Finite Group Databasebeta

← C11×#19415 #14596608

Subgroups — C11×#19415 #14596608

Order 2816.

640 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
1C11×#3229C211yesmaximal, characteristic, complemented
2C11×#3076C211yesmaximal, characteristic
3C11×#3039C211yesmaximal, characteristic
4C11×#2988C211yesmaximal, characteristic
5C11×#1680C212yesmaximal, complemented
6C11×#1679C212yesmaximal, complemented
7C11×#1672C212yesmaximal, complemented
8C11×#1671C212yesmaximal, complemented
9C11×#1570C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C2×C11×#332C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C11×#533C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C4×C11×#41C2211yescharacteristic
16C11×#498C2212yes—
17C11×#487C2212yes—
18C11×#483—22no—
19C11×#479—21no—
20C11×#478—21no—
21C11×#477C2211yescharacteristic
22C11×#476C2211yescharacteristic
23C11×#475—21no—
24C11×#475—21no—
25C11×#475C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#462—21no—
28C11×#462C2212yes—
29C11×#461—21no—
30C11×#461C2212yes—
31C8×Q8×C11C2212yes—
32C8×D4×C11—22no—
33C8×D4×C11C2212yes—
34C11×#431—21no—
35C11×#431C2211yescharacteristic
36C11×#427—21no—
37C11×#423C2211yescharacteristic
38C2×C11×C4⋊C8—21no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C11×#419—21no—
42C11×#416—21no—
43C11×#334C2212yes—
44C11×#334C2212yes—
45C11×#333C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11—21no—
51C11×#137—44no—
52C2×C11×Q16—22no—
53C2×C11×SD16—22no—
54C2×C11×M16—21no—
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C22×C8×C11—22no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#125—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11D411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11D411yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C11×#117—21no—
76C11×#117—21no—
77C11×#117D411yescharacteristic
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C11×#107—21no—
83C11×#107—21no—
84C11×#106—22no—
85C11×#106—22no—
86C11×#106—21no—
87C11×#106—21no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8D411yescharacteristic
94C11×C4⋊C8C2312yes—
95C11×C4⋊C8C2311yescharacteristic
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2312yes—
98C11×#103—21no—
99C11×#103—21no—
100C11×#103—22no—
101C11×#103—22no—
102C11×#103—22no—
103C11×#103—22no—
104C11×#102—21no—
105C11×#102—21no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8D412yes—
108C4×C8×C11—22no—
109C4×C8×C11C2312yes—
110#19415C1111yesmaximal, characteristic, direct product factor, Sylow
111C11×#41—22no—
112C11×#41SD1614yes—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—41no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D411yescharacteristic
120C2×D4×C11—21no—
121C2×D4×C11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C11×Q16—44no—
130C11×SD16—44no—
131C11×M16—42no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—42no—
137C2×C8×C11—81no—
138C2×C8×C11—82no—
139C2×C8×C11C2×D412yes—
140C2×C8×C11C2×D412yes—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4C2×D411yescharacteristic
154C11×C4⋊C4C2×D411yescharacteristic
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C11×C22⋊C4—41no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—41no—
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11#4111yescharacteristic
166C42×C11C2411yescharacteristic
167#3229C2×C1111yescharacteristic, complemented
168#3076C2×C1111yescharacteristic
169#3039C2×C1111yescharacteristic
170#2988C2×C1111yescharacteristic
171#1680C2×C1112yescomplemented
172#1679C2×C1112yescomplemented
173#1672C2×C1112yescomplemented
174#1671C2×C1112yescomplemented
175#1570C2×C1111yescharacteristic, complemented
176#1550C2×C1111yescharacteristic, complemented
177C2×#332C2×C1111yescharacteristic, complemented
178C23×C11—21no—
179C23×C11#12111yescharacteristic
180Q8×C11—21no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—81no—
186Q8×C11—82no—
187Q8×C11C2×SD1612yes—
188D4×C11—24no—
189D4×C11—21no—
190D4×C11C2×SD1612yes—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—24no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—81no—
204C2×C4×C11—82no—
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C2×SD1612yes—
209C2×C4×C11#13512yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C8×C11—22no—
214C8×C11—22no—
215C8×C11—42no—
216C8×C11—41no—
217C8×C11—41no—
218C8×C11—42no—
219C2×#137—21no—
220#533C22×C1111yescharacteristic
221C2×C4⋊Q8C22×C1111yescharacteristic
222C4×#41C22×C1111yescharacteristic
223#498C22×C1112yes—
224#487C22×C1112yes—
225#483—22no—
226#479—21no—
227#478—21no—
228#477C22×C1111yescharacteristic
229#476C22×C1111yescharacteristic
230#475—21no—
231#475—21no—
232#475C22×C1111yescharacteristic
233#474C22×C1111yescharacteristic
234#462—21no—
235#462C22×C1112yes—
236#461—21no—
237#461C22×C1112yes—
238C8×Q8C22×C1112yes—
239C8×D4—22no—
240C8×D4C22×C1112yes—
241#431—21no—
242#431C22×C1111yescharacteristic
243#427—21no—
