Finite Group Databasebeta

← C11×#21525 #14598718

Subgroups — C11×#21525 #14598718

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
3C2×C11×#405C211yesmaximal, characteristic
4C11×#2323C212yesmaximal
5C11×#1969C211yesmaximal, characteristic, complemented
6C11×#1942C211yesmaximal, characteristic, complemented
7C11×#1935C212yesmaximal, complemented
8C11×#1894C212yesmaximal
9C11×#1808C211yesmaximal, characteristic
10C4×C11×#107C211yesmaximal, characteristic, complemented
11C11×#1763C212yesmaximal, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117C2211yescharacteristic
18C11×#467C418yescomplemented
19C4×C11×Q16—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C11×#405—24no—
27C2×C11×#97C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#391C2212yes—
32C11×#389—22no—
33C11×#389C2212yes—
34C11×#388—22no—
35C11×#388—22no—
36C11×#387—22no—
37C11×#380C2212yes—
38C4×C11×C4⋊C4C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11C2×C414yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8C2×C418yes—
59C4×Q8×C11—24no—
60C4×Q8×C11—24no—
61C11×#117—22no—
62C11×#117—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#107—22no—
80C11×#107—22no—
81C11×#107C2×C414yes—
82C11×#103—24no—
83C11×#103—24no—
84C11×#103C2×C418yes—
85C11×#97—22no—
86C11×#97—22no—
87C4×C8×C11—22no—
88C4×C8×C11D414yes—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94#21525C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C22×C414yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C11×Q16—28no—
119C11×M16—28no—
120C2×C8×C11—28no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C22×C412yes—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11C2×D412yes—
131C2×C8×C11#4112yes—
132C2×C8×C11#4112yes—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—82no—
143C11×C4⋊C4C22×C414yes—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—82no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—44no—
151C42×C11—82no—
152C42×C11C2×D412yes—
153C42×C11#4112yes—
154C2×#467C2×C1111yescharacteristic
155C2×C4×Q16C2×C1111yescharacteristic, complemented
156C2×#405C2×C1111yescharacteristic
157#2323C2×C1112yes—
158#1969C2×C1111yescharacteristic, complemented
159#1942C2×C1111yescharacteristic, complemented
160#1935C2×C1112yescomplemented
161#1894C2×C1112yes—
162#1808C2×C1111yescharacteristic
163C4×#107C2×C1111yescharacteristic, complemented
164#1763C2×C1112yescomplemented
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11C4×D412yes—
172C23×C11C22×D411yescharacteristic
173Q8×C11—24no—
174Q8×C11—24no—
175Q8×C11—42no—
176Q8×C11—42no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11C4×D412yes—
206C2×C4×C11#12112yes—
207C2×C4×C11#12112yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C8×C11—22no—
215C8×C11—22no—
216C8×C11—22no—
217C8×C11C4×D414yes—
218C22×Q16C22×C1111yescharacteristic
219C22×M16C22×C1111yescharacteristic
220C23×C8C22×C1111yescharacteristic
221C2×C22⋊Q8C22×C1112yes—
222C2×C4×Q8C22×C1112yes—
223C2×#117C22×C1111yescharacteristic
224#467C4×C1118yescomplemented
225C4×Q16—24no—
226C2×#107C22×C1111yescharacteristic
227C2×#107C22×C1111yescharacteristic
228C2×#107C22×C1111yescharacteristic
229C2×#103C22×C1112yes—
230C2×#103C22×C1112yes—
231C2×#103C22×C1112yes—
232#405—24no—
233C2×#97C22×C1111yescharacteristic
234C2×#97C22×C1111yescharacteristic
235C2×C4×C8C22×C1111yescharacteristic
236C2×C4×C8C22×C1111yescharacteristic
237#391C22×C1112yes—
238#389—22no—
239#389C22×C1112yes—
240#388—22no—
241#388—22no—
242#387—22no—
243#380C22×C1112yes—
244C4×C4⋊C4C22×C1112yes—
245#340C22×C1112yes—
246#340C22×C1112yes—
247#340C22×C1112yes—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—41no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11C2×C4×D411yescharacteristic
256C22×C11C2×#12111yescharacteristic
257C22×C11#53211yescharacteristic
258C22×C11#57611yescharacteristic
259C22×C11#57811yescharacteristic
260C22×C11#57811yescharacteristic
261C22×C11#57811yescharacteristic
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—44no—
266C4×C11—41no—
267C4×C11—41no—
268C4×C11—44no—
269C4×C11—82no—
270C4×C11—82no—
271C4×C11C2×C4×D411yescharacteristic
272C4×C11C4×#4111yescharacteristic
273C4×C11#52511yescharacteristic
274C4×C11#52911yescharacteristic
