Finite Group Databasebeta

← C11×#23781 #14600974

Subgroups — C11×#23781 #14600974

Order 2816.

808 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C11×#2293C211yesmaximal, characteristic
3C11×#2099C211yesmaximal, characteristic, complemented
4C11×#2093C211yesmaximal, characteristic
5C11×#2087C212yesmaximal, complemented
6C11×#2065C212yesmaximal
7C11×#2058C211yesmaximal, characteristic, complemented
8C11×#2023C211yesmaximal, characteristic
9C11×#1776C212yesmaximal, complemented
10C11×#1767C211yesmaximal, characteristic, complemented
11C11×#1762C212yesmaximal
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117—21no—
16C2×C11×#107C2212yes—
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2212yes—
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C11×#97C2212yes—
22C11×#391—21no—
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389—21no—
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2212yes—
29C11×#388—21no—
30C11×#388—21no—
31C11×#384C2211yescharacteristic
32C4×C11×C4⋊C4—21no—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C22⋊C4—21no—
36C43×C11C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2211yescharacteristic
42C11×#336C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—24no—
49C4×Q8×C11—44no—
50C4×D4×C11—22no—
51C4×D4×C11Q814yescomplemented
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—22no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
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×#107—24no—
79C11×#106—24no—
80C11×C4⋊C8—24no—
81C11×#102—24no—
82C11×#102—24no—
83C11×#97—24no—
84C11×#95—21no—
85C11×#95—21no—
86C11×#95—22no—
87C11×#95—21no—
88C11×#95—22no—
89#23781C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C2×Q8×C11—24no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11C2×Q812yes—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—24no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11#4114yes—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C2×Q812yes—
132C11×C4⋊C4#4114yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4—42no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—41no—
144C42×C11—42no—
145C42×C11—44no—
146C42×C11C2×Q812yes—
147C42×C11#4112yes—
148C4×C4⋊Q8C2×C1111yescharacteristic, complemented
149#2293C2×C1111yescharacteristic
150#2099C2×C1111yescharacteristic, complemented
151#2093C2×C1111yescharacteristic
152#2087C2×C1112yescomplemented
153#2065C2×C1112yes—
154#2058C2×C1111yescharacteristic, complemented
155#2023C2×C1111yescharacteristic
156#1776C2×C1112yescomplemented
157#1767C2×C1111yescharacteristic, complemented
158#1762C2×C1112yes—
159C23×C11—22no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11C22×D411yescharacteristic
167Q8×C11—48no—
168D4×C11—24no—
169D4×C11—42no—
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—21no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—48no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11C22⋊Q812yes—
200C2×C4×C11C22⋊Q812yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4112yes—
207C2×C4×C11C2×#4112yes—
208C8×C11—24no—
209C8×C11—42no—
210C2×C4⋊Q8C22×C1111yescharacteristic
211C2×C4×Q8—21no—
212C2×C4×D4C22×C1111yescharacteristic
213C2×#117—21no—
214C2×#107C22×C1112yes—
215C2×#106C22×C1112yes—
216C2×C4⋊C8C22×C1112yes—
217C2×#102C22×C1112yes—
218C2×#102C22×C1112yes—
219C2×#97C22×C1112yes—
220#391—21no—
221#390C22×C1111yescharacteristic
222#390C22×C1111yescharacteristic
223#389—21no—
224#389C22×C1112yes—
225#389C22×C1111yescharacteristic
226#389C22×C1111yescharacteristic
227#388—21no—
228#388—21no—
229#384C22×C1111yescharacteristic
230C4×C4⋊C4—21no—
231C4×C4⋊C4C22×C1112yes—
232C4×C4⋊C4C22×C1111yescharacteristic
233C4×C22⋊C4—21no—
234C43C22×C1111yescharacteristic
235#340C22×C1112yes—
236#340C22×C1112yes—
237#340C22×C1112yes—
238#340C22×C1112yes—
239#336C22×C1111yescharacteristic
240#336C22×C1111yescharacteristic
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11C2×C22⋊Q811yescharacteristic
249C22×C11#52511yescharacteristic
250C22×C11#53211yescharacteristic
251C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
252C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
253C22×C11C2×#13711yescharacteristic
