Finite Group Databasebeta

← C11×#19260 #14596453

Subgroups — C11×#19260 #14596453

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3167C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C11×#3037C211yesmaximal, characteristic
4C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
5C11×#1680C212yesmaximal, complemented
6C11×#1678C212yesmaximal, complemented
7C11×#1672C212yesmaximal, complemented
8C11×#1666C212yesmaximal, complemented
9C11×#1566C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic
12C2×C11×#137—21no—
13C11×#533C2211yescharacteristic
14C11×#532C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#498C2211yescharacteristic
17C11×#492C2211yescharacteristic
18C11×#487C2211yescharacteristic
19C11×#486C2211yescharacteristic
20C11×#479—22no—
21C11×#477C2212yes—
22C11×#475C2212yes—
23C11×#465—21no—
24C11×#465—21no—
25C11×#464—22no—
26C11×#462C2212yes—
27C11×#460C2212yes—
28C8×Q8×C11—21no—
29C8×Q8×C11—21no—
30C8×Q8×C11C2212yes—
31C8×Q8×C11C2212yes—
32C4×C11×SD16—21no—
33C4×C11×SD16—21no—
34C11×#428—21no—
35C11×#423C2211yescharacteristic
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8—21no—
38C2×C11×C4⋊C8C2211yescharacteristic
39C11×#419—21no—
40C11×#417—21no—
41C2×C4×C8×C11—21no—
42C2×C4×C8×C11C2211yescharacteristic
43C11×#334C2212yes—
44C11×#334C2212yes—
45C11×#333C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11D411yescharacteristic
51C11×#137—44no—
52C2×C11×Q16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C22×C8×C11—21no—
59C22×C8×C11D411yescharacteristic
60C22×C8×C11D411yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127C2311yescharacteristic
65C11×#125—21no—
66C11×#124—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×#121—21no—
70C11×#121—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11D412yes—
76C4×Q8×C11C2312yes—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C11×#117—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#107—22no—
85C11×#106—21no—
86C11×#106—21no—
87C11×#106—22no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—22no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2312yes—
94C11×C4⋊C8C2312yes—
95C11×C4⋊C8C2312yes—
96C11×#103—22no—
97C11×#103—22no—
98C11×#103—21no—
99C11×#103—21no—
100C11×#103—22no—
101C11×#102—21no—
102C11×#102—21no—
103C11×#102—22no—
104C4×C8×C11—22no—
105C4×C8×C11—22no—
106C4×C8×C11D411yescharacteristic
107C4×C8×C11D411yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#19260C1111yesmaximal, characteristic, direct product factor, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11SD1614yescomplemented
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C11×Q16—44no—
131C11×SD16—42no—
132C11×SD16—42no—
133C11×SD16—44no—
134C11×M16—42no—
135C11×M16—42no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—41no—
141C2×C8×C11—42no—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—41no—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11#4111yescharacteristic
167C42×C11C2411yescharacteristic
168#3167C2×C1111yescharacteristic
169#3078C2×C1111yescharacteristic, complemented
170#3037C2×C1111yescharacteristic
171C2×C8×Q8C2×C1111yescharacteristic, complemented
172#1680C2×C1112yescomplemented
173#1678C2×C1112yescomplemented
174#1672C2×C1112yescomplemented
175#1666C2×C1112yescomplemented
176#1566C2×C1111yescharacteristic, complemented
177#1550C2×C1111yescharacteristic, complemented
178#1547C2×C1111yescharacteristic
179C23×C11—41no—
180C23×C11#12111yescharacteristic
181Q8×C11—22no—
182Q8×C11—24no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—81no—
188Q8×C11C2×SD1614yes—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—81no—
194D4×C11—82no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—82no—
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11C2×SD1612yes—
210C2×C4×C11#13512yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C8×C11—21no—
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—42no—
218C8×C11—42no—
219C8×C11—42no—
220C8×C11#13712yescomplemented
221C2×#137—21no—
222#533C22×C1111yescharacteristic
223#532C22×C1111yescharacteristic
224C2×C4×Q8C22×C1111yescharacteristic
225#498C22×C1111yescharacteristic
226#492C22×C1111yescharacteristic
227#487C22×C1111yescharacteristic
228#486C22×C1111yescharacteristic
229#479—22no—
230#477C22×C1112yes—
231#475C22×C1112yes—
232#465—21no—
233#465—21no—
234#464—22no—
235#462C22×C1112yes—
236#460C22×C1112yes—
237C8×Q8—21no—
238C8×Q8—21no—
239C8×Q8C22×C1112yes—
240C8×Q8C22×C1112yes—
241C4×SD16—21no—
242C4×SD16—21no—
243#428—21no—
244#423C22×C1111yescharacteristic
245#423C22×C1111yescharacteristic
246C2×C4⋊C8—21no—
247C2×C4⋊C8C22×C1111yescharacteristic
248#419—21no—
249#417—21no—
250C2×C4×C8—21no—
251C2×C4×C8C22×C1111yescharacteristic