275C22×Q8C23×C1112yes—
276C23×C4C23×C1111yescharacteristic
277C2×Q16—22no—
278C2×Q16—22no—
279C2×Q16C2×C4×C1114yes—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8C2×C4×C1114yes—
286C22×C8C23×C1111yescharacteristic
287C22×C8C23×C1111yescharacteristic
288C22×C8C23×C1111yescharacteristic
289C22×C8C23×C1111yescharacteristic
290C22⋊Q8—24no—
291C22⋊Q8C2×C4×C1118yes—
292C4×Q8—24no—
293C4×Q8—24no—
294#117—22no—
295#117—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4D4×C1111yescharacteristic
300C2×C4⋊C4D4×C1111yescharacteristic
301C2×C4⋊C4C23×C1112yes—
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1112yes—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4D4×C1111yescharacteristic
307C2×C22⋊C4D4×C1111yescharacteristic
308C2×C42—22no—
309C2×C42—22no—
310C2×C42C23×C1111yescharacteristic
311C2×C42C23×C1111yescharacteristic
312#107—22no—
313#107—22no—
314#107C2×C4×C1114yes—
315#103—24no—
316#103—24no—
317#103C2×C4×C1118yes—
318#97—22no—
319#97—22no—
320C4×C8—22no—
321C4×C8D4×C1114yes—
322#95—22no—
323#95—22no—
324#95—22no—
325#95—22no—
326#95—22no—
327C2×C11—42no—
328C2×C11C4×#12111yescharacteristic
329C2×C11#295011yescharacteristic
330C2×C11#295111yescharacteristic
331C2×C11#305911yescharacteristic
332C2×C11#306111yescharacteristic
333C2×C11#317511yescharacteristic
334C2×C11#317711yescharacteristic
335C24C2×D4×C1111yescharacteristic
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8C22×C4×C1114yes—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4C22×C4×C1112yes—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C2×D4×C1111yescharacteristic
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C11×#4112yes—
357C22×C4C24×C1111yescharacteristic
358Q16—28no—
359M16—28no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—28no—
367C2×C8C22×C4×C1112yes—
368C2×C8C22×C4×C1112yes—
369C2×C8C2×D4×C1112yes—
370C2×C8C2×D4×C1112yes—
371C2×C8C11×#4112yes—
372C2×C8C11×#4112yes—
373C4⋊C4—28no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—44no—
382C4⋊C4—82no—
383C4⋊C4C22×C4×C1114yes—
384C22⋊C4—28no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—82no—
388C42—21no—
389C42—21no—
390C42—44no—
391C42—82no—
392C42C2×D4×C1112yes—
393C42C11×#4112yes—
394C11#2152511yescharacteristic, direct product factor, Sylow
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23C4×D4×C1112yes—
402C23C22×D4×C1111yescharacteristic
403Q8—24no—
404Q8—24no—
405Q8—42no—
406Q8—42no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4C4×D4×C1112yes—
436C2×C4C11×#12112yes—
437C2×C4C11×#12112yes—
438C2×C4C23×C4×C1111yescharacteristic
439C2×C4C22×D4×C1111yescharacteristic
440C2×C4C2×C11×#4111yescharacteristic
441C2×C4C2×C11×#4111yescharacteristic
442C2×C4C2×C11×#4111yescharacteristic
443C2×C4C2×C11×#4111yescharacteristic
444C8—22no—
445C8—22no—
446C8—22no—
447C8C4×D4×C1114yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22C2×C4×D4×C1111yescharacteristic
456C22C2×C11×#12111yescharacteristic
457C22C11×#53211yescharacteristic
458C22C11×#57611yescharacteristic
459C22C11×#57811yescharacteristic
460C22C11×#57811yescharacteristic
461C22C11×#57811yescharacteristic
462C4—22no—
463C4—22no—
464C4—22no—
465C4—44no—
466C4—41no—
467C4—41no—
468C4—44no—
469C4—82no—
470C4—82no—
471C4C2×C4×D4×C1111yescharacteristic
472C4C4×C11×#4111yescharacteristic
473C4C11×#52511yescharacteristic
474C4C11×#52911yescharacteristic
475C2—42no—
476C2C4×C11×#12111yescharacteristic
477C2C11×#295011yescharacteristic
478C2C11×#295111yescharacteristic
479C2C11×#305911yescharacteristic
480C2C11×#306111yescharacteristic
481C2C11×#317511yescharacteristic
482C2C11×#317711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×Q16C2semidirect
5. C11×#1969C2semidirect
6. C11×#1942C2semidirect
7. C11×#1935C2semidirect
10. C4×C11×#107C2semidirect
11. C11×#1763C2semidirect
18. C11×#467C4semidirect
94. #21525C11direct (N × H)
155. C2×C4×Q16C2×C11semidirect
158. #1969C2×C11semidirect
159. #1942C2×C11semidirect
160. #1935C2×C11semidirect
163. C4×#107C2×C11semidirect
164. #1763C2×C11semidirect
224. #467C4×C11semidirect
394. C11#21525direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C4×C11×Q162
C2×C11×#4052
C11×#23232
C11×#19692
C11×#19422
C11×#19352
C11×#18942
C11×#18082
C4×C11×#1072
C11×#17632
#2152511