Finite Group Databasebeta

← C4×C11×#461 #14598691

Subgroups — C4×C11×#461 #14598691

Order 2816.

1104 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic
2C2×C4×C11×SD16C212yesmaximal
3C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
4C42×D4×C11C211yesmaximal, characteristic
5C11×#1981C211yesmaximal, characteristic, complemented
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1927C212yesmaximal, complemented
8C11×#1877C212yesmaximal
9C11×#1802C211yesmaximal, characteristic
10C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
11C4×C11×#103C212yesmaximal, complemented
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×C42×C11—21no—
19C11×#461C418yesdirect product factor
20C4×C11×SD16—28no—
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#102C2212yes—
28C2×C4×C8×C11C2212yes—
29C11×#391C2212yes—
30C11×#389—21no—
31C11×#389—21no—
32C11×#384C2211yescharacteristic
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C4×C11×C22⋊C4—21no—
40C4×C11×C22⋊C4—21no—
41C43×C11C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C2×C11×SD16—24no—
51C2×C11×SD16—24no—
52C2×C11×SD16C2×C418yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8C2×C414yescomplemented
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11C2×C414yes—
64C4×D4×C11D414yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—22no—
81C2×C42×C11—44no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C11×#106—24no—
90C11×C4⋊C8—22no—
91C11×C4⋊C8C2×C414yescomplemented
92C11×#103—24no—
93C11×#103—24no—
94C11×#103C2×C418yescomplemented
95C11×#102—24no—
96C4×C8×C11—24no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—22no—
101C11×#95—22no—
102C4×#461C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C22×C414yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C22×C412yes—
114C2×D4×C11C2×D412yes—
115C2×D4×C11#4112yes—
116C22×C4×C11—24no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C11×SD16—216no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11C22×C414yes—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4C22×C412yes—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4#4112yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—41no—
165C42×C11—44no—
166C42×C11—42no—
167C42×C11—42no—
168C42×C11—42no—
169C42×C11SD1614yescomplemented
170C42×C11C22×C412yes—
171C42×C11C2×D412yes—
172C42×C11#4112yes—
173C42×C11#4112yes—
174C2×#461C2×C1111yescharacteristic
175C2×C4×SD16C2×C1112yes—
176C4×C4⋊Q8C2×C1111yescharacteristic, complemented
177C42×D4C2×C1111yescharacteristic
178#1981C2×C1111yescharacteristic, complemented
179#1948C2×C1111yescharacteristic, complemented
180#1927C2×C1112yescomplemented
181#1877C2×C1112yes—
182#1802C2×C1111yescharacteristic
183C4×C4⋊C8C2×C1111yescharacteristic, complemented
184C4×#103C2×C1112yescomplemented
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11C22×D411yescharacteristic
193Q8×C11—24no—
194Q8×C11—24no—
195Q8×C11—42no—
196Q8×C11—42no—
197D4×C11—22no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11C4×D414yes—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—48no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—48no—
224C2×C4×C11—48no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11C4×D412yes—
229C2×C4×C11C4×D412yes—
230C2×C4×C11#12112yes—
231C2×C4×C11#12112yes—
232C2×C4×C11C2×SD1612yes—
233C2×C4×C11C2×SD1612yes—
