Finite Group Databasebeta

← C11×#18927 #14596120

Subgroups — C11×#18927 #14596120

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic
2C11×#3227C211yesmaximal, characteristic, complemented
3C11×#3209C211yesmaximal, characteristic, complemented
4C2×C11×#474C211yesmaximal, characteristic, complemented
5C11×#1652C214yesmaximal, complemented
6C11×#1641C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#556C2212yes—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550C2212yes—
15C11×#547—21no—
16C11×#538—22no—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C11×#525—22no—
22C11×#520—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#498C2212yescomplemented
25C11×#494—21no—
26C11×#487—21no—
27C11×#486C2212yescomplemented
28C11×#481—22no—
29C11×#476—22no—
30C11×#474—22no—
31C11×#474C2214yes—
32C11×#462C2214yescomplemented
33C11×#451—22no—
34C11×#431C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C2×C11×#107—21no—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yes—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C22×Q8×C11—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C2×C11×Q16—24no—
49C22×C8×C11—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2312yes—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127—22no—
58C11×#127C2311yescharacteristic
59C11×#126—24no—
60C11×#125—21no—
61C11×#124—24no—
62C11×#124—22no—
63C11×#124—21no—
64C11×#123—24no—
65C11×#123—24no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8D412yes—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—24no—
72C11×#121—21no—
73C11×#121—22no—
74C11×#121D412yes—
75C11×#120—24no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11C2312yes—
79C4×D4×C11—24no—
80C4×D4×C11—24no—
81C4×D4×C11—22no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11D412yes—
86C4×D4×C11D412yes—
87C4×D4×C11C2312yes—
88C11×#117—22no—
89C11×#117—21no—
90C11×#117—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C22⋊C4—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×#102—24no—
105C11×#102—24no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2312yes—
110#18927C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41—84no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—82no—
120C2×Q8×C11C2×D412yes—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C2×D412yes—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—24no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—41no—
137C22×C4×C11—82no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C11×Q16—84no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—42no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
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—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C42×C11—24no—
170C42×C11—22no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175#3506C2×C1111yescharacteristic
176#3227C2×C1111yescharacteristic, complemented
177#3209C2×C1111yescharacteristic, complemented
178C2×#474C2×C1111yescharacteristic, complemented
179#1652C2×C1114yescomplemented
180#1641C2×C1114yescomplemented
181#1540C2×C1111yescharacteristic, complemented
182#1481C2×C1111yescharacteristic, complemented
183#1478C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—42no—
187C23×C11—81no—
188C23×C11—81no—
189C23×C11#12011yescharacteristic
190Q8×C11—24no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—44no—
194Q8×C11—81no—
195Q8×C11—82no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—42no—
199D4×C11—44no—
200D4×C11—41no—
201D4×C11—41no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—84no—
205D4×C11—84no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—42no—
215C2×C4×C11—82no—
216C2×C4×C11—81no—
217C2×C4×C11—84no—
218C2×C4×C11—82no—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#13512yes—
223C2×C4×C11#13712yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C8×C11—42no—
228C8×C11—42no—
229C8×C11—42no—
230#559—22no—
231#556C22×C1112yes—
232#555—21no—
233#553—22no—
234#550C22×C1112yes—
235#547—21no—
236#538—22no—
237#535—21no—
238#533C22×C1111yescharacteristic
239#532C22×C1111yescharacteristic
240C2×C4⋊Q8C22×C1111yescharacteristic
241#525—22no—
242#520—21no—
243C2×C4×D4C22×C1111yescharacteristic
244#498C22×C1112yescomplemented
245#494—21no—
246#487—21no—
247#486C22×C1112yescomplemented
248#481—22no—
249#476—22no—
250#474—22no—
251#474C22×C1114yes—
252#462C22×C1114yescomplemented
253#451—22no—
254#431C22×C1111yescharacteristic
255#431C22×C1111yescharacteristic
256C2×#107—21no—
257C2×C4⋊C8C22×C1111yescharacteristic
258C2×#102—21no—
259#332C22×C1112yescomplemented
260#331C22×C1112yescomplemented
261Q8⋊C8C22×C1114yescomplemented
