Finite Group Databasebeta

← C11×#18925 #14596118

Subgroups — C11×#18925 #14596118

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3230C211yesmaximal, characteristic
3C11×#3209C211yesmaximal, characteristic
4C2×C11×#475C211yesmaximal, characteristic
5C11×#1648C214yesmaximal, complemented
6C11×#1645C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic
8C11×#1481C211yesmaximal, characteristic
9C11×#1479C211yesmaximal, characteristic
10Q82×C11—21no—
11Q82×C11C2212yes—
12C11×#557—21no—
13C11×#557—22no—
14C11×#557—22no—
15C11×#557C2212yes—
16C11×#544—22no—
17C11×#544—21no—
18C11×#533—22no—
19C11×#533C2211yescharacteristic
20C11×#533C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#519—21no—
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#500C2212yes—
25C11×#494—21no—
26C11×#487—21no—
27C11×#487C2212yes—
28C11×#484—22no—
29C11×#477—22no—
30C11×#475—22no—
31C11×#475C2214yes—
32C11×#462C2214yes—
33C11×#451—22no—
34C11×#431C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C2×C11×#106—21no—
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—
46C22×C8×C11—21no—
47C11×C4⋊Q8—24no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—24no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8C2312yes—
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×#125—24no—
62C11×#125—24no—
63C11×#125—22no—
64C11×#125—24no—
65C11×#125—22no—
66C11×#125—21no—
67C11×#125—21no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8D412yes—
72C11×C22⋊Q8D412yes—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—24no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11D412yes—
85C4×Q8×C11D412yes—
86C4×Q8×C11C2312yes—
87C4×Q8×C11C2312yes—
88C11×#117—24no—
89C11×#117—21no—
90C11×#117—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C11×#107—24no—
98C11×#106—24no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2312yes—
102C11×C4⋊C8C2312yes—
103C11×#103—24no—
104C11×#103—24no—
105C11×#103—24no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2312yes—
110#18925C1111yesmaximal, characteristic, direct product factor, Sylow
111C2×Q8×C11—24no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—41no—
118C2×Q8×C11—82no—
119C2×Q8×C11Q1614yescomplemented
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11C2×D412yes—
122C2×Q8×C11C2×D412yes—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C11×Q16—84no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—42no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4C2×D412yes—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C42×C11—24no—
162C42×C11—24no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2411yescharacteristic
171#3502C2×C1111yescharacteristic
172#3230C2×C1111yescharacteristic
173#3209C2×C1111yescharacteristic
174C2×#475C2×C1111yescharacteristic
175#1648C2×C1114yescomplemented
176#1645C2×C1114yescomplemented
177#1542C2×C1111yescharacteristic
178#1481C2×C1111yescharacteristic
179#1479C2×C1111yescharacteristic
180C23×C11#12011yescharacteristic
181Q8×C11—22no—
182Q8×C11—24no—
183Q8×C11—24no—
184Q8×C11—42no—
185Q8×C11—42no—
186Q8×C11—44no—
187Q8×C11—81no—
188Q8×C11—82no—
189Q8×C11—84no—
190Q8×C11C2×Q1614yes—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—81no—
202C2×C4×C11—82no—
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11C2×Q1612yes—
207C2×C4×C11#13712yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C8×C11—42no—
212C8×C11—42no—
213C8×C11—42no—
214Q82—21no—
215Q82C22×C1112yes—
216#557—21no—
217#557—22no—
218#557—22no—
219#557C22×C1112yes—
220#544—22no—
221#544—21no—
222#533—22no—
223#533C22×C1111yescharacteristic
224#533C22×C1111yescharacteristic
225C2×C4⋊Q8C22×C1111yescharacteristic
226#519—21no—
227C2×C4×Q8C22×C1111yescharacteristic
228#500C22×C1112yes—
229#494—21no—
230#487—21no—
231#487C22×C1112yes—
232#484—22no—
233#477—22no—
234#475—22no—
235#475C22×C1114yes—
236#462C22×C1114yes—
237#451—22no—
238#431C22×C1111yescharacteristic
