Finite Group Databasebeta

← C11×#23061 #14600254

Subgroups — C11×#23061 #14600254

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic
2C11×#2369C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1948C211yesmaximal, characteristic, complemented
6C11×#1934C212yesmaximal
7C11×#1926C212yesmaximal
8C11×#1920C212yesmaximal, complemented
9C4×C11×#106C212yesmaximal, complemented
10C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×C11×#117—21no—
15C11×#476C418yescomplemented
16C2×C11×#106C2212yes—
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C4×C8×C11C2212yes—
23C2×C4×C8×C11C2211yescharacteristic
24C11×#391—22no—
25C11×#390C2212yes—
26C11×#389—21no—
27C11×#389C2212yes—
28C11×#388—22no—
29C11×#384C2211yescharacteristic
30C11×#380—21no—
31C4×C11×C4⋊C4—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×D4×C11—22no—
51C4×D4×C11C2×C414yes—
52C11×#117—44no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—22no—
68C2×C42×C11—21no—
69C2×C42×C11—22no—
70C2×C42×C11C2312yes—
71C2×C42×C11C2311yescharacteristic
72C11×#106—24no—
73C11×#106C2×C418yes—
74C11×C4⋊C8C2×C414yes—
75C11×#102—22no—
76C11×#102—22no—
77C11×#102C2×C418yes—
78C4×C8×C11—24no—
79C4×C8×C11—22no—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95—21no—
84C11×#95D412yes—
85#23061C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11—21no—
87C2×Q8×C11—24no—
88C2×Q8×C11—81no—
89C2×Q8×C11—81no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11C22×C412yes—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—22no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11C22×C414yes—
117C2×C8×C11#4112yes—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—81no—
129C11×C4⋊C4—82no—
130C11×C4⋊C4SD1614yes—
131C11×C4⋊C4C22×C414yes—
132C11×C4⋊C4C22×C412yes—
133C11×C4⋊C4#4112yes—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—44no—
136C11×C22⋊C4—82no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—44no—
140C42×C11—42no—
141C42×C11—82no—
142C42×C11C22×C412yes—
143C42×C11#4112yes—
144C2×#476C2×C1111yescharacteristic
145#2369C2×C1111yescharacteristic, complemented
146#2354C2×C1111yescharacteristic
147#1990C2×C1111yescharacteristic, complemented
148#1948C2×C1111yescharacteristic, complemented
149#1934C2×C1112yes—
150#1926C2×C1112yes—
151#1920C2×C1112yescomplemented
152C4×#106C2×C1112yescomplemented
153C8×C4⋊C4C2×C1111yescharacteristic, complemented
154C4×#102C2×C1111yescharacteristic
155C23×C11—22no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C22×D411yescharacteristic
163Q8×C11—84no—
164D4×C11—22no—
165D4×C11—22no—
166D4×C11—41no—
167D4×C11—41no—
168C2×C4×C11—22no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—48no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11C4×D412yes—
192C2×C4×C11C4×D412yes—
193C2×C4×C11C2×SD1614yes—
194C2×C4×C11C2×SD1612yes—
195C2×C4×C11#13512yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C112−1+411yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C8×C11—24no—
203C8×C11—22no—
204C8×C11—41no—
205C2×C4⋊Q8C22×C1111yescharacteristic
206C2×C4×D4C22×C1111yescharacteristic
207C2×#117—21no—
208#476C4×C1118yescomplemented
209C2×#106C22×C1112yes—
210C2×#106C22×C1112yes—
211C2×C4⋊C8C22×C1111yescharacteristic
212C2×#102C22×C1111yescharacteristic
213C2×#102C22×C1111yescharacteristic
214C2×#102C22×C1112yes—
215C2×C4×C8C22×C1112yes—
216C2×C4×C8C22×C1111yescharacteristic
217#391—22no—
218#390C22×C1112yes—
219#389—21no—
220#389C22×C1112yes—
221#388—22no—
222#384C22×C1111yescharacteristic
223#380—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4C22×C1112yes—
226C4×C4⋊C4C22×C1112yes—
227C4×C4⋊C4C22×C1111yescharacteristic
228C4×C4⋊C4C22×C1111yescharacteristic
229#340C22×C1111yescharacteristic
230#340C22×C1112yes—
231#340C22×C1112yes—
232#340C22×C1112yes—
233#340C22×C1111yescharacteristic
234#336C22×C1112yes—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11C2×C4×D411yescharacteristic
243C22×C11#54711yescharacteristic
244C22×C11#54811yescharacteristic
245C22×C11C22×SD1611yescharacteristic
246C22×C11C2×#13511yescharacteristic
247C22×C11#57611yescharacteristic
248C22×C11#57711yescharacteristic
249C4×C11—24no—
