Finite Group Databasebeta

← C11×#23821 #14601014

Subgroups — C11×#23821 #14601014

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×C11×#124C211yesmaximal, characteristic
3C11×#2101C212yesmaximal, complemented
4C11×#2072C211yesmaximal, characteristic, complemented
5C11×#2071C211yesmaximal, characteristic
6C11×#2042C212yesmaximal
7C11×#2024C211yesmaximal, characteristic, complemented
8C11×#2023C211yesmaximal, characteristic
9C11×#1763C212yesmaximal, complemented
10C11×#1762C212yesmaximal
11C11×#1745C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#124C2211yescharacteristic
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#103C2212yes—
18C2×C11×#103C2212yes—
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C11×#97C2212yes—
22C11×#391—21no—
23C11×#391C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389—21no—
26C11×#389C2212yes—
27C11×#388—21no—
28C11×#388—21no—
29C11×#384C2211yescharacteristic
30C11×#382C2211yescharacteristic
31C4×C11×C4⋊C4—21no—
32C4×C11×C4⋊C4C2212yes—
33C4×C11×C22⋊C4—21no—
34C4×C11×C22⋊C4—21no—
35C43×C11C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C8×C11C2312yes—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—24no—
50C11×#124—22no—
51C11×#124—22no—
52C4×Q8×C11—24no—
53C4×Q8×C11—44no—
54C4×D4×C11—24no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70C2×C42×C11—22no—
71C2×C42×C11D411yescharacteristic
72C2×C42×C11D411yescharacteristic
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C11×#103—24no—
79C11×#103—24no—
80C11×#102—24no—
81C11×#102—24no—
82C11×#97—24no—
83C11×#95—21no—
84C11×#95—21no—
85C11×#95—21no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89#23821C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C2×Q8×C11—24no—
92C2×Q8×C11—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11#4112yes—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—21no—
101C2×D4×C11#4112yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4#4114yes—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4—42no—
138C11×C22⋊C4—42no—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11—22no—
144C42×C11—41no—
145C42×C11—41no—
146C42×C11—44no—
147C42×C11—42no—
148C42×C11#4114yes—
149C4×C4⋊Q8C2×C1111yescharacteristic, complemented
150C4×#124C2×C1111yescharacteristic
151#2101C2×C1112yescomplemented
152#2072C2×C1111yescharacteristic, complemented
153#2071C2×C1111yescharacteristic
154#2042C2×C1112yes—
155#2024C2×C1111yescharacteristic, complemented
156#2023C2×C1111yescharacteristic
157#1763C2×C1112yescomplemented
158#1762C2×C1112yes—
159#1745C2×C1111yescharacteristic, complemented
160C23×C11—22no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11C22×D411yescharacteristic
168Q8×C11—24no—
169Q8×C11—48no—
170Q8×C11—42no—
171D4×C11—24no—
172D4×C11—42no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—84no—
203C2×C4×C11#12412yes—
204C2×C4×C11#12412yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11#13712yes—
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4112yes—
210C2×C4×C11C2×#4112yes—
211C8×C11—42no—
212C8×C11—42no—
213C2×C4⋊Q8C22×C1111yescharacteristic
214C2×#124C22×C1111yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×Q8C22×C1111yescharacteristic
217C2×C4×D4C22×C1111yescharacteristic
218C2×#103C22×C1112yes—
219C2×#103C22×C1112yes—
220C2×#102C22×C1112yes—
221C2×#102C22×C1112yes—
222C2×#97C22×C1112yes—
223#391—21no—
224#391C22×C1111yescharacteristic
225#390C22×C1111yescharacteristic
226#389—21no—
227#389C22×C1112yes—
228#388—21no—
229#388—21no—
230#384C22×C1111yescharacteristic
231#382C22×C1111yescharacteristic
232C4×C4⋊C4—21no—
233C4×C4⋊C4C22×C1112yes—
234C4×C22⋊C4—21no—
235C4×C22⋊C4—21no—
236C43C22×C1111yescharacteristic
237#340C22×C1112yes—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#336C22×C1111yescharacteristic
242#336C22×C1111yescharacteristic
243#336C22×C1112yes—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11#52511yescharacteristic