239#431C22×C1111yescharacteristic
240C2×#106—21no—
241C2×C4⋊C8C22×C1111yescharacteristic
242C2×#103—21no—
243#333C22×C1112yes—
244#332C22×C1112yes—
245Q8⋊C8C22×C1114yes—
246Q8⋊C8C22×C1114yes—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11#45112yes—
250C22×C11C2×#12011yescharacteristic
251C4×C11—24no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—82no—
261C4×C11#45112yes—
262C4×C11C22×Q1611yescharacteristic
263C4×C11C2×#13711yescharacteristic
264C4×C11#57712yes—
265C22×Q8—21no—
266C22×Q8D4×C1111yescharacteristic
267C2×Q16—24no—
268C22×C8—21no—
269C4⋊Q8—24no—
270C4⋊Q8—22no—
271C4⋊Q8—22no—
272C4⋊Q8—24no—
273C4⋊Q8—22no—
274C4⋊Q8—22no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8D4×C1111yescharacteristic
279C4⋊Q8D4×C1111yescharacteristic
280C4⋊Q8C23×C1112yes—
281C4⋊Q8C23×C1111yescharacteristic
282C4⋊Q8C23×C1111yescharacteristic
283#125—24no—
284#125—24no—
285#125—22no—
286#125—24no—
287#125—22no—
288#125—21no—
289#125—21no—
290C22⋊Q8—24no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8D4×C1112yes—
294C22⋊Q8D4×C1112yes—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—24no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D4×C1112yes—
307C4×Q8D4×C1112yes—
308C4×Q8C23×C1112yes—
309C4×Q8C23×C1112yes—
310#117—24no—
311#117—21no—
312#117—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4D4×C1111yescharacteristic
317C2×C42—21no—
318C2×C42C23×C1111yescharacteristic
319#107—24no—
320#106—24no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8C23×C1112yes—
324C4⋊C8C23×C1112yes—
325#103—24no—
326#103—24no—
327#103—24no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C4×C8—21no—
331C4×C8C23×C1112yes—
332C2×C11—22no—
333C2×C11C2×#45111yescharacteristic
334C2×C11#301011yescharacteristic
335C2×C11#302211yescharacteristic
336C2×Q8—24no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—41no—
343C2×Q8—82no—
344C2×Q8C11×Q1614yescomplemented
345C2×Q8C2×D4×C1112yes—
346C2×Q8C2×D4×C1112yes—
347C2×Q8C2×D4×C1112yes—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1111yescharacteristic
354Q16—84no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—42no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4C2×D4×C1112yes—
382C4⋊C4C2×D4×C1112yes—
383C4⋊C4C2×D4×C1112yes—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C42—24no—
387C42—24no—
388C42—22no—
389C42—22no—
390C42—22no—
391C42—22no—
392C42C2×D4×C1111yescharacteristic
393C42C2×D4×C1111yescharacteristic
394C42C2×D4×C1111yescharacteristic
395C42C24×C1111yescharacteristic
396C11#1892511yescharacteristic, direct product factor, Sylow
397C23C11×#12011yescharacteristic
398Q8—22no—
399Q8—24no—
400Q8—24no—
401Q8—42no—
402Q8—42no—
403Q8—44no—
404Q8—81no—
405Q8—82no—
406Q8—84no—
407Q8C2×C11×Q1614yes—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—81no—
419C2×C4—82no—
420C2×C4C11×#12011yescharacteristic
421C2×C4C11×#12011yescharacteristic
422C2×C4C11×#12011yescharacteristic
423C2×C4C2×C11×Q1612yes—
424C2×C4C11×#13712yes—
425C2×C4C22×D4×C1111yescharacteristic
426C2×C4C22×D4×C1111yescharacteristic
427C2×C4C22×D4×C1111yescharacteristic
428C8—42no—
429C8—42no—
430C8—42no—
431C22—21no—
432C22—21no—
433C22C11×#45112yes—
434C22C2×C11×#12011yescharacteristic
435C4—24no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—42no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—82no—
445C4C11×#45112yes—
446C4C22×C11×Q1611yescharacteristic
447C4C2×C11×#13711yescharacteristic
448C4C11×#57712yes—
449C2—22no—
450C2C2×C11×#45111yescharacteristic
451C2C11×#301011yescharacteristic
452C2C11×#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×#1648C2semidirect
6. C11×#1645C2semidirect
110. #18925C11direct (N × H)
119. C2×Q8×C11Q16semidirect
175. #1648C2×C11semidirect
176. #1645C2×C11semidirect
344. C2×Q8C11×Q16semidirect
396. C11#18925direct (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×#32302
C11×#32092
C2×C11×#4752
C11×#16482
C11×#16452
C11×#15422
C11×#14812
C11×#14792
#1892511