Finite Group Databasebeta

← C11×#18195 #14595388

Subgroups — C11×#18195 #14595388

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C2×C11×#448C212yesmaximal, complemented
3C11×#2409C211yesmaximal, characteristic, complemented
4C11×#1604C214yesmaximal, complemented
5C11×#1601C214yesmaximal, complemented
6C11×#1519C212yesmaximal, complemented
7C11×#1459C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—21no—
9C23×Q8×C11C2211yescharacteristic, complemented
10C22×C11×SD16—22no—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537C2212yes—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C11×#448—24no—
23C11×#448C2218yescomplemented
24C2×C11×#103—22no—
25C2×C11×C22⋊C8C2212yescomplemented
26C11×#395C2212yescomplemented
27C11×#393C2212yescomplemented
28C11×#391—21no—
29C11×#386—21no—
30C11×#385—21no—
31C11×#380C2211yescharacteristic, complemented
32C11×#327C2218yescomplemented
33C11×#324C2212yescomplemented
34C11×#323C2212yescomplemented
35C11×H(5,𝔽2)—44no—
36C11×H(5,𝔽2)—44no—
37C2×C11×#41—24no—
38C2×C11×#41—22no—
39C22×Q8×C11—21no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—44no—
43C22×Q8×C11C2312yes—
44C22×D4×C11—24no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11D412yes—
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×SD16—28no—
54C2×C11×SD16—48no—
55C22×C8×C11—22no—
56C11×C4⋊Q8—21no—
57C11×#127—21no—
58C11×#124—22no—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—44no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121—24no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121D414yes—
71C11×#121C2314yes—
72C11×#120—24no—
73C11×#120—24no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4C2311yescharacteristic
89C2×C42×C11D411yescharacteristic
90C11×#103—28no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8C2314yes—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95C2312yes—
96#18195C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—22no—
98C24×C11—22no—
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D411yescharacteristic
101C11×#41—44no—
102C11×#41—416no—
103C11×#41—44no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—28no—
107C2×Q8×C11—24no—
108C2×Q8×C11—44no—
109C2×Q8×C11—42no—
110C2×Q8×C11—44no—
111C2×Q8×C11—48no—
112C2×Q8×C11—41no—
113C2×Q8×C11—41no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—44no—
124C2×D4×C11—416no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—82no—
130C2×D4×C11SD1614yescomplemented
131C2×D4×C11C2×D414yes—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—42no—
140C22×C4×C11—44no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2411yescharacteristic
150C11×SD16—416no—
151C2×C8×C11—24no—
152C2×C8×C11—44no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4C2×D414yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—42no—
168C42×C11—21no—
169C42×C11—21no—
170#3496C2×C1111yescharacteristic
171C2×#448C2×C1112yescomplemented
172#2409C2×C1111yescharacteristic, complemented
173#1604C2×C1114yescomplemented
174#1601C2×C1114yescomplemented
175#1519C2×C1112yescomplemented
176#1459C2×C1111yescharacteristic, complemented
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—24no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11—82no—
189C23×C11—82no—
190C23×C11#12012yes—
191C23×C11C2×SD1612yes—
192C23×C11C2×SD1612yescomplemented
193C23×C11AGL(1,ℤ/8)12yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—28no—
196Q8×C11—44no—
197Q8×C11—44no—
198Q8×C11—44no—
199Q8×C11—44no—
200D4×C11—28no—
201D4×C11—44no—
202D4×C11—44no—
203D4×C11—48no—
204D4×C11—44no—
205D4×C11—44no—
206D4×C11—48no—
207D4×C11—44no—
208D4×C11—82no—
209D4×C11—82no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—48no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—81no—
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11C2×SD1612yescomplemented
236C2×C4×C11C22×D412yes—
237C8×C11—44no—
238C2×H(5,𝔽2)—21no—
239C23×Q8C22×C1111yescharacteristic, complemented
240C22×SD16—22no—
241#547—22no—
242#546—24no—
243D42—22no—
244#537C22×C1112yes—
245#534—21no—
246#534C22×C1112yes—
247#532—21no—
248C2×C22⋊Q8—21no—
249C2×#121—21no—
250C2×#121C22×C1112yes—
251C2×C4×D4C22×C1111yescharacteristic
252#448—24no—
253#448C22×C1118yescomplemented
254C2×#103—22no—
255C2×C22⋊C8C22×C1112yescomplemented
256#395C22×C1112yescomplemented
257#393C22×C1112yescomplemented
258#391—21no—
259#386—21no—
260#385—21no—
261#380C22×C1111yescharacteristic, complemented
262#327C22×C1118yescomplemented
263#324C22×C1112yescomplemented
264#323C22×C1112yescomplemented
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—21no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—81no—
279C22×C11—164no—
280C22×C11—164no—
281C22×C11#45014yes—
282C22×C11C2×#12011yescharacteristic
283C22×C11C22×SD1611yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11—22no—
286C4×C11—21no—
287C4×C11—22no—
288C4×C11—44no—
289C4×C11—41no—
290C4×C11—44no—
291C4×C11—41no—
292C4×C11—82no—
293C4×C11B(4,𝔽2)12yes—
294H(5,𝔽2)—44no—
