Finite Group Databasebeta

← C11×#18924 #14596117

Subgroups — C11×#18924 #14596117

Order 2816.

878 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
1C11×#3502C211yesmaximal, characteristic
2C11×#3229C211yesmaximal, characteristic
3C11×#3229C211yesmaximal, characteristic
4C2×C11×#462C211yesmaximal, characteristic
5C11×#1653C214yesmaximal, complemented
6C11×#1645C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic
8C11×#1481C211yesmaximal, characteristic
9C11×#1479C211yesmaximal, characteristic
10C22×C11×Q16—21no—
11Q82×C11—21no—
12Q82×C11C2212yes—
13C11×#557—21no—
14C11×#557—22no—
15C11×#557—22no—
16C11×#557C2212yes—
17C11×#544—22no—
18C11×#544—21no—
19C11×#533—22no—
20C11×#533C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8C2211yescharacteristic
23C11×#519—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#498—21no—
26C11×#498C2212yes—
27C11×#487—21no—
28C11×#487C2212yes—
29C11×#483—22no—
30C11×#483—22no—
31C11×#475—22no—
32C11×#475C2214yes—
33C11×#462—22no—
34C11×#462C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#333C2212yes—
40C11×#332C2212yes—
41C11×Q8⋊C8C2214yes—
42C11×Q8⋊C8C2214yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C2×C11×Q16—24no—
46C2×C11×Q16—44no—
47C22×C8×C11—21no—
48C11×C4⋊Q8—24no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2312yes—
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×#125—24no—
63C11×#125—24no—
64C11×#125—22no—
65C11×#125—24no—
66C11×#125—22no—
67C11×#125—21no—
68C11×#125—21no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8D412yes—
73C11×C22⋊Q8D412yes—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—24no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11D412yes—
86C4×Q8×C11D412yes—
87C4×Q8×C11C2312yes—
88C4×Q8×C11C2312yes—
89C11×#117—24no—
90C11×#117—21no—
91C11×#117—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C11×#106—24no—
99C11×#106—24no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18924C1111yesmaximal, characteristic, direct product factor, Sylow
112C2×Q8×C11—24no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×Q8×C11SD1614yes—
122C2×Q8×C11C2×D412yes—
123C2×Q8×C11C2×D412yes—
124C2×Q8×C11C2×D412yes—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C11×Q16—48no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—42no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C42×C11—24no—
164C42×C11—24no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173#3502C2×C1111yescharacteristic
174#3229C2×C1111yescharacteristic
175#3229C2×C1111yescharacteristic
176C2×#462C2×C1111yescharacteristic
177#1653C2×C1114yescomplemented
178#1645C2×C1114yescomplemented
179#1542C2×C1111yescharacteristic
180#1481C2×C1111yescharacteristic
181#1479C2×C1111yescharacteristic
182C23×C11#12011yescharacteristic
183Q8×C11—22no—
184Q8×C11—24no—
185Q8×C11—24no—
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—81no—
191Q8×C11—84no—
192Q8×C11—82no—
193Q8×C11C2×SD1614yes—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—81no—
205C2×C4×C11—82no—
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12011yescharacteristic
208C2×C4×C11#12011yescharacteristic
209C2×C4×C11C2×SD1612yes—
210C2×C4×C11#13712yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C8×C11—42no—
215C8×C11—42no—
216C8×C11—42no—
217C22×Q16—21no—
218Q82—21no—
219Q82C22×C1112yes—
220#557—21no—
221#557—22no—
222#557—22no—
223#557C22×C1112yes—
224#544—22no—
225#544—21no—
226#533—22no—
227#533C22×C1111yescharacteristic
228#533C22×C1111yescharacteristic
229C2×C4⋊Q8C22×C1111yescharacteristic
230#519—21no—
231C2×C4×Q8C22×C1111yescharacteristic
232#498—21no—
233#498C22×C1112yes—
234#487—21no—
235#487C22×C1112yes—
236#483—22no—
237#483—22no—
238#475—22no—
239#475C22×C1114yes—
240#462—22no—
241#462C22×C1114yes—
242#431C22×C1111yescharacteristic
243#431C22×C1111yescharacteristic
244C2×C4⋊C8C22×C1111yescharacteristic
