311yescharacteristic
459C2C11×#300911yescharacteristic
460C2C11×#301111yescharacteristic
461C2C11×#308212yes—
462C2C11×#313712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2026C2semidirect
6. C11×#2024C2semidirect
44. C22×Q8×C11Q8semidirect
93. #23457C11direct (N × H)
163. #2026C2×C11semidirect
164. #2024C2×C11semidirect
269. C22×Q8Q8×C11semidirect
389. C11#23457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#4192
C22×C11×#1032
C11×#23102
C11×#20262
C11×#20242
C11×#17362
C11×#17352
C11×#17292
#2345711