250C4×C11—22no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—44no—
255C4×C11—81no—
256C4×C11—82no—
257C4×C11C4×SD1614yes—
258C4×C11C4×#4111yescharacteristic
259C4×C11#51911yescharacteristic
260C4×C11#55211yescharacteristic
261C4×C11#55611yescharacteristic
262C22×Q8—21no—
263C22×D4C23×C1111yescharacteristic
264C23×C4—21no—
265C22×C8C23×C1111yescharacteristic
266C22×C8C23×C1112yes—
267C22×C8C23×C1111yescharacteristic
268C4⋊Q8—22no—
269C4⋊Q8C2×C4×C1114yes—
270C4×D4—22no—
271C4×D4C2×C4×C1114yes—
272#117—44no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4D4×C1111yescharacteristic
278C2×C4⋊C4D4×C1111yescharacteristic
279C2×C4⋊C4C23×C1112yes—
280C2×C4⋊C4C23×C1111yescharacteristic
281C2×C4⋊C4C23×C1111yescharacteristic
282C2×C4⋊C4C23×C1112yes—
283C2×C4⋊C4C23×C1111yescharacteristic
284C2×C22⋊C4—21no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C42—22no—
288C2×C42—21no—
289C2×C42—22no—
290C2×C42C23×C1112yes—
291C2×C42C23×C1111yescharacteristic
292#106—24no—
293#106C2×C4×C1118yes—
294C4⋊C8C2×C4×C1114yes—
295#102—22no—
296#102—22no—
297#102C2×C4×C1118yes—
298C4×C8—24no—
299C4×C8—22no—
300#95—22no—
301#95—22no—
302#95—22no—
303#95—21no—
304#95D4×C1112yes—
305C2×C11—82no—
306C2×C11#236211yescharacteristic
307C2×C11C2×C4×SD1611yescharacteristic
308C2×C11#294611yescharacteristic
309C2×C11#333511yescharacteristic
310C2×C11#334111yescharacteristic
311C2×C11#336011yescharacteristic
312C2×C11#336211yescharacteristic
313C24—21no—
314C2×Q8—24no—
315C2×Q8—81no—
316C2×Q8—81no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4C22×C4×C1112yes—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4C2×D4×C1112yes—
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C24×C1111yescharacteristic
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8C22×C4×C1114yes—
344C2×C8C11×#4112yes—
345C4⋊C4—24no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—81no—
356C4⋊C4—82no—
357C4⋊C4C11×SD1614yes—
358C4⋊C4C22×C4×C1114yes—
359C4⋊C4C22×C4×C1112yes—
360C4⋊C4C11×#4112yes—
361C22⋊C4—24no—
362C22⋊C4—44no—
363C22⋊C4—82no—
364C42—22no—
365C42—22no—
366C42—44no—
367C42—42no—
368C42—82no—
369C42C22×C4×C1112yes—
370C42C11×#4112yes—
371C11#2306111yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C22×D4×C1111yescharacteristic
380Q8—84no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—48no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4C4×D4×C1112yes—
409C2×C4C4×D4×C1112yes—
410C2×C4C2×C11×SD1614yes—
411C2×C4C2×C11×SD1612yes—
412C2×C4C11×#13512yes—
413C2×C4C23×C4×C1111yescharacteristic
414C2×C4C2×C11×#4111yescharacteristic
415C2×C4C2×C11×#4111yescharacteristic
416C2×C4C2×C11×#4111yescharacteristic
417C2×C4C11×2−1+411yescharacteristic
418C2×C4C11×2−1+411yescharacteristic
419C8—24no—
420C8—22no—
421C8—41no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22C2×C4×D4×C1111yescharacteristic
430C22C11×#54711yescharacteristic
431C22C11×#54811yescharacteristic
432C22C22×C11×SD1611yescharacteristic
433C22C2×C11×#13511yescharacteristic
434C22C11×#57611yescharacteristic
435C22C11×#57711yescharacteristic
436C4—22no—
437C4—24no—
438C4—42no—
439C4—44no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—82no—
444C4C4×C11×SD1614yes—
445C4C4×C11×#4111yescharacteristic
446C4C11×#51911yescharacteristic
447C4C11×#55211yescharacteristic
448C4C11×#55611yescharacteristic
449C2—82no—
450C2C11×#236211yescharacteristic
451C2C2×C4×C11×SD1611yescharacteristic
452C2C11×#294611yescharacteristic
453C2C11×#333511yescharacteristic
454C2C11×#334111yescharacteristic
455C2C11×#336011yescharacteristic
456C2C11×#336211yescharacteristic
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
8. C11×#1920C2semidirect
9. C4×C11×#106C2semidirect
10. C8×C11×C4⋊C4C2semidirect
15. C11×#476C4semidirect
85. #23061C11direct (N × H)
145. #2369C2×C11semidirect
147. #1990C2×C11semidirect
148. #1948C2×C11semidirect
151. #1920C2×C11semidirect
152. C4×#106C2×C11semidirect
153. C8×C4⋊C4C2×C11semidirect
208. #476C4×C11semidirect
371. C11#23061direct (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
C11×#23542
C11×#19902
C11×#19482
C11×#19342
C11×#19262
C11×#19202
C4×C11×#1062
C8×C11×C4⋊C42
C4×C11×#1022
#2306111