244#423C22×C1111yescharacteristic
245C2×C4⋊C8—21no—
246C2×C4⋊C8C22×C1111yescharacteristic
247C2×C4⋊C8C22×C1111yescharacteristic
248#419—21no—
249#416—21no—
250#334C22×C1112yes—
251#334C22×C1112yes—
252#333C22×C1112yes—
253#332C22×C1112yes—
254#332C22×C1112yes—
255#332C22×C1112yes—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—22no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11#46512yes—
262C22×C11C2×#12111yescharacteristic
263C4×C11—21no—
264C4×C11—22no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—41no—
268C4×C11—41no—
269C4×C11—81no—
270C4×C11—82no—
271C4×C11—81no—
272C4×C11#46512yes—
273C4×C11C22×SD1611yescharacteristic
274C4×C11C2×#13511yescharacteristic
275C4×C11#57711yescharacteristic
276C4×C11#57811yescharacteristic
277C2×#41D4×C1111yescharacteristic
278C22×Q8—21no—
279#137—44no—
280C2×Q16—22no—
281C2×SD16—22no—
282C2×M16—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—22no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8C23×C1112yes—
290C4⋊Q8C23×C1111yescharacteristic
291C4⋊Q8C23×C1111yescharacteristic
292#125—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8D4×C1111yescharacteristic
298C4×Q8C23×C1111yescharacteristic
299C4×D4—21no—
300C4×D4—21no—
301C4×D4D4×C1111yescharacteristic
302C4×D4C23×C1111yescharacteristic
303#117—21no—
304#117—21no—
305#117D4×C1111yescharacteristic
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C42—21no—
309C2×C42C23×C1111yescharacteristic
310#107—21no—
311#107—21no—
312#106—22no—
313#106—22no—
314#106—21no—
315#106—21no—
316C4⋊C8—22no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8D4×C1111yescharacteristic
321C4⋊C8D4×C1111yescharacteristic
322C4⋊C8C23×C1112yes—
323C4⋊C8C23×C1111yescharacteristic
324C4⋊C8C23×C1111yescharacteristic
325C4⋊C8C23×C1112yes—
326#103—21no—
327#103—21no—
328#103—22no—
329#103—22no—
330#103—22no—
331#103—22no—
332#102—21no—
333#102—21no—
334C22⋊C8—22no—
335C22⋊C8D4×C1112yes—
336C4×C8—22no—
337C4×C8C23×C1112yes—
338C2×C11—22no—
339C2×C11—42no—
340C2×C11#304611yescharacteristic
341C2×C11C2×#46511yescharacteristic
342C2×C11#306911yescharacteristic
343#41—22no—
344#41C11×SD1614yes—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—41no—
349C2×Q8—42no—
350C2×Q8—42no—
351C2×Q8C2×D4×C1111yescharacteristic
352C2×D4—21no—
353C2×D4C2×D4×C1111yescharacteristic
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—41no—
358C22×C4C2×D4×C1111yescharacteristic
359C22×C4C2×D4×C1111yescharacteristic
360C22×C4C11×#4111yescharacteristic
361Q16—44no—
362SD16—44no—
363M16—42no—
364C2×C8—22no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—22no—
368C2×C8—42no—
369C2×C8—82no—
370C2×C8—81no—
371C2×C8C2×D4×C1112yes—
372C2×C8C2×D4×C1112yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C2×D4×C1111yescharacteristic
386C4⋊C4C2×D4×C1111yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—41no—
391C42—21no—
392C42—21no—
393C42—21no—
394C42—41no—
395C42C2×D4×C1111yescharacteristic
396C42C2×D4×C1111yescharacteristic
397C42C11×#4111yescharacteristic
398C42C24×C1111yescharacteristic
399C11#1941511yescharacteristic, direct product factor, Sylow
400C23—21no—
401C23C11×#12111yescharacteristic
402Q8—21no—
403Q8—42no—
404Q8—42no—
405Q8—41no—
406Q8—41no—
407Q8—81no—
408Q8—82no—
409Q8C2×C11×SD1612yes—
410D4—24no—
411D4—21no—
412D4C2×C11×SD1612yes—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—24no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—81no—
426C2×C4—82no—
427C2×C4C11×#12111yescharacteristic
428C2×C4C11×#12111yescharacteristic
429C2×C4C11×#12111yescharacteristic
430C2×C4C2×C11×SD1612yes—
431C2×C4C11×#13512yes—
432C2×C4C22×D4×C1111yescharacteristic
433C2×C4C22×D4×C1111yescharacteristic
434C2×C4C2×C11×#4111yescharacteristic
435C8—22no—
436C8—22no—
437C8—42no—
438C8—41no—
439C8—41no—
440C8—42no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22C11×#46512yes—
447C22C2×C11×#12111yescharacteristic
448C4—21no—
449C4—22no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—82no—
456C4—81no—
457C4C11×#46512yes—
458C4C22×C11×SD1611yescharacteristic
459C4C2×C11×#13511yescharacteristic
460C4C11×#57711yescharacteristic
461C4C11×#57811yescharacteristic
462C2—22no—
463C2—42no—
464C2C11×#304611yescharacteristic
465C2C2×C11×#46511yescharacteristic
466C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3229C2semidirect
5. C11×#1680C2semidirect
6. C11×#1679C2semidirect
7. C11×#1672C2semidirect
8. C11×#1671C2semidirect
9. C11×#1570C2semidirect
10. C11×#1550C2semidirect
11. C2×C11×#332C2semidirect
110. #19415C11direct (N × H)
167. #3229C2×C11semidirect
171. #1680C2×C11semidirect
172. #1679C2×C11semidirect
173. #1672C2×C11semidirect
174. #1671C2×C11semidirect
175. #1570C2×C11semidirect
176. #1550C2×C11semidirect
177. C2×#332C2×C11semidirect
399. C11#19415direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#30762
C11×#30392
C11×#29882
C11×#16802
C11×#16792
C11×#16722
C11×#16712
C11×#15702
C11×#15502
C2×C11×#3322
#1941511