Finite Group Databasebeta

← C11×#23515 #14600708

Subgroups — C11×#23515 #14600708

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C211yesmaximal, characteristic
2C22×C11×#99C212yesmaximal, complemented
3C11×#2315C211yesmaximal, characteristic, complemented
4C11×#2308C212yesmaximal, complemented
5C11×#2044C218yesmaximal, complemented
6C2×C11×#342C211yesmaximal, characteristic, complemented
7C23×D4×C11C2212yes—
8C11×#534—24no—
9C11×#534—22no—
10C11×#534C2214yes—
11C2×C11×#123—22no—
12C2×C11×#121—22no—
13C2×C11×#120—22no—
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C2×C11×#99—28no—
19C2×C11×#99C2218yescomplemented
20C11×#386—24no—
21C11×#386C2218yescomplemented
22C11×#385—22no—
23C11×#385C2214yescomplemented
24C11×#381—22no—
25C11×#380—22no—
26C11×#379—22no—
27C11×#342C2214yescomplemented
28C25×C11D412yes—
29C25×C11C2311yescharacteristic
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—24no—
35C22×D4×C11—24no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11—22no—
39C22×D4×C11D414yes—
40C22×D4×C11C2314yes—
41C23×C4×C11—21no—
42C23×C4×C11—22no—
43C23×C4×C11D412yes—
44C23×C4×C11D412yes—
45C23×C4×C11C2312yes—
46C11×#123—28no—
47C11×#123—28no—
48C11×#121—28no—
49C11×#121—28no—
50C11×#120—28no—
51C11×#120—28no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—28no—
67C2×C11×C22⋊C4D412yes—
68C2×C11×C22⋊C4D414yescomplemented
69C2×C11×C22⋊C4C2314yes—
70C2×C11×C22⋊C4C2312yes—
71C2×C11×C22⋊C4C2312yes—
72C11×#99—216no—
73C11×#95—24no—
74C11×#95—28no—
75#23515C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—22no—
77C24×C11—22no—
78C24×C11—24no—
79C24×C11—24no—
80C24×C11—82no—
81C24×C11—84no—
82C24×C11C2×D414yes—
83C24×C11C2×D412yes—
84C24×C11C2×D412yes—
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D411yescharacteristic
87C24×C11C2×D412yes—
88C24×C11#4112yes—
89C24×C11#4114yes—
90C24×C11C2411yescharacteristic
91C2×D4×C11—24no—
92C2×D4×C11—24no—
93C2×D4×C11—28no—
94C2×D4×C11—28no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—28no—
102C2×D4×C11—44no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11—44no—
109C2×D4×C11—44no—
110C2×D4×C11—84no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—44no—
123C22×C4×C11—82no—
124C22×C4×C11—82no—
125C22×C4×C11—82no—
126C22×C4×C11—84no—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D414yes—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—84no—
131C11×C22⋊C4—216no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—88no—
143C11×C22⋊C4C2×D414yescomplemented
144C2×#534C2×C1111yescharacteristic
145C22×#99C2×C1112yescomplemented
146#2315C2×C1111yescharacteristic, complemented
147#2308C2×C1112yescomplemented
148#2044C2×C1118yescomplemented
149C2×#342C2×C1111yescharacteristic, complemented
150C23×C11—24no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—44no—
156C23×C11—42no—
157C23×C11—44no—
158C23×C11—48no—
159C23×C11—48no—
160C23×C11—44no—
161C23×C11—44no—
162C23×C11—84no—
163C23×C11—82no—
164C23×C11—84no—
165C23×C11—82no—
166C23×C11—88no—
167C23×C11—88no—
168C23×C11#12012yes—
169C23×C11#12011yescharacteristic
170C23×C11#12011yescharacteristic
