Finite Group Databasebeta

← C11×#23060 #14600253

Subgroups — C11×#23060 #14600253

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic
2C11×#2365C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1947C211yesmaximal, characteristic, complemented
6C11×#1934C212yesmaximal
7C11×#1925C212yesmaximal
8C11×#1918C212yesmaximal, complemented
9C4×C11×#107C212yesmaximal, complemented
10C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117—21no—
16C11×#474C418yescomplemented
17C2×C11×#107C2212yes—
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×C4×C8×C11C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#391—21no—
26C11×#390C2212yes—
27C11×#389C2212yes—
28C11×#388—22no—
29C11×#387—22no—
30C11×#384C2211yescharacteristic
31C11×#380—21no—
32C4×C11×C4⋊C4C2212yes—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C11×#340C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2211yescharacteristic
41C11×#336C2212yes—
42C22×Q8×C11—21no—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8C2×C414yes—
50C4×Q8×C11—44no—
51C4×D4×C11—22no—
52C4×D4×C11C2×C414yes—
53C11×#117—44no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11—21no—
71C2×C42×C11C2312yes—
72C2×C42×C11C2311yescharacteristic
73C11×#107—24no—
74C11×#107C2×C418yes—
75C11×C4⋊C8C2×C414yes—
76C11×#102—22no—
77C11×#102—22no—
78C11×#102C2×C418yes—
79C4×C8×C11—24no—
80C4×C8×C11—22no—
81C11×#95—22no—
82C11×#95—21no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95D412yes—
86#23060C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—21no—
88C2×Q8×C11—24no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11C22×C412yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C2×C8×C11—22no—
111C2×C8×C11—21no—
112C2×C8×C11—22no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11C22×C414yes—
118C2×C8×C11#4112yes—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—44no—
130C11×C4⋊C4—81no—
131C11×C4⋊C4D814yes—
132C11×C4⋊C4C22×C414yes—
133C11×C4⋊C4C22×C412yes—
134C11×C4⋊C4#4112yes—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—44no—
137C11×C22⋊C4—82no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—44no—
141C42×C11—44no—
142C42×C11—42no—
143C42×C11C22×C412yes—
144C42×C11#4112yes—
145C2×#474C2×C1111yescharacteristic
146#2365C2×C1111yescharacteristic, complemented
147#2354C2×C1111yescharacteristic
148#1990C2×C1111yescharacteristic, complemented
149#1947C2×C1111yescharacteristic, complemented
150#1934C2×C1112yes—
151#1925C2×C1112yes—
152#1918C2×C1112yescomplemented
153C4×#107C2×C1112yescomplemented
154C8×C4⋊C4C2×C1111yescharacteristic, complemented
155C4×#102C2×C1111yescharacteristic
156C23×C11—22no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11C22×D411yescharacteristic
164Q8×C11—48no—
165D4×C11—22no—
166D4×C11—22no—
167D4×C11—41no—
168D4×C11—41no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—48no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11C4×D412yes—
193C2×C4×C11C4×D412yes—
194C2×C4×C11C2×D814yes—
195C2×C4×C11C2×D812yes—
196C2×C4×C11#13512yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C8×C11—24no—
204C8×C11—22no—
205C8×C11—41no—
206C2×C4⋊Q8C22×C1111yescharacteristic
207C2×C4×Q8—21no—
208C2×C4×D4C22×C1111yescharacteristic
209C2×#117—21no—
210#474C4×C1118yescomplemented
211C2×#107C22×C1112yes—
212C2×#107C22×C1112yes—
213C2×C4⋊C8C22×C1111yescharacteristic
214C2×#102C22×C1111yescharacteristic
215C2×#102C22×C1111yescharacteristic
216C2×#102C22×C1112yes—
217C2×C4×C8C22×C1112yes—
218C2×C4×C8C22×C1111yescharacteristic
219#391—21no—
220#390C22×C1112yes—
221#389C22×C1112yes—
222#388—22no—
223#387—22no—
224#384C22×C1111yescharacteristic
225#380—21no—
226C4×C4⋊C4C22×C1112yes—
227C4×C4⋊C4C22×C1112yes—
228C4×C4⋊C4C22×C1111yescharacteristic
229C4×C4⋊C4C22×C1111yescharacteristic
230#340C22×C1111yescharacteristic
231#340C22×C1112yes—
232#340C22×C1112yes—
233#340C22×C1112yes—
234#340C22×C1111yescharacteristic
235#336C22×C1112yes—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11C2×C4×D411yescharacteristic
244C22×C11#54711yescharacteristic
245C22×C11#54811yescharacteristic
246C22×C11C22×D811yescharacteristic
247C22×C11C2×#13511yescharacteristic
248C22×C11#57711yescharacteristic
249C22×C11#57811yescharacteristic
250C4×C11—24no—