234C2×C4×C11C2×SD1612yes—
235C2×C4×C11#13512yes—
236C2×C4×C11#13712yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C8×C11—24no—
244C8×C11—42no—
245C22×SD16C22×C1112yes—
246C2×C4⋊Q8C22×C1111yescharacteristic
247C2×C4×Q8C22×C1112yes—
248C2×C4×D4C22×C1111yescharacteristic
249C2×C4×D4C22×C1111yescharacteristic
250C2×C4×D4C22×C1111yescharacteristic
251C22×C42—21no—
252#461C4×C1118yesdirect product factor
253C4×SD16—28no—
254C2×#106C22×C1112yes—
255C2×C4⋊C8C22×C1111yescharacteristic
256C2×C4⋊C8C22×C1111yescharacteristic
257C2×#103C22×C1112yes—
258C2×#103C22×C1112yes—
259C2×#103C22×C1112yes—
260C2×#102C22×C1112yes—
261C2×C4×C8C22×C1112yes—
262#391C22×C1112yes—
263#389—21no—
264#389—21no—
265#384C22×C1111yescharacteristic
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4C22×C1111yescharacteristic
269C4×C4⋊C4C22×C1111yescharacteristic
270C4×C4⋊C4C22×C1111yescharacteristic
271C4×C22⋊C4—21no—
272C4×C22⋊C4—21no—
273C4×C22⋊C4—21no—
274C43C22×C1111yescharacteristic
275#340C22×C1112yes—
276#340C22×C1112yes—
277#336C22×C1112yes—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11C2×C4×D411yescharacteristic
286C22×C11C2×#12111yescharacteristic
287C22×C11#52511yescharacteristic
288C22×C11C22×SD1611yescharacteristic
289C22×C11C2×#13511yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C22×C11#57511yescharacteristic
292C4×C11—22no—
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—42no—
296C4×C11—41no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11—82no—
301C4×C11C4×SD1614yescomplemented
302C4×C11#46114yesdirect product factor
303C4×C11C2×C4×D411yescharacteristic
304C4×C11C4×#4111yescharacteristic
305C4×C11#52911yescharacteristic
306C4×C11#53211yescharacteristic
307C22×Q8C23×C1112yes—
308C22×D4C23×C1111yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C2×SD16—24no—
313C2×SD16—24no—
314C2×SD16C2×C4×C1118yes—
315C22×C8C23×C1112yes—
316C22×C8C23×C1112yes—
317C4⋊Q8—22no—
318C4⋊Q8C2×C4×C1114yescomplemented
319C4×Q8—24no—
320C4×Q8—24no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4C2×C4×C1114yes—
326C4×D4D4×C1114yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4C23×C1112yes—
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C42—22no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—44no—
344C2×C42D4×C1111yescharacteristic
345C2×C42D4×C1111yescharacteristic
346C2×C42D4×C1111yescharacteristic
347C2×C42D4×C1111yescharacteristic
348C2×C42C23×C1111yescharacteristic
349C2×C42C23×C1111yescharacteristic
350C2×C42C23×C1111yescharacteristic
351#106—24no—
352C4⋊C8—22no—
353C4⋊C8C2×C4×C1114yescomplemented
354#103—24no—
355#103—24no—
356#103C2×C4×C1118yescomplemented
357#102—24no—
358C4×C8—24no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—22no—
363#95—22no—
364C2×C11—44no—
365C2×C11C4×#12111yescharacteristic
366C2×C11C2×C4×SD1611yescharacteristic
367C2×C11C4×#13711yescharacteristic
368C2×C11C2×#46111yescharacteristic
369C2×C11#303511yescharacteristic
370C2×C11#310111yescharacteristic
371C2×C11#310711yescharacteristic
372C24—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8C22×C4×C1114yes—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4C22×C4×C1112yes—
383C2×D4C2×D4×C1112yes—
384C2×D4C11×#4112yes—
385C22×C4—24no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C24×C1111yescharacteristic