171C23×C11#12112yes—
172C23×C11#12114yes—
173C23×C11#12112yes—
174C23×C11#12114yes—
175C23×C11#12314yes—
176C23×C11#12314yes—
177C23×C11#12412yes—
178C23×C11#12412yes—
179C23×C11C22×D412yes—
180C23×C11C22×D411yescharacteristic
181C23×C11C22×D411yescharacteristic
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4112yes—
184D4×C11—44no—
185D4×C11—44no—
186D4×C11—44no—
187D4×C11—44no—
188D4×C11—48no—
189D4×C11—48no—
190D4×C11—88no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11—48no—
202C2×C4×C11—48no—
203C2×C4×C11—44no—
204C2×C4×C11—42no—
205C2×C4×C11—44no—
206C2×C4×C11—82no—
207C2×C4×C11—84no—
208C2×C4×C11—88no—
209C23×D4C22×C1112yes—
210#534—24no—
211#534—22no—
212#534C22×C1114yes—
213C2×#123—22no—
214C2×#121—22no—
215C2×#120—22no—
216C22×C22⋊C4C22×C1111yescharacteristic
217C22×C22⋊C4C22×C1112yes—
218C22×C22⋊C4C22×C1111yescharacteristic
219C22×C22⋊C4C22×C1111yescharacteristic
220C2×#99—28no—
221C2×#99C22×C1118yescomplemented
222#386—24no—
223#386C22×C1118yescomplemented
224#385—22no—
225#385C22×C1114yescomplemented
226#381—22no—
227#380—22no—
228#379—22no—
229#342C22×C1114yescomplemented
230C22×C11—22no—
231C22×C11—24no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—24no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—44no—
238C22×C11—44no—
239C22×C11—42no—
240C22×C11—44no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—42no—
246C22×C11—48no—
247C22×C11—44no—
248C22×C11—48no—
249C22×C11—84no—
250C22×C11—88no—
251C22×C11—88no—
252C22×C11#39412yes—
253C22×C11#39414yes—
254C22×C11#39412yes—
255C22×C11C2×#12011yescharacteristic
256C22×C11C2×#12111yescharacteristic
257C22×C11C2×#12112yes—
258C22×C11C2×#12312yes—
259C22×C11C2×#12411yescharacteristic
260C4×C11—44no—
261C4×C11—44no—
262C4×C11—44no—
263C4×C11—84no—
264C4×C11—82no—
265C25D4×C1112yes—
266C25C23×C1111yescharacteristic
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—24no—
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4D4×C1114yes—
277C22×D4C23×C1114yes—
278C23×C4—21no—
279C23×C4—22no—
280C23×C4D4×C1112yes—
281C23×C4D4×C1112yes—
282C23×C4C23×C1112yes—
283#123—28no—
284#123—28no—
285#121—28no—
286#121—28no—
287#120—28no—
288#120—28no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4D4×C1112yes—
305C2×C22⋊C4D4×C1114yescomplemented
306C2×C22⋊C4C23×C1114yes—
307C2×C22⋊C4C23×C1112yes—
308C2×C22⋊C4C23×C1112yes—
309#99—216no—
310#95—24no—
311#95—28no—
312C2×C11—21no—
313C2×C11—22no—
314C2×C11—22no—
315C2×C11—22no—
316C2×C11—24no—
317C2×C11—21no—
318C2×C11—22no—
319C2×C11—84no—
320C2×C11C2×#39411yescharacteristic
321C2×C11#302612yes—
322C24—22no—
323C24—22no—
324C24—24no—
325C24—24no—
326C24—82no—
327C24—84no—
328C24C2×D4×C1114yes—
329C24C2×D4×C1112yes—
330C24C2×D4×C1112yes—
331C24C2×D4×C1111yescharacteristic
332C24C2×D4×C1111yescharacteristic
333C24C2×D4×C1112yes—
334C24C11×#4112yes—
335C24C11×#4114yes—
336C24C24×C1111yescharacteristic
337C2×D4—24no—
338C2×D4—24no—
339C2×D4—28no—
340C2×D4—28no—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—24no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—28no—
348C2×D4—44no—
349C2×D4—44no—
