Finite Group Databasebeta

← C11×#18909 #14596102

Subgroups — C11×#18909 #14596102

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#3230C211yesmaximal, characteristic, complemented
3C11×#3206C211yesmaximal, characteristic
4C2×C11×#475C211yesmaximal, characteristic, complemented
5C11×#1650C214yesmaximal, complemented
6C11×#1643C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic
9C11×#1479C211yesmaximal, characteristic, complemented
10C11×#559—21no—
11C11×#557—21no—
12C11×#556—22no—
13C11×#556C2212yes—
14C11×#554C2212yes—
15C11×#552—22no—
16C11×#539—22no—
17C11×#536—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C11×#529—22no—
22C11×#520—21no—
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#500C2212yes—
25C11×#492—21no—
26C11×#487—21no—
27C11×#487C2212yes—
28C11×#484—22no—
29C11×#477—22no—
30C11×#475—22no—
31C11×#475C2214yes—
32C11×#461C2214yes—
33C11×#448—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×D4⋊C8C2214yes—
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11D411yescharacteristic
46C2×C11×SD16—24no—
47C22×C8×C11—21no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8C2312yes—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127D411yescharacteristic
57C11×#126—24no—
58C11×#126—24no—
59C11×#125—24no—
60C11×#125—22no—
61C11×#125—21no—
62C11×#124—22no—
63C11×#124—22no—
64C11×#124—21no—
65C11×#123—24no—
66C11×#123—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8D412yes—
72C11×#121—21no—
73C11×#121D412yes—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11D412yes—
80C4×Q8×C11D412yes—
81C4×Q8×C11C2312yes—
82C4×D4×C11—24no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11C2312yes—
87C11×#117—24no—
88C11×#117—21no—
89C11×#117—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
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#18909C1111yesmaximal, characteristic, direct product factor, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—41no—
120C2×Q8×C11—82no—
121C2×Q8×C11C2×D412yes—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—22no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C11×SD16—84no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—42no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
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—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C42×C11—24no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173#3507C2×C1111yescharacteristic
174#3230C2×C1111yescharacteristic, complemented
175#3206C2×C1111yescharacteristic
176C2×#475C2×C1111yescharacteristic, complemented
177#1650C2×C1114yescomplemented
178#1643C2×C1114yescomplemented
179#1542C2×C1111yescharacteristic, complemented
180#1480C2×C1111yescharacteristic
181#1479C2×C1111yescharacteristic, complemented
182C23×C11—22no—
183C23×C11#12011yescharacteristic
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—44no—
191Q8×C11—82no—
192D4×C11—24no—
193D4×C11—44no—
194D4×C11—42no—
195D4×C11—81no—
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—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—81no—
208C2×C4×C11—84no—
209C2×C4×C11—82no—
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#13512yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C8×C11—42no—
219C8×C11—42no—
220C8×C11—42no—
221#559—21no—
222#557—21no—
223#556—22no—
224#556C22×C1112yes—
225#554C22×C1112yes—
226#552—22no—
227#539—22no—
228#536—21no—
229#533C22×C1111yescharacteristic
230#532C22×C1111yescharacteristic
231C2×C4⋊Q8C22×C1111yescharacteristic
232#529—22no—
233#520—21no—
234C2×C4×Q8C22×C1111yescharacteristic
235#500C22×C1112yes—
236#492—21no—
237#487—21no—
238#487C22×C1112yes—
239#484—22no—
240#477—22no—
241#475—22no—
242#475C22×C1114yes—
243#461C22×C1114yes—
244#448—22no—
245#431C22×C1111yescharacteristic
246#431C22×C1111yescharacteristic
247C2×#106—21no—
248C2×C4⋊C8C22×C1111yescharacteristic
249C2×#103—21no—
250#333C22×C1112yes—
251#332C22×C1112yes—
252Q8⋊C8C22×C1114yes—
253D4⋊C8C22×C1114yes—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11#45212yes—