406SD16—216no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8C22×C4×C1114yes—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—42no—
421C4⋊C4—44no—
422C4⋊C4—42no—
423C4⋊C4C22×C4×C1112yes—
424C4⋊C4C2×D4×C1112yes—
425C4⋊C4C11×#4112yes—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C42—22no—
430C42—22no—
431C42—21no—
432C42—21no—
433C42—41no—
434C42—44no—
435C42—42no—
436C42—42no—
437C42—42no—
438C42C11×SD1614yescomplemented
439C42C22×C4×C1112yes—
440C42C2×D4×C1112yes—
441C42C11×#4112yes—
442C42C11×#4112yes—
443C11C4×#46111yescharacteristic, direct product factor, Sylow
444C23—22no—
445C23—22no—
446C23—22no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23C22×D4×C1111yescharacteristic
452Q8—24no—
453Q8—24no—
454Q8—42no—
455Q8—42no—
456D4—22no—
457D4—22no—
458D4—22no—
459D4C4×D4×C1114yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—48no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—48no—
483C2×C4—48no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4C4×D4×C1112yes—
488C2×C4C4×D4×C1112yes—
489C2×C4C11×#12112yes—
490C2×C4C11×#12112yes—
491C2×C4C2×C11×SD1612yes—
492C2×C4C2×C11×SD1612yes—
493C2×C4C2×C11×SD1612yes—
494C2×C4C11×#13512yes—
495C2×C4C11×#13712yes—
496C2×C4C23×C4×C1111yescharacteristic
497C2×C4C22×D4×C1111yescharacteristic
498C2×C4C2×C11×#4111yescharacteristic
499C2×C4C2×C11×#4111yescharacteristic
500C2×C4C2×C11×#4111yescharacteristic
501C2×C4C2×C11×#4111yescharacteristic
502C8—24no—
503C8—42no—
504C22—24no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22C2×C4×D4×C1111yescharacteristic
512C22C2×C11×#12111yescharacteristic
513C22C11×#52511yescharacteristic
514C22C22×C11×SD1611yescharacteristic
515C22C2×C11×#13511yescharacteristic
516C22C2×C11×#13711yescharacteristic
517C22C11×#57511yescharacteristic
518C4—22no—
519C4—22no—
520C4—22no—
521C4—42no—
522C4—42no—
523C4—44no—
524C4—42no—
525C4—41no—
526C4—82no—
527C4C4×C11×SD1614yescomplemented
528C4C11×#46114yesdirect product factor
529C4C2×C4×D4×C1111yescharacteristic
530C4C4×C11×#4111yescharacteristic
531C4C11×#52911yescharacteristic
532C4C11×#53211yescharacteristic
533C2—44no—
534C2C4×C11×#12111yescharacteristic
535C2C2×C4×C11×SD1611yescharacteristic
536C2C4×C11×#13711yescharacteristic
537C2C2×C11×#46111yescharacteristic
538C2C11×#303511yescharacteristic
539C2C11×#310111yescharacteristic
540C2C11×#310711yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×C11×C4⋊Q8C2semidirect
5. C11×#1981C2semidirect
6. C11×#1948C2semidirect
7. C11×#1927C2semidirect
10. C4×C11×C4⋊C8C2semidirect
11. C4×C11×#103C2semidirect
19. C11×#461C4direct (N × H)
56. C11×C4⋊Q8C2×C4semidirect
91. C11×C4⋊C8C2×C4semidirect
94. C11×#103C2×C4semidirect
102. C4×#461C11direct (N × H)
169. C42×C11SD16semidirect
176. C4×C4⋊Q8C2×C11semidirect
178. #1981C2×C11semidirect
179. #1948C2×C11semidirect
180. #1927C2×C11semidirect
183. C4×C4⋊C8C2×C11semidirect
184. C4×#103C2×C11semidirect
252. #461C4×C11direct (N × H)
301. C4×C11C4×SD16semidirect
302. C4×C11#461direct (N × H)
318. C4⋊Q8C2×C4×C11semidirect
353. C4⋊C8C2×C4×C11semidirect
356. #103C2×C4×C11semidirect
438. C42C11×SD16semidirect
443. C11C4×#461direct (N × H)
527. C4C4×C11×SD16semidirect
528. C4C11×#461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C4×C11×SD162
C4×C11×C4⋊Q82
C42×D4×C112
C11×#19812
C11×#19482
C11×#19272
C11×#18772
C11×#18022
C4×C11×C4⋊C82
C4×C11×#1032
C4×#46111