254C22×C11#57511yescharacteristic
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—41no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11—82no—
266C4×C11#52912yes—
267C4×C11#53312yes—
268C22×Q8—21no—
269C22×D4C23×C1111yescharacteristic
270C23×C4—21no—
271C22×C8C23×C1112yes—
272C22×C8C23×C1112yes—
273C4⋊Q8—24no—
274C4×Q8—44no—
275C4×D4—22no—
276C4×D4Q8×C1114yescomplemented
277#117—44no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1111yescharacteristic
286C2×C4⋊C4C23×C1111yescharacteristic
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C4⋊C4C23×C1112yes—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C42—21no—
295C2×C42—22no—
296C2×C42D4×C1111yescharacteristic
297C2×C42D4×C1111yescharacteristic
298C2×C42D4×C1111yescharacteristic
299C2×C42D4×C1111yescharacteristic
300C2×C42C23×C1111yescharacteristic
301C2×C42C23×C1111yescharacteristic
302C2×C42C23×C1111yescharacteristic
303#107—24no—
304#106—24no—
305C4⋊C8—24no—
306#102—24no—
307#102—24no—
308#97—24no—
309#95—21no—
310#95—21no—
311#95—22no—
312#95—21no—
313#95—22no—
314C2×C11—82no—
315C2×C11#239611yescharacteristic
316C2×C11#307711yescharacteristic
317C2×C11#307911yescharacteristic
318C2×C11#311211yescharacteristic
319C2×C11#311411yescharacteristic
320C2×C11#318111yescharacteristic
321C2×C11#318411yescharacteristic
322C24—21no—
323C2×Q8—24no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—21no—
329C2×D4C2×Q8×C1112yes—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—24no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4C2×D4×C1111yescharacteristic
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C2×D4×C1111yescharacteristic
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C24×C1111yescharacteristic
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8C11×#4114yes—
351C4⋊C4—24no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—42no—
359C4⋊C4—44no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4C2×Q8×C1112yes—
364C4⋊C4C11×#4114yes—
365C22⋊C4—24no—
366C22⋊C4—42no—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—22no—
375C42—41no—
376C42—42no—
377C42—44no—
378C42C2×Q8×C1112yes—
379C42C11×#4112yes—
380C11#2378111yescharacteristic, direct product factor, Sylow
381C23—22no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23C22×D4×C1111yescharacteristic
389Q8—48no—
390D4—24no—
391D4—42no—
392C2×C4—21no—
393C2×C4—21no—
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—22no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—48no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4C11×C22⋊Q812yes—
422C2×C4C11×C22⋊Q812yes—
423C2×C4C11×AGL(1,ℤ/8)12yes—
424C2×C4C11×AGL(1,ℤ/8)12yes—
425C2×C4C11×#13712yes—
426C2×C4C22×Q8×C1111yescharacteristic
427C2×C4C2×C11×#4111yescharacteristic
428C2×C4C2×C11×#4112yes—
429C2×C4C2×C11×#4112yes—
430C8—24no—
431C8—42no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22C2×C11×C22⋊Q811yescharacteristic
440C22C11×#52511yescharacteristic
441C22C11×#53211yescharacteristic
442C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
443C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
444C22C2×C11×#13711yescharacteristic
445C22C11×#57511yescharacteristic
446C4—22no—
447C4—22no—
448C4—22no—
449C4—22no—
450C4—22no—
451C4—41no—
452C4—42no—
453C4—44no—
454C4—81no—
455C4—82no—
456C4—81no—
457C4C11×#52912yes—
458C4C11×#53312yes—
459C2—82no—
460C2C11×#239611yescharacteristic
461C2C11×#307711yescharacteristic
462C2C11×#307911yescharacteristic
463C2C11×#311211yescharacteristic
464C2C11×#311411yescharacteristic
465C2C11×#318111yescharacteristic
466C2C11×#318411yescharacteristic
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×#2099C2semidirect
5. C11×#2087C2semidirect
7. C11×#2058C2semidirect
9. C11×#1776C2semidirect
10. C11×#1767C2semidirect
51. C4×D4×C11Q8semidirect
89. #23781C11direct (N × H)
148. C4×C4⋊Q8C2×C11semidirect
150. #2099C2×C11semidirect
152. #2087C2×C11semidirect
154. #2058C2×C11semidirect
156. #1776C2×C11semidirect
157. #1767C2×C11semidirect
276. C4×D4Q8×C11semidirect
380. C11#23781direct (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
C11×#22932
C11×#20992
C11×#20932
C11×#20872
C11×#20652
C11×#20582
C11×#20232
C11×#17762
C11×#17672
C11×#17622
#2378111