Finite Group Databasebeta

← C11×#23762 #14600955

Subgroups — C11×#23762 #14600955

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×C22⋊Q8C211yesmaximal, characteristic
2C11×#2285C211yesmaximal, characteristic
3C11×#2100C211yesmaximal, characteristic, complemented
4C11×#2095C211yesmaximal, characteristic, complemented
5C11×#2084C211yesmaximal, characteristic, complemented
6C11×#2075C212yesmaximal
7C11×#2072C211yesmaximal, characteristic, complemented
8C11×#2035C212yesmaximal
9C11×#1776C212yesmaximal, complemented
10C11×#1763C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C11×#117—21no—
15C22×C42×C11C2211yescharacteristic
16C2×C11×#107C2212yes—
17C2×C11×#106C2212yes—
18C2×C11×#103C2212yes—
19C2×C11×#103C2212yes—
20C2×C11×C22⋊C8C2212yes—
21C2×C11×#97C2212yes—
22C11×#391C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#387—21no—
25C11×#385—21no—
26C11×#384C2211yescharacteristic
27C11×#384C2211yescharacteristic
28C11×#382—21no—
29C11×#380—21no—
30C11×#380C2212yes—
31C11×#380C2211yescharacteristic
32C4×C11×C4⋊C4—21no—
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4—21no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2211yescharacteristic
42C11×#336C2211yescharacteristic
43C22×Q8×C11C2311yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2312yes—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—22no—
51C4×Q8×C11—24no—
52C11×#117—44no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—21no—
68C2×C42×C11—24no—
69C2×C42×C11—22no—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11D411yescharacteristic
73C2×C42×C11D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C11×#107—24no—
77C11×#106—24no—
78C11×#103—24no—
79C11×#103—24no—
80C11×C22⋊C8—24no—
81C11×#97—24no—
82C11×#95—21no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95—21no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—21no—
89#23762C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11C2×D411yescharacteristic
91C2×Q8×C11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11#4112yes—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—41no—
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#4114yes—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4#4112yes—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—42no—
140C11×C22⋊C4—44no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11—42no—
145C42×C11—44no—
146C42×C11—42no—
147C42×C11#4114yes—
148C4×C22⋊Q8C2×C1111yescharacteristic
149#2285C2×C1111yescharacteristic
150#2100C2×C1111yescharacteristic, complemented
151#2095C2×C1111yescharacteristic, complemented
152#2084C2×C1111yescharacteristic, complemented
153#2075C2×C1112yes—
154#2072C2×C1111yescharacteristic, complemented
155#2035C2×C1112yes—
156#1776C2×C1112yescomplemented
157#1763C2×C1112yescomplemented
158#1749C2×C1111yescharacteristic
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11AGL(1,ℤ/8)12yes—
166C23×C11C22×D411yescharacteristic
167Q8×C11—24no—
168Q8×C11—42no—
169C2×C4×C11—28no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
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—22no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—44no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11#12312yes—
203C2×C4×C11#12312yes—
204C2×C4×C11#13712yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C2×#4112yes—
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4112yes—
210C8×C11—24no—
211C8×C11—42no—
212C2×C22⋊Q8C22×C1111yescharacteristic
213C2×C4×Q8C22×C1111yescharacteristic
214C2×#117—21no—
215C22×C42C22×C1111yescharacteristic
216C2×#107C22×C1112yes—
217C2×#106C22×C1112yes—
218C2×#103C22×C1112yes—
219C2×#103C22×C1112yes—
220C2×C22⋊C8C22×C1112yes—
221C2×#97C22×C1112yes—
222#391C22×C1111yescharacteristic
223#389C22×C1111yescharacteristic
224#387—21no—
225#385—21no—
226#384C22×C1111yescharacteristic
227#384C22×C1111yescharacteristic
228#382—21no—
229#380—21no—
230#380C22×C1111yescharacteristic
231#380C22×C1112yes—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4C22×C1112yes—
235C4×C4⋊C4C22×C1111yescharacteristic
236C4×C22⋊C4—21no—