252#334C22×C1112yes—
253#334C22×C1112yes—
254#333C22×C1112yes—
255#332C22×C1112yes—
256#332C22×C1112yes—
257#331C22×C1112yes—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11#46512yes—
264C22×C11C2×#12111yescharacteristic
265C4×C11—21no—
266C4×C11—24no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11#46512yes—
274C4×C11C22×SD1611yescharacteristic
275C4×C11C2×#13511yescharacteristic
276C4×C11C2×#13711yescharacteristic
277C4×C11#57511yescharacteristic
278C2×#41—21no—
279C22×Q8D4×C1111yescharacteristic
280#137—44no—
281C2×Q16—22no—
282C2×SD16—22no—
283C2×SD16—21no—
284C2×SD16—21no—
285C2×M16—21no—
286C2×M16—21no—
287C22×C8—21no—
288C22×C8D4×C1111yescharacteristic
289C22×C8D4×C1111yescharacteristic
290C4⋊Q8C23×C1111yescharacteristic
291C4⋊Q8C23×C1111yescharacteristic
292C4⋊Q8C23×C1111yescharacteristic
293#127C23×C1111yescharacteristic
294#125—21no—
295#124—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298#121—21no—
299#121—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8D4×C1112yes—
305C4×Q8C23×C1112yes—
306C4×D4—21no—
307C4×D4—21no—
308#117—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4D4×C1111yescharacteristic
311C2×C42—21no—
312C2×C42C23×C1111yescharacteristic
313#107—22no—
314#106—21no—
315#106—21no—
316#106—22no—
317C4⋊C8—22no—
318C4⋊C8—22no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8C23×C1112yes—
323C4⋊C8C23×C1112yes—
324C4⋊C8C23×C1112yes—
325#103—22no—
326#103—22no—
327#103—21no—
328#103—21no—
329#103—22no—
330#102—21no—
331#102—21no—
332#102—22no—
333C4×C8—22no—
334C4×C8—22no—
335C4×C8D4×C1111yescharacteristic
336C4×C8D4×C1111yescharacteristic
337C4×C8C23×C1111yescharacteristic
338C4×C8C23×C1111yescharacteristic
339C2×C11—22no—
340C2×C11—161no—
341C2×C11#303711yescharacteristic
342C2×C11C2×#46511yescharacteristic
343C2×C11#306711yescharacteristic
344#41—42no—
345#41—42no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8C11×SD1614yescomplemented
352C2×Q8C2×D4×C1112yes—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4C2×D4×C1111yescharacteristic
361C22×C4C2×D4×C1111yescharacteristic
362C22×C4C11×#4111yescharacteristic
363Q16—44no—
364SD16—42no—
365SD16—44no—
366SD16—42no—
367M16—42no—
368M16—42no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—41no—
374C2×C8—42no—
375C2×C8C2×D4×C1111yescharacteristic
376C2×C8C2×D4×C1111yescharacteristic
377C2×C8C2×D4×C1111yescharacteristic
378C2×C8C2×D4×C1111yescharacteristic
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4C2×D4×C1112yes—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C42—22no—
395C42—22no—
396C42—41no—
397C42C2×D4×C1111yescharacteristic
398C42C2×D4×C1111yescharacteristic
399C42C11×#4111yescharacteristic
400C42C24×C1111yescharacteristic
401C11#1926011yescharacteristic, direct product factor, Sylow
402C23—41no—
403C23C11×#12111yescharacteristic
404Q8—22no—
405Q8—24no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—81no—
411Q8C2×C11×SD1614yes—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—82no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4C11×#12111yescharacteristic
430C2×C4C11×#12111yescharacteristic
431C2×C4C11×#12111yescharacteristic
432C2×C4C2×C11×SD1612yes—
433C2×C4C11×#13512yes—
434C2×C4C22×D4×C1111yescharacteristic
435C2×C4C22×D4×C1111yescharacteristic
436C2×C4C2×C11×#4111yescharacteristic
437C8—21no—
438C8—21no—
439C8—21no—
440C8—42no—
441C8—42no—
442C8—42no—
443C8C11×#13712yescomplemented
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22C11×#46512yes—
450C22C2×C11×#12111yescharacteristic
451C4—21no—
452C4—24no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4C11×#46512yes—
460C4C22×C11×SD1611yescharacteristic
461C4C2×C11×#13511yescharacteristic
462C4C2×C11×#13711yescharacteristic
463C4C11×#57511yescharacteristic
464C2—22no—
465C2—161no—
466C2C11×#303711yescharacteristic
467C2C2×C11×#46511yescharacteristic
468C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
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
2. C11×#3078C2semidirect
4. C2×C8×Q8×C11C2semidirect
5. C11×#1680C2semidirect
6. C11×#1678C2semidirect
7. C11×#1672C2semidirect
8. C11×#1666C2semidirect
9. C11×#1566C2semidirect
10. C11×#1550C2semidirect
110. #19260C11direct (N × H)
118. C2×Q8×C11SD16semidirect
169. #3078C2×C11semidirect
171. C2×C8×Q8C2×C11semidirect
172. #1680C2×C11semidirect
173. #1678C2×C11semidirect
174. #1672C2×C11semidirect
175. #1666C2×C11semidirect
176. #1566C2×C11semidirect
177. #1550C2×C11semidirect
220. C8×C11#137semidirect
351. C2×Q8C11×SD16semidirect
401. C11#19260direct (N × H)
443. C8C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#31672
C11×#30782
C11×#30372
C2×C8×Q8×C112
C11×#16802
C11×#16782
C11×#16722
C11×#16662
C11×#15662
C11×#15502
C11×#15472
#1926011