252C22×C11#52511yescharacteristic
253C22×C11C2×#12411yescharacteristic
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C22×C11#57511yescharacteristic
257C22×C11#57511yescharacteristic
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—44no—
263C4×C11—41no—
264C4×C11—41no—
265C4×C11—42no—
266C4×C11—82no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11#52912yes—
270C4×C11#52912yes—
271C22×Q8—21no—
272C22×Q8C23×C1111yescharacteristic
273C22×D4C23×C1111yescharacteristic
274C23×C4—21no—
275C22×C8C23×C1112yes—
276C22×C8C23×C1112yes—
277C4⋊Q8—24no—
278#124—22no—
279#124—22no—
280C4×Q8—24no—
281C4×Q8—44no—
282C4×D4—24no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C4⋊C4C23×C1111yescharacteristic
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C42—22no—
298C2×C42—21no—
299C2×C42D4×C1111yescharacteristic
300C2×C42D4×C1111yescharacteristic
301C2×C42D4×C1111yescharacteristic
302C2×C42D4×C1111yescharacteristic
303C2×C42C23×C1111yescharacteristic
304C2×C42C23×C1111yescharacteristic
305C2×C42C23×C1111yescharacteristic
306#103—24no—
307#103—24no—
308#102—24no—
309#102—24no—
310#97—24no—
311#95—21no—
312#95—21no—
313#95—21no—
314#95—21no—
315#95—22no—
316#95—22no—
317C2×C11—82no—
318C2×C11#239811yescharacteristic
319C2×C11#311411yescharacteristic
320C2×C11#311511yescharacteristic
321C2×C11#311611yescharacteristic
322C2×C11#311711yescharacteristic
323C2×C11#314011yescharacteristic
324C2×C11#314111yescharacteristic
325C24—21no—
326C2×Q8—24no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×Q8C11×#4112yes—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4C11×#4112yes—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C24×C1111yescharacteristic
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—44no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4C11×#4114yes—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C42—22no—
375C42—22no—
376C42—21no—
377C42—21no—
378C42—22no—
379C42—41no—
380C42—41no—
381C42—44no—
382C42—42no—
383C42C11×#4114yes—
384C11#2382111yescharacteristic, direct product factor, Sylow
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23C22×D4×C1111yescharacteristic
393Q8—24no—
394Q8—48no—
395Q8—42no—
396D4—24no—
397D4—42no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—84no—
428C2×C4C11×#12412yes—
429C2×C4C11×#12412yes—
430C2×C4C11×AGL(1,ℤ/8)12yes—
431C2×C4C11×#13712yes—
432C2×C4C2×C11×#4111yescharacteristic
433C2×C4C2×C11×#4111yescharacteristic
434C2×C4C2×C11×#4112yes—
435C2×C4C2×C11×#4112yes—
436C8—42no—
437C8—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22C11×#52511yescharacteristic
446C22C11×#52511yescharacteristic
447C22C2×C11×#12411yescharacteristic
448C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
449C22C2×C11×#13711yescharacteristic
450C22C11×#57511yescharacteristic
451C22C11×#57511yescharacteristic
452C4—22no—
453C4—22no—
454C4—22no—
455C4—22no—
456C4—42no—
457C4—44no—
458C4—41no—
459C4—41no—
460C4—82no—
461C4—81no—
462C4—81no—
463C4C11×#52912yes—
464C4C11×#52912yes—
465C2—82no—
466C2C11×#239811yescharacteristic
467C2C11×#311411yescharacteristic
468C2C11×#311511yescharacteristic
469C2C11×#311611yescharacteristic
470C2C11×#311711yescharacteristic
471C2C11×#314011yescharacteristic
472C2C11×#314111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C11×C4⋊Q8C2semidirect
3. C11×#2101C2semidirect
4. C11×#2072C2semidirect
7. C11×#2024C2semidirect
9. C11×#1763C2semidirect
11. C11×#1745C2semidirect
89. #23821C11direct (N × H)
149. C4×C4⋊Q8C2×C11semidirect
151. #2101C2×C11semidirect
152. #2072C2×C11semidirect
155. #2024C2×C11semidirect
157. #1763C2×C11semidirect
159. #1745C2×C11semidirect
384. C11#23821direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×C4⋊Q82
C4×C11×#1242
C11×#21012
C11×#20722
C11×#20712
C11×#20422
C11×#20242
C11×#20232
C11×#17632
C11×#17622
C11×#17452
#2382111