295H(5,𝔽2)—44no—
296C2×#41—24no—
297C2×#41—22no—
298C22×Q8—21no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—44no—
302C22×Q8C23×C1112yes—
303C22×D4—24no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4D4×C1111yescharacteristic
308C22×D4D4×C1112yes—
309C23×C4—21no—
310C23×C4D4×C1111yescharacteristic
311C23×C4C23×C1111yescharacteristic
312C2×SD16—28no—
313C2×SD16—48no—
314C22×C8—22no—
315C4⋊Q8—21no—
316#127—21no—
317#124—22no—
318#123—24no—
319#123—24no—
320C22⋊Q8—24no—
321C22⋊Q8—44no—
322#121—22no—
323#121—22no—
324#121—24no—
325#121—22no—
326#121—22no—
327#121—22no—
328#121—22no—
329#121D4×C1114yes—
330#121C23×C1114yes—
331#120—24no—
332#120—24no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4D4×C1112yes—
341C2×C4⋊C4C23×C1111yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4D4×C1111yescharacteristic
347C2×C22⋊C4C23×C1111yescharacteristic
348C2×C42D4×C1111yescharacteristic
349#103—28no—
350C22⋊C8—22no—
351C22⋊C8C23×C1114yes—
352#95—22no—
353#95—22no—
354#95C23×C1112yes—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—24no—
358C2×C11—42no—
359C2×C11—84no—
360C2×C11C2×#45011yescharacteristic
361C2×C11#302211yescharacteristic
362C2×C11C2×B(4,𝔽2)11yescharacteristic
363C24—22no—
364C24—22no—
365C24C2×D4×C1111yescharacteristic
366C24C2×D4×C1111yescharacteristic
367#41—44no—
368#41—416no—
369#41—44no—
370C2×Q8—22no—
371C2×Q8—24no—
372C2×Q8—28no—
373C2×Q8—24no—
374C2×Q8—44no—
375C2×Q8—42no—
376C2×Q8—44no—
377C2×Q8—48no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—24no—
383C2×D4—22no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—44no—
390C2×D4—416no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—82no—
396C2×D4C11×SD1614yescomplemented
397C2×D4C2×D4×C1114yes—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—42no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1112yes—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1112yes—
415C22×C4C24×C1111yescharacteristic
416SD16—416no—
417C2×C8—24no—
418C2×C8—44no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—44no—
425C4⋊C4C2×D4×C1114yes—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—44no—
433C22⋊C4—42no—
434C42—21no—
435C42—21no—
436C11#1819511yescharacteristic, direct product factor, Sylow
437C23—21no—
438C23—21no—
439C23—24no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—44no—
445C23—44no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23C11×#12012yes—
451C23C2×C11×SD1612yes—
452C23C2×C11×SD1612yescomplemented
453C23C11×AGL(1,ℤ/8)12yes—
454C23C22×D4×C1111yescharacteristic
455Q8—28no—
456Q8—44no—
457Q8—44no—
458Q8—44no—
459Q8—44no—
460D4—28no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—44no—
465D4—44no—
466D4—48no—
467D4—44no—
468D4—82no—
469D4—82no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—48no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—48no—
484C2×C4—42no—
485C2×C4—44no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—81no—
493C2×C4C11×#12011yescharacteristic
494C2×C4C11×#12011yescharacteristic
495C2×C4C2×C11×SD1612yescomplemented
496C2×C4C22×D4×C1112yes—
497C8—44no—
498C22—21no—
499C22—22no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—44no—
509C22—44no—
510C22—44no—
511C22—81no—
512C22—164no—
513C22—164no—
514C22C11×#45014yes—
515C22C2×C11×#12011yescharacteristic
516C22C22×C11×SD1611yescharacteristic
517C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
518C4—22no—
519C4—22no—
520C4—21no—
521C4—44no—
522C4—41no—
523C4—44no—
524C4—41no—
525C4—82no—
526C4C11×B(4,𝔽2)12yes—
527C2—21no—
528C2—21no—
529C2—24no—
530C2—42no—
531C2—84no—
532C2C2×C11×#45011yescharacteristic
533C2C11×#302211yescharacteristic
534C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3496C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#448C2semidirect
3. C11×#2409C2semidirect
4. C11×#1604C2semidirect
5. C11×#1601C2semidirect
6. C11×#1519C2semidirect
7. C11×#1459C2semidirect
9. C23×Q8×C11C22semidirect
23. C11×#448C22semidirect
25. C2×C11×C22⋊C8C22semidirect
26. C11×#395C22semidirect
27. C11×#393C22semidirect
31. C11×#380C22semidirect
32. C11×#327C22semidirect
33. C11×#324C22semidirect
34. C11×#323C22semidirect
96. #18195C11direct (N × H)
130. C2×D4×C11SD16semidirect
171. C2×#448C2×C11semidirect
172. #2409C2×C11semidirect
173. #1604C2×C11semidirect
174. #1601C2×C11semidirect
175. #1519C2×C11semidirect
176. #1459C2×C11semidirect
192. C23×C11C2×SD16semidirect
235. C2×C4×C11C2×SD16semidirect
239. C23×Q8C22×C11semidirect
253. #448C22×C11semidirect
255. C2×C22⋊C8C22×C11semidirect
256. #395C22×C11semidirect
257. #393C22×C11semidirect
261. #380C22×C11semidirect
262. #327C22×C11semidirect
263. #324C22×C11semidirect
264. #323C22×C11semidirect
396. C2×D4C11×SD16semidirect
436. C11#18195direct (N × H)
452. C23C2×C11×SD16semidirect
495. C2×C4C2×C11×SD16semidirect

Maximal subgroups

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

subgroupindex
C11×#34962
C2×C11×#4482
C11×#24092
C11×#16042
C11×#16012
C11×#15192
C11×#14592
#1819511