245C2×#103—21no—
246#333C22×C1112yes—
247#332C22×C1112yes—
248Q8⋊C8C22×C1114yes—
249Q8⋊C8C22×C1114yes—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11#44812yes—
253C22×C11C2×#12011yescharacteristic
254C4×C11—24no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—82no—
264C4×C11#44812yes—
265C4×C11C22×SD1611yescharacteristic
266C4×C11C2×#13711yescharacteristic
267C4×C11#57812yes—
268C22×Q8—21no—
269C22×Q8D4×C1111yescharacteristic
270C2×Q16—24no—
271C2×Q16—44no—
272C22×C8—21no—
273C4⋊Q8—24no—
274C4⋊Q8—22no—
275C4⋊Q8—22no—
276C4⋊Q8—24no—
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8D4×C1111yescharacteristic
283C4⋊Q8D4×C1111yescharacteristic
284C4⋊Q8C23×C1112yes—
285C4⋊Q8C23×C1111yescharacteristic
286C4⋊Q8C23×C1111yescharacteristic
287#125—24no—
288#125—24no—
289#125—22no—
290#125—24no—
291#125—22no—
292#125—21no—
293#125—21no—
294C22⋊Q8—24no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8D4×C1112yes—
298C22⋊Q8D4×C1112yes—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—24no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8D4×C1112yes—
311C4×Q8D4×C1112yes—
312C4×Q8C23×C1112yes—
313C4×Q8C23×C1112yes—
314#117—24no—
315#117—21no—
316#117—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4D4×C1111yescharacteristic
321C2×C42—21no—
322C2×C42C23×C1111yescharacteristic
323#106—24no—
324#106—24no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8C23×C1112yes—
328C4⋊C8C23×C1112yes—
329#103—24no—
330#103—24no—
331#103—24no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C4×C8—21no—
335C4×C8C23×C1112yes—
336C2×C11—22no—
337C2×C11C2×#44811yescharacteristic
338C2×C11#301111yescharacteristic
339C2×C11#302211yescharacteristic
340C2×Q8—24no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—41no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8C11×SD1614yes—
350C2×Q8C2×D4×C1112yes—
351C2×Q8C2×D4×C1112yes—
352C2×Q8C2×D4×C1112yes—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1111yescharacteristic
358C22×C4C2×D4×C1111yescharacteristic
359Q16—48no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—42no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4C2×D4×C1112yes—
387C4⋊C4C2×D4×C1112yes—
388C4⋊C4C2×D4×C1112yes—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C42—24no—
392C42—24no—
393C42—22no—
394C42—22no—
395C42—22no—
396C42—22no—
397C42C2×D4×C1111yescharacteristic
398C42C2×D4×C1111yescharacteristic
399C42C2×D4×C1111yescharacteristic
400C42C24×C1111yescharacteristic
401C11#1892411yescharacteristic, direct product factor, Sylow
402C23C11×#12011yescharacteristic
403Q8—22no—
404Q8—24no—
405Q8—24no—
406Q8—42no—
407Q8—42no—
408Q8—42no—
409Q8—42no—
410Q8—81no—
411Q8—84no—
412Q8—82no—
413Q8C2×C11×SD1614yes—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—81no—
425C2×C4—82no—
426C2×C4C11×#12011yescharacteristic
427C2×C4C11×#12011yescharacteristic
428C2×C4C11×#12011yescharacteristic
429C2×C4C2×C11×SD1612yes—
430C2×C4C11×#13712yes—
431C2×C4C22×D4×C1111yescharacteristic
432C2×C4C22×D4×C1111yescharacteristic
433C2×C4C22×D4×C1111yescharacteristic
434C8—42no—
435C8—42no—
436C8—42no—
437C22—21no—
438C22—21no—
439C22C11×#44812yes—
440C22C2×C11×#12011yescharacteristic
441C4—24no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4C11×#44812yes—
452C4C22×C11×SD1611yescharacteristic
453C4C2×C11×#13711yescharacteristic
454C4C11×#57812yes—
455C2—22no—
456C2C2×C11×#44811yescharacteristic
457C2C11×#301111yescharacteristic
458C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#120
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
5. C11×#1653C2semidirect
6. C11×#1645C2semidirect
111. #18924C11direct (N × H)
177. #1653C2×C11semidirect
178. #1645C2×C11semidirect
401. C11#18924direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#32292
C2×C11×#4622
C11×#16532
C11×#16452
C11×#15422
C11×#14812
C11×#14792
#1892411