350C2×D4—44no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4—44no—
356C2×D4—84no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—44no—
369C22×C4—82no—
370C22×C4—82no—
371C22×C4—82no—
372C22×C4—84no—
373C22×C4C2×D4×C1114yes—
374C22×C4C2×D4×C1114yes—
375C4⋊C4—28no—
376C4⋊C4—84no—
377C22⋊C4—216no—
378C22⋊C4—24no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—22no—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—42no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—44no—
388C22⋊C4—88no—
389C22⋊C4C2×D4×C1114yescomplemented
390C11#2351511yescharacteristic, direct product factor, Sylow
391C23—24no—
392C23—24no—
393C23—24no—
394C23—42no—
395C23—42no—
396C23—44no—
397C23—42no—
398C23—44no—
399C23—48no—
400C23—48no—
401C23—44no—
402C23—44no—
403C23—84no—
404C23—82no—
405C23—84no—
406C23—82no—
407C23—88no—
408C23—88no—
409C23C11×#12012yes—
410C23C11×#12011yescharacteristic
411C23C11×#12011yescharacteristic
412C23C11×#12112yes—
413C23C11×#12114yes—
414C23C11×#12112yes—
415C23C11×#12114yes—
416C23C11×#12314yes—
417C23C11×#12314yes—
418C23C11×#12412yes—
419C23C11×#12412yes—
420C23C22×D4×C1112yes—
421C23C22×D4×C1111yescharacteristic
422C23C22×D4×C1111yescharacteristic
423C23C2×C11×#4111yescharacteristic
424C23C2×C11×#4112yes—
425D4—44no—
426D4—44no—
427D4—44no—
428D4—44no—
429D4—48no—
430D4—48no—
431D4—88no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—48no—
443C2×C4—48no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—82no—
448C2×C4—84no—
449C2×C4—88no—
450C22—22no—
451C22—24no—
452C22—22no—
453C22—22no—
454C22—24no—
455C22—42no—
456C22—44no—
457C22—44no—
458C22—44no—
459C22—42no—
460C22—44no—
461C22—42no—
462C22—42no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—48no—
467C22—44no—
468C22—48no—
469C22—84no—
470C22—88no—
471C22—88no—
472C22C11×#39412yes—
473C22C11×#39414yes—
474C22C11×#39412yes—
475C22C2×C11×#12011yescharacteristic
476C22C2×C11×#12111yescharacteristic
477C22C2×C11×#12112yes—
478C22C2×C11×#12312yes—
479C22C2×C11×#12411yescharacteristic
480C4—44no—
481C4—44no—
482C4—44no—
483C4—84no—
484C4—82no—
485C2—21no—
486C2—22no—
487C2—22no—
488C2—22no—
489C2—24no—
490C2—21no—
491C2—22no—
492C2—84no—
493C2C2×C11×#39411yescharacteristic
494C2C11×#302612yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC2×C11×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#99C2semidirect
3. C11×#2315C2semidirect
4. C11×#2308C2semidirect
5. C11×#2044C2semidirect
6. C2×C11×#342C2semidirect
19. C2×C11×#99C22semidirect
21. C11×#386C22semidirect
23. C11×#385C22semidirect
27. C11×#342C22semidirect
68. C2×C11×C22⋊C4D4semidirect
75. #23515C11direct (N × H)
143. C11×C22⋊C4C2×D4semidirect
145. C22×#99C2×C11semidirect
146. #2315C2×C11semidirect
147. #2308C2×C11semidirect
148. #2044C2×C11semidirect
149. C2×#342C2×C11semidirect
221. C2×#99C22×C11semidirect
223. #386C22×C11semidirect
225. #385C22×C11semidirect
229. #342C22×C11semidirect
305. C2×C22⋊C4D4×C11semidirect
389. C22⋊C4C2×D4×C11semidirect
390. C11#23515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5342
C22×C11×#992
C11×#23152
C11×#23082
C11×#20442
C2×C11×#3422
#2351511