262D4⋊C8C22×C1114yes—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—84no—
272C22×C11#45212yes—
273C22×C11C2×#12011yescharacteristic
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11#45212yes—
283C4×C11C2×#13511yescharacteristic
284C4×C11C2×#13711yescharacteristic
285C4×C11#57612yes—
286C2×#41—22no—
287C2×#41—21no—
288C22×Q8—21no—
289C22×D4D4×C1111yescharacteristic
290C23×C4—21no—
291C2×Q16—24no—
292C22×C8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8D4×C1111yescharacteristic
297C4⋊Q8D4×C1111yescharacteristic
298C4⋊Q8C23×C1112yes—
299C4⋊Q8C23×C1111yescharacteristic
300#127—22no—
301#127C23×C1111yescharacteristic
302#126—24no—
303#125—21no—
304#124—24no—
305#124—22no—
306#124—21no—
307#123—24no—
308#123—24no—
309C22⋊Q8—22no—
310C22⋊Q8—21no—
311C22⋊Q8D4×C1112yes—
312#121—22no—
313#121—22no—
314#121—24no—
315#121—21no—
316#121—22no—
317#121D4×C1112yes—
318#120—24no—
319C4×Q8—22no—
320C4×Q8—21no—
321C4×Q8C23×C1112yes—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—22no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4D4×C1112yes—
329C4×D4D4×C1112yes—
330C4×D4C23×C1112yes—
331#117—22no—
332#117—21no—
333#117—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4D4×C1111yescharacteristic
338C2×C22⋊C4—21no—
339C2×C42C23×C1111yescharacteristic
340#107—24no—
341#106—24no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8C23×C1112yes—
345C4⋊C8C23×C1112yes—
346#103—24no—
347#102—24no—
348#102—24no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C4×C8—21no—
352C4×C8C23×C1112yes—
353C2×C11—22no—
354C2×C11—82no—
355C2×C11—82no—
356C2×C11C2×#45211yescharacteristic
357C2×C11#300811yescharacteristic
358C2×C11#302211yescharacteristic
359C24—21no—
360#41—42no—
361#41—42no—
362#41—84no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—41no—
367C2×Q8—82no—
368C2×Q8C2×D4×C1112yes—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4C2×D4×C1112yes—
378C2×D4C2×D4×C1112yes—
379C22×C4—24no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—41no—
385C22×C4—82no—
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1111yescharacteristic
389Q16—84no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—42no—
394C4⋊C4—24no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C1112yes—
407C4⋊C4C2×D4×C1112yes—
408C4⋊C4C2×D4×C1112yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C42—24no—
418C42—22no—
419C42C2×D4×C1111yescharacteristic
420C42C2×D4×C1111yescharacteristic
421C42C2×D4×C1111yescharacteristic
422C42C24×C1111yescharacteristic
423C11#1892711yescharacteristic, direct product factor, Sylow
424C23—22no—
425C23—22no—
426C23—42no—
427C23—81no—
428C23—81no—
429C23C11×#12011yescharacteristic
430Q8—24no—
431Q8—41no—
432Q8—41no—
433Q8—44no—
434Q8—81no—
435Q8—82no—
436D4—22no—
437D4—22no—
438D4—42no—
439D4—44no—
440D4—41no—
441D4—41no—
442D4—42no—
443D4—42no—
444D4—84no—
445D4—84no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—81no—
457C2×C4—84no—
458C2×C4—82no—
459C2×C4C11×#12011yescharacteristic
460C2×C4C11×#12011yescharacteristic
461C2×C4C11×#12011yescharacteristic
462C2×C4C11×#13512yes—
463C2×C4C11×#13712yes—
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C22×D4×C1111yescharacteristic
466C2×C4C22×D4×C1111yescharacteristic
467C8—42no—
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—84no—
479C22C11×#45212yes—
480C22C2×C11×#12011yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—82no—
489C4C11×#45212yes—
490C4C2×C11×#13511yescharacteristic
491C4C2×C11×#13711yescharacteristic
492C4C11×#57612yes—
493C2—22no—
494C2—82no—
495C2—82no—
496C2C2×C11×#45211yescharacteristic
497C2C11×#300811yescharacteristic
498C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3506C2
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×#3227C2semidirect
3. C11×#3209C2semidirect
4. C2×C11×#474C2semidirect
5. C11×#1652C2semidirect
6. C11×#1641C2semidirect
7. C11×#1540C2semidirect
8. C11×#1481C2semidirect
9. C11×#1478C2semidirect
24. C11×#498C22semidirect
27. C11×#486C22semidirect
32. C11×#462C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×Q8⋊C8C22semidirect
110. #18927C11direct (N × H)
176. #3227C2×C11semidirect
177. #3209C2×C11semidirect
178. C2×#474C2×C11semidirect
179. #1652C2×C11semidirect
180. #1641C2×C11semidirect
181. #1540C2×C11semidirect
182. #1481C2×C11semidirect
183. #1478C2×C11semidirect
244. #498C22×C11semidirect
247. #486C22×C11semidirect
252. #462C22×C11semidirect
259. #332C22×C11semidirect
260. #331C22×C11semidirect
261. Q8⋊C8C22×C11semidirect
423. C11#18927direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#32272
C11×#32092
C2×C11×#4742
C11×#16522
C11×#16412
C11×#15402
C11×#14812
C11×#14782
#1892711