251C4×C11—22no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—44no—
256C4×C11—81no—
257C4×C11—82no—
258C4×C11C4×D814yes—
259C4×C11C4×#4111yescharacteristic
260C4×C11#51911yescharacteristic
261C4×C11#55211yescharacteristic
262C4×C11#55611yescharacteristic
263C22×Q8—21no—
264C22×D4C23×C1111yescharacteristic
265C23×C4—21no—
266C22×C8C23×C1111yescharacteristic
267C22×C8C23×C1112yes—
268C22×C8C23×C1111yescharacteristic
269C4⋊Q8—22no—
270C4⋊Q8C2×C4×C1114yes—
271C4×Q8—44no—
272C4×D4—22no—
273C4×D4C2×C4×C1114yes—
274#117—44no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4D4×C1111yescharacteristic
280C2×C4⋊C4D4×C1111yescharacteristic
281C2×C4⋊C4C23×C1112yes—
282C2×C4⋊C4C23×C1111yescharacteristic
283C2×C4⋊C4C23×C1111yescharacteristic
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42—21no—
292C2×C42C23×C1112yes—
293C2×C42C23×C1111yescharacteristic
294#107—24no—
295#107C2×C4×C1118yes—
296C4⋊C8C2×C4×C1114yes—
297#102—22no—
298#102—22no—
299#102C2×C4×C1118yes—
300C4×C8—24no—
301C4×C8—22no—
302#95—22no—
303#95—21no—
304#95—22no—
305#95—22no—
306#95D4×C1112yes—
307C2×C11—82no—
308C2×C11#236211yescharacteristic
309C2×C11C2×C4×D811yescharacteristic
310C2×C11#294711yescharacteristic
311C2×C11#333411yescharacteristic
312C2×C11#334011yescharacteristic
313C2×C11#335811yescharacteristic
314C2×C11#336411yescharacteristic
315C24—21no—
316C2×Q8—24no—
317C2×Q8—42no—
318C2×Q8—42no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4C22×C4×C1112yes—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1112yes—
336C22×C4C2×D4×C1111yescharacteristic
337C22×C4C24×C1111yescharacteristic
338C2×C8—22no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8C22×C4×C1114yes—
346C2×C8C11×#4112yes—
347C4⋊C4—24no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—42no—
357C4⋊C4—44no—
358C4⋊C4—81no—
359C4⋊C4C11×D814yes—
360C4⋊C4C22×C4×C1114yes—
361C4⋊C4C22×C4×C1112yes—
362C4⋊C4C11×#4112yes—
363C22⋊C4—24no—
364C22⋊C4—44no—
365C22⋊C4—82no—
366C42—22no—
367C42—22no—
368C42—44no—
369C42—44no—
370C42—42no—
371C42C22×C4×C1112yes—
372C42C11×#4112yes—
373C11#2306011yescharacteristic, direct product factor, Sylow
374C23—22no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23C22×D4×C1111yescharacteristic
382Q8—48no—
383D4—22no—
384D4—22no—
385D4—41no—
386D4—41no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—48no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4C4×D4×C1112yes—
411C2×C4C4×D4×C1112yes—
412C2×C4C2×C11×D814yes—
413C2×C4C2×C11×D812yes—
414C2×C4C11×#13512yes—
415C2×C4C23×C4×C1111yescharacteristic
416C2×C4C2×C11×#4111yescharacteristic
417C2×C4C2×C11×#4111yescharacteristic
418C2×C4C2×C11×#4111yescharacteristic
419C2×C4C11×2−1+411yescharacteristic
420C2×C4C11×2−1+411yescharacteristic
421C8—24no—
422C8—22no—
423C8—41no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22C2×C4×D4×C1111yescharacteristic
432C22C11×#54711yescharacteristic
433C22C11×#54811yescharacteristic
434C22C22×C11×D811yescharacteristic
435C22C2×C11×#13511yescharacteristic
436C22C11×#57711yescharacteristic
437C22C11×#57811yescharacteristic
438C4—22no—
439C4—24no—
440C4—42no—
441C4—44no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—82no—
446C4C4×C11×D814yes—
447C4C4×C11×#4111yescharacteristic
448C4C11×#51911yescharacteristic
449C4C11×#55211yescharacteristic
450C4C11×#55611yescharacteristic
451C2—82no—
452C2C11×#236211yescharacteristic
453C2C2×C4×C11×D811yescharacteristic
454C2C11×#294711yescharacteristic
455C2C11×#333411yescharacteristic
456C2C11×#334011yescharacteristic
457C2C11×#335811yescharacteristic
458C2C11×#336411yescharacteristic
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×#2365C2semidirect
4. C11×#1990C2semidirect
5. C11×#1947C2semidirect
8. C11×#1918C2semidirect
9. C4×C11×#107C2semidirect
10. C8×C11×C4⋊C4C2semidirect
16. C11×#474C4semidirect
86. #23060C11direct (N × H)
146. #2365C2×C11semidirect
148. #1990C2×C11semidirect
149. #1947C2×C11semidirect
152. #1918C2×C11semidirect
153. C4×#107C2×C11semidirect
154. C8×C4⋊C4C2×C11semidirect
210. #474C4×C11semidirect
373. C11#23060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C11×#23652
C11×#23542
C11×#19902
C11×#19472
C11×#19342
C11×#19252
C11×#19182
C4×C11×#1072
C8×C11×C4⋊C42
C4×C11×#1022
#2306011