Finite Group Databasebeta

← C11×#22963 #14600156

Subgroups — C11×#22963 #14600156

Order 2816.

898 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
1C2×C11×#476C211yesmaximal, characteristic
2C11×#2369C211yesmaximal, characteristic, complemented
3D4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1948C211yesmaximal, characteristic, complemented
6C11×#1941C212yesmaximal, complemented
7C11×#1919C212yesmaximal, complemented
8C11×#1864C212yesmaximal
9C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
10C4×C11×#102C211yesmaximal, characteristic
11C4×C11×#102C212yesmaximal
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C11×C4⋊C4—21no—
16C11×#476C418yescomplemented
17C2×C11×#106C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×C4×C8×C11C2212yes—
25C11×#391—22no—
26C11×#389—21no—
27C11×#389C2212yes—
28C11×#389C2212yes—
29C11×#385—22no—
30C11×#384C2211yescharacteristic
31C11×#380—21no—
32C4×C11×C4⋊C4—21no—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C11×#340C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×Q8×C11—21no—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yescomplemented
51C4×D4×C11—24no—
52C4×D4×C11—22no—
53C4×D4×C11—42no—
54C4×D4×C11C2×C414yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—44no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11—21no—
71C2×C42×C11—22no—
72C2×C42×C11C2312yes—
73C2×C42×C11C2311yescharacteristic
74C11×#106—42no—
75C11×#106C2×C418yescomplemented
76C11×C4⋊C8C2×C414yescomplemented
77C11×#102—22no—
78C11×#102C2×C418yes—
79C11×#102Q814yescomplemented
80C4×C8×C11—22no—
81C4×C8×C11—42no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95D412yes—
87#22963C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—21no—
89C2×Q8×C11—24no—
90C2×Q8×C11—81no—
91C2×Q8×C11—81no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11C22×C412yes—
96C2×D4×C11C2×Q812yes—
97C2×D4×C11#4112yes—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—44no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—44no—
108C22×C4×C11—82no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C414yes—
122C2×C8×C11C2×Q812yes—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—81no—
135C11×C4⋊C4—82no—
136C11×C4⋊C4SD1614yes—
137C11×C4⋊C4C22×C414yes—
138C11×C4⋊C4C22×C412yes—
139C11×C4⋊C4C2×Q812yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—44no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11—42no—
145C42×C11—82no—
146C42×C11C22×C412yes—
147C42×C11#4112yes—
148C2×#476C2×C1111yescharacteristic
149#2369C2×C1111yescharacteristic, complemented
150D4×C4⋊C4C2×C1111yescharacteristic
151#1990C2×C1111yescharacteristic, complemented
152#1948C2×C1111yescharacteristic, complemented
153#1941C2×C1112yescomplemented
154#1919C2×C1112yescomplemented
155#1864C2×C1112yes—
156C8×C4⋊C4C2×C1111yescharacteristic, complemented
157C4×#102C2×C1112yes—
158C4×#102C2×C1111yescharacteristic
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11C22×D411yescharacteristic
167Q8×C11—84no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11C4×Q814yes—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—48no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—88no—
196C2×C4×C11C4×D412yes—
197C2×C4×C11C4×D412yes—
198C2×C4×C11C2×SD1614yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×Q811yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C8×C11—24no—
208C8×C11—22no—
209C8×C11—41no—
210C2×C4⋊Q8C22×C1111yescharacteristic
211C2×C4×D4C22×C1112yes—
212C2×C4×D4C22×C1111yescharacteristic
213C22×C4⋊C4—21no—
214#476C4×C1118yescomplemented
215C2×#106C22×C1112yes—
216C2×#106C22×C1112yes—
217C2×C4⋊C8C22×C1111yescharacteristic
218C2×#102C22×C1111yescharacteristic
219C2×#102C22×C1112yes—
220C2×#102C22×C1111yescharacteristic
221C2×C4×C8C22×C1111yescharacteristic
222C2×C4×C8C22×C1112yes—
223#391—22no—
224#389—21no—
225#389C22×C1112yes—
226#389C22×C1112yes—
227#385—22no—
228#384C22×C1111yescharacteristic
229#380—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4C22×C1112yes—
232C4×C4⋊C4C22×C1111yescharacteristic
233C4×C4⋊C4C22×C1111yescharacteristic
234#340C22×C1112yes—
235#340C22×C1111yescharacteristic
236#340C22×C1112yes—
237#340C22×C1111yescharacteristic
238#340C22×C1112yes—
239#336C22×C1112yes—
240C22×C11—24no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#54611yescharacteristic
249C22×C11D4×Q811yescharacteristic
250C22×C11C22×SD1611yescharacteristic
251C22×C11C2×#13511yescharacteristic
252C22×C11#57611yescharacteristic
253C22×C11#57711yescharacteristic
254C4×C11—22no—
255C4×C11—24no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—44no—
259C4×C11—42no—
260C4×C11—82no—