237#340C22×C1112yes—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#336C22×C1111yescharacteristic
242#336C22×C1111yescharacteristic
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11C2×#12311yescharacteristic
251C22×C11#52511yescharacteristic
252C22×C11#53211yescharacteristic
253C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
254C22×C11C2×#13711yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C22×C11#57511yescharacteristic
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—42no—
262C4×C11—41no—
263C4×C11—42no—
264C4×C11—81no—
265C4×C11—82no—
266C4×C11—82no—
267C4×C11—81no—
268C4×C11#52912yes—
269C4×C11#52912yes—
270C22×Q8C23×C1111yescharacteristic
271C23×C4D4×C1111yescharacteristic
272C23×C4D4×C1111yescharacteristic
273C23×C4C23×C1111yescharacteristic
274C22×C8C23×C1112yes—
275C22×C8C23×C1112yes—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C4×Q8—24no—
279#117—44no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C42—24no—
296C2×C42—22no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42D4×C1111yescharacteristic
300C2×C42D4×C1111yescharacteristic
301C2×C42C23×C1111yescharacteristic
302C2×C42C23×C1111yescharacteristic
303#107—24no—
304#106—24no—
305#103—24no—
306#103—24no—
307C22⋊C8—24no—
308#97—24no—
309#95—21no—
310#95—21no—
311#95—22no—
312#95—21no—
313#95—21no—
314#95—22no—
315#95—21no—
316C2×C11—42no—
317C2×C11#239511yescharacteristic
318C2×C11#309211yescharacteristic
319C2×C11#309511yescharacteristic
320C2×C11#311211yescharacteristic
321C2×C11#311611yescharacteristic
322C2×C11#318011yescharacteristic
323C2×C11#318511yescharacteristic
324C24C2×D4×C1111yescharacteristic
325C2×Q8—21no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8C11×#4112yes—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—41no—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C24×C1111yescharacteristic
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8C11×#4114yes—
357C4⋊C4—24no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4C11×#4112yes—
372C22⋊C4—24no—
373C22⋊C4—44no—
374C22⋊C4—42no—
375C42—22no—
376C42—22no—
377C42—22no—
378C42—44no—
379C42—42no—
380C42—42no—
381C42C11×#4114yes—
382C11#2376211yescharacteristic, direct product factor, Sylow
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23C11×AGL(1,ℤ/8)12yes—
390C23C22×D4×C1111yescharacteristic
391Q8—24no—
392Q8—42no—
393C2×C4—28no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—44no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4C11×#12312yes—
427C2×C4C11×#12312yes—
428C2×C4C11×#13712yes—
429C2×C4C11×#13712yes—
430C2×C4C2×C11×#4112yes—
431C2×C4C2×C11×#4111yescharacteristic
432C2×C4C2×C11×#4111yescharacteristic
433C2×C4C2×C11×#4112yes—
434C8—24no—
435C8—42no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22C2×C11×#12311yescharacteristic
444C22C11×#52511yescharacteristic
445C22C11×#53211yescharacteristic
446C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
447C22C2×C11×#13711yescharacteristic
448C22C2×C11×#13711yescharacteristic
449C22C11×#57511yescharacteristic
450C4—22no—
451C4—22no—
452C4—22no—
453C4—22no—
454C4—41no—
455C4—42no—
456C4—42no—
457C4—82no—
458C4—81no—
459C4—81no—
460C4—82no—
461C4C11×#52912yes—
462C4C11×#52912yes—
463C2—42no—
464C2C11×#239511yescharacteristic
465C2C11×#309211yescharacteristic
466C2C11×#309511yescharacteristic
467C2C11×#311211yescharacteristic
468C2C11×#311611yescharacteristic
469C2C11×#318011yescharacteristic
470C2C11×#318511yescharacteristic
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
3. C11×#2100C2semidirect
4. C11×#2095C2semidirect
5. C11×#2084C2semidirect
7. C11×#2072C2semidirect
9. C11×#1776C2semidirect
10. C11×#1763C2semidirect
89. #23762C11direct (N × H)
150. #2100C2×C11semidirect
151. #2095C2×C11semidirect
152. #2084C2×C11semidirect
154. #2072C2×C11semidirect
156. #1776C2×C11semidirect
157. #1763C2×C11semidirect
382. C11#23762direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×C22⋊Q82
C11×#22852
C11×#21002
C11×#20952
C11×#20842
C11×#20752
C11×#20722
C11×#20352
C11×#17762
C11×#17632
C11×#17492
#2376211