260C22×C11C2×#12011yescharacteristic
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11#45212yes—
271C4×C11C2×#13511yescharacteristic
272C4×C11C2×#13711yescharacteristic
273C4×C11#57712yes—
274C2×#41—21no—
275C22×Q8—21no—
276C22×Q8D4×C1111yescharacteristic
277C2×SD16—24no—
278C22×C8—21no—
279C4⋊Q8—22no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8D4×C1111yescharacteristic
284C4⋊Q8C23×C1112yes—
285C4⋊Q8C23×C1111yescharacteristic
286C4⋊Q8C23×C1111yescharacteristic
287#127D4×C1111yescharacteristic
288#126—24no—
289#126—24no—
290#125—24no—
291#125—22no—
292#125—21no—
293#124—22no—
294#124—22no—
295#124—21no—
296#123—24no—
297#123—24no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300C22⋊Q8—24no—
301C22⋊Q8—21no—
302C22⋊Q8D4×C1112yes—
303#121—21no—
304#121D4×C1112yes—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8D4×C1112yes—
311C4×Q8D4×C1112yes—
312C4×Q8C23×C1112yes—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—21no—
317C4×D4C23×C1112yes—
318#117—24no—
319#117—21no—
320#117—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4D4×C1111yescharacteristic
326C2×C42—21no—
327C2×C42C23×C1111yescharacteristic
328#107—24no—
329#106—24no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8C23×C1112yes—
333C4⋊C8C23×C1112yes—
334#103—24no—
335#103—24no—
336#103—24no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C4×C8—21no—
340C4×C8C23×C1112yes—
341C2×C11—22no—
342C2×C11—82no—
343C2×C11C2×#45211yescharacteristic
344C2×C11#301011yescharacteristic
345C2×C11#302211yescharacteristic
346#41—42no—
347#41—42no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—41no—
355C2×Q8—82no—
356C2×Q8C2×D4×C1112yes—
357C2×Q8C2×D4×C1112yes—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4C2×D4×C1112yes—
362C22×C4—21no—
363C22×C4—24no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—41no—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1111yescharacteristic
370SD16—84no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—42no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C1112yes—
392C4⋊C4C2×D4×C1112yes—
393C4⋊C4C2×D4×C1112yes—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C42—24no—
401C42—22no—
402C42—22no—
403C42—22no—
404C42C2×D4×C1111yescharacteristic
405C42C2×D4×C1111yescharacteristic
406C42C2×D4×C1111yescharacteristic
407C42C24×C1111yescharacteristic
408C11#1890911yescharacteristic, direct product factor, Sylow
409C23—22no—
410C23C11×#12011yescharacteristic
411Q8—22no—
412Q8—22no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416Q8—42no—
417Q8—44no—
418Q8—82no—
419D4—24no—
420D4—44no—
421D4—42no—
422D4—81no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—81no—
435C2×C4—84no—
436C2×C4—82no—
437C2×C4C11×#12011yescharacteristic
438C2×C4C11×#12011yescharacteristic
439C2×C4C11×#12011yescharacteristic
440C2×C4C11×#13512yes—
441C2×C4C11×#13712yes—
442C2×C4C22×D4×C1111yescharacteristic
443C2×C4C22×D4×C1111yescharacteristic
444C2×C4C22×D4×C1111yescharacteristic
445C8—42no—
446C8—42no—
447C8—42no—
448C22—21no—
449C22—21no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22C11×#45212yes—
454C22C2×C11×#12011yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—82no—
464C4C11×#45212yes—
465C4C2×C11×#13511yescharacteristic
466C4C2×C11×#13711yescharacteristic
467C4C11×#57712yes—
468C2—22no—
469C2—82no—
470C2C2×C11×#45211yescharacteristic
471C2C11×#301011yescharacteristic
472C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
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×#3230C2semidirect
4. C2×C11×#475C2semidirect
5. C11×#1650C2semidirect
6. C11×#1643C2semidirect
7. C11×#1542C2semidirect
9. C11×#1479C2semidirect
110. #18909C11direct (N × H)
174. #3230C2×C11semidirect
176. C2×#475C2×C11semidirect
177. #1650C2×C11semidirect
178. #1643C2×C11semidirect
179. #1542C2×C11semidirect
181. #1479C2×C11semidirect
408. C11#18909direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#32302
C11×#32062
C2×C11×#4752
C11×#16502
C11×#16432
C11×#15422
C11×#14802
C11×#14792
#1890911