261C4×C11—81no—
262C4×C11C4×SD1614yes—
263C4×C11C2×C4×Q811yescharacteristic
264C4×C11#52011yescharacteristic
265C4×C11#55211yescharacteristic
266C4×C11#55411yescharacteristic
267C22×Q8—21no—
268C22×D4C23×C1111yescharacteristic
269C23×C4—21no—
270C23×C4—22no—
271C22×C8C23×C1111yescharacteristic
272C22×C8C23×C1112yes—
273C22×C8C23×C1111yescharacteristic
274C4⋊Q8—22no—
275C4⋊Q8C2×C4×C1114yescomplemented
276C4×D4—24no—
277C4×D4—22no—
278C4×D4—42no—
279C4×D4C2×C4×C1114yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4D4×C1111yescharacteristic
287C2×C4⋊C4D4×C1111yescharacteristic
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1111yescharacteristic
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C42—21no—
296C2×C42—22no—
297C2×C42C23×C1112yes—
298C2×C42C23×C1111yescharacteristic
299#106—42no—
300#106C2×C4×C1118yescomplemented
301C4⋊C8C2×C4×C1114yescomplemented
302#102—22no—
303#102C2×C4×C1118yes—
304#102Q8×C1114yescomplemented
305C4×C8—22no—
306C4×C8—42no—
307#95—22no—
308#95—22no—
309#95—21no—
310#95—22no—
311#95D4×C1112yes—
312C2×C11—44no—
313C2×C11#236011yescharacteristic
314C2×C11C2×C4×SD1611yescharacteristic
315C2×C11#294611yescharacteristic
316C2×C11#329511yescharacteristic
317C2×C11#330311yescharacteristic
318C2×C11Q8×SD1611yescharacteristic
319C2×C11#338011yescharacteristic
320C24—21no—
321C2×Q8—24no—
322C2×Q8—81no—
323C2×Q8—81no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4C22×C4×C1112yes—
328C2×D4C2×Q8×C1112yes—
329C2×D4C11×#4112yes—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—44no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—44no—
340C22×C4—82no—
341C22×C4C2×D4×C1112yes—
342C22×C4C2×D4×C1111yescharacteristic
343C22×C4C2×D4×C1112yes—
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C24×C1111yescharacteristic
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8C22×C4×C1114yes—
354C2×C8C2×Q8×C1112yes—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—44no—
365C4⋊C4—42no—
366C4⋊C4—81no—
367C4⋊C4—82no—
368C4⋊C4C11×SD1614yes—
369C4⋊C4C22×C4×C1114yes—
370C4⋊C4C22×C4×C1112yes—
371C4⋊C4C2×Q8×C1112yes—
372C22⋊C4—24no—
373C22⋊C4—44no—
374C42—22no—
375C42—22no—
376C42—42no—
377C42—82no—
378C42C22×C4×C1112yes—
379C42C11×#4112yes—
380C11#2296311yescharacteristic, direct product factor, Sylow
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23C22×D4×C1111yescharacteristic
389Q8—84no—
390D4—22no—
391D4—22no—
392D4—22no—
393D4C4×Q8×C1114yes—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—48no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—88no—
418C2×C4C4×D4×C1112yes—
419C2×C4C4×D4×C1112yes—
420C2×C4C2×C11×SD1614yes—
421C2×C4C2×C11×SD1612yes—
422C2×C4C11×#13512yes—
423C2×C4C23×C4×C1111yescharacteristic
424C2×C4C22×Q8×C1111yescharacteristic
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C2×C11×#4111yescharacteristic
427C2×C4C11×H(5,𝔽2)11yescharacteristic
428C2×C4C11×2−1+411yescharacteristic
429C8—24no—
430C8—22no—
431C8—41no—
432C22—24no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×C4×D4×C1111yescharacteristic
440C22C11×#54611yescharacteristic
441C22D4×Q8×C1111yescharacteristic
442C22C22×C11×SD1611yescharacteristic
443C22C2×C11×#13511yescharacteristic
444C22C11×#57611yescharacteristic
445C22C11×#57711yescharacteristic
446C4—22no—
447C4—24no—
448C4—42no—
449C4—44no—
450C4—42no—
451C4—42no—
452C4—82no—
453C4—81no—
454C4C4×C11×SD1614yes—
455C4C2×C4×Q8×C1111yescharacteristic
456C4C11×#52011yescharacteristic
457C4C11×#55211yescharacteristic
458C4C11×#55411yescharacteristic
459C2—44no—
460C2C11×#236011yescharacteristic
461C2C2×C4×C11×SD1611yescharacteristic
462C2C11×#294611yescharacteristic
463C2C11×#329511yescharacteristic
464C2C11×#330311yescharacteristic
465C2Q8×C11×SD1611yescharacteristic
466C2C11×#338011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2369C2semidirect
4. C11×#1990C2semidirect
5. C11×#1948C2semidirect
6. C11×#1941C2semidirect
7. C11×#1919C2semidirect
9. C8×C11×C4⋊C4C2semidirect
16. C11×#476C4semidirect
50. C11×C4⋊Q8C2×C4semidirect
75. C11×#106C2×C4semidirect
76. C11×C4⋊C8C2×C4semidirect
79. C11×#102Q8semidirect
87. #22963C11direct (N × H)
149. #2369C2×C11semidirect
151. #1990C2×C11semidirect
152. #1948C2×C11semidirect
153. #1941C2×C11semidirect
154. #1919C2×C11semidirect
156. C8×C4⋊C4C2×C11semidirect
214. #476C4×C11semidirect
275. C4⋊Q8C2×C4×C11semidirect
300. #106C2×C4×C11semidirect
301. C4⋊C8C2×C4×C11semidirect
304. #102Q8×C11semidirect
380. C11#22963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C11×#23692
D4×C11×C4⋊C42
C11×#19902
C11×#19482
C11×#19412
C11×#19192
C11×#18642
C8×C11×C4⋊C42
C4×C11×#1022
#2296311