Finite Group Databasebeta

← C22×C11×#421 #14637284

Subgroups — C22×C11×#421 #14637284

Order 2816.

5198 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×#41C211yesmaximal, characteristic
2C23×C11×M16C211yesmaximal, characteristic, complemented
3C22×C11×#117C211yesmaximal, characteristic, complemented
4C2×C11×#421C2124yesmaximal, direct product factor
5C22×C11×#104C214yesmaximal, complemented
6C22×C11×#41—21no—
7C22×C11×#41—26no—
8C22×C11×#41—26no—
9C22×C11×#41—21no—
10C22×C11×#41C412yescomplemented
11C22×C11×#41C4112yescomplemented
12C22×C11×#41C2212yes—
13C22×C11×#41C22112yes—
14C23×Q8×C11C411yescharacteristic, complemented
15C23×D4×C11—21no—
16C23×D4×C11C411yescharacteristic, complemented
17C24×C4×C11—21no—
18C24×C4×C11C2211yescharacteristic
19C22×C11×M16—26no—
20C22×C11×M16—21no—
21C22×C11×M16C2212yescomplemented
22C22×C11×M16C22112yescomplemented
23C23×C8×C11—21no—
24C2×C11×#117—26no—
25C2×C11×#117C22112yescomplemented
26C22×C11×C4⋊C4—21no—
27C22×C11×C22⋊C4—21no—
28C22×C42×C11C2212yescomplemented
29C11×#421C22164yesdirect product factor
30C2×C11×#104C22148yescomplemented
31C25×C11—21no—
32C25×C11D411yescharacteristic
33C2×C11×#41—212no—
34C2×C11×#41—212no—
35C2×C11×#41—212no—
36C2×C11×#41—248no—
37C2×C11×#41—26no—
38C2×C11×#41—212no—
39C2×C11×#41—224no—
40C2×C11×#41—212no—
41C2×C11×#41—26no—
42C2×C11×#41—224no—
43C2×C11×#41C2×C4112yes—
44C2×C11×#41C2×C4124yescomplemented
45C2×C11×#41C2×C4148yescomplemented
46C2×C11×#41C23112yes—
47C2×C11×#41C23116yes—
48C22×Q8×C11—21no—
49C22×Q8×C11—26no—
50C22×Q8×C11C2×C412yes—
51C22×Q8×C11C2×C4112yescomplemented
52C22×D4×C11—22no—
53C22×D4×C11—212no—
54C22×D4×C11—22no—
55C22×D4×C11—212no—
56C22×D4×C11—26no—
57C22×D4×C11—21no—
58C22×D4×C11C2×C412yes—
59C22×D4×C11C2×C4112yescomplemented
60C23×C4×C11—21no—
61C23×C4×C11—22no—
62C23×C4×C11—212no—
63C23×C4×C11—212no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2×C416yes—
69C23×C4×C11D411yescharacteristic
70C23×C4×C11D416yes—
71C23×C4×C11D416yes—
72C23×C4×C11D411yescharacteristic
73C23×C4×C11D411yescharacteristic
74C23×C4×C11C2316yes—
75C23×C4×C11C2311yescharacteristic
76C2×C11×M16—212no—
77C2×C11×M16—26no—
78C2×C11×M16—224no—
79C2×C11×M16C23112yescomplemented
80C2×C11×M16C23116yescomplemented
81C22×C8×C11—212no—
82C22×C8×C11—22no—
83C11×#117—224no—
84C11×#117C23116yescomplemented
85C2×C11×C4⋊C4—212no—
86C2×C11×C22⋊C4—212no—
87C2×C42×C11—26no—
88C2×C42×C11C23112yescomplemented
89C11×#104C23164yescomplemented
90C22×#421C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—22no—
92C24×C11—212no—
93C24×C11—44no—
94C24×C11—48no—
95C24×C11C22⋊C411yescharacteristic
96C24×C11C22⋊C411yescharacteristic
97C24×C11C22⋊C416yes—
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D416yes—
100C11×#41—224no—
101C11×#41—248no—
102C11×#41—248no—
103C11×#41—248no—
104C11×#41—212no—
105C11×#41—216no—
106C11×#41—216no—
107C11×#41—212no—
108C11×#41C22×C4124yes—
109C11×#41C22×C4132yescomplemented
110C11×#41C2418yes—
111C2×Q8×C11—26no—
112C2×Q8×C11—212no—
113C2×Q8×C11—224no—
114C2×Q8×C11C22×C4112yes—
115C2×Q8×C11C22×C4116yescomplemented
116C2×D4×C11—212no—
117C2×D4×C11—224no—
118C2×D4×C11—248no—
119C2×D4×C11—212no—
120C2×D4×C11—216no—
121C2×D4×C11—26no—
122C2×D4×C11—224no—
123C2×D4×C11—212no—
124C2×D4×C11C22×C4112yes—
125C2×D4×C11C22×C4116yescomplemented
126C22×C4×C11—22no—
127C22×C4×C11—212no—
128C22×C4×C11—212no—
129C22×C4×C11—224no—
130C22×C4×C11—248no—
131C22×C4×C11—212no—
132C22×C4×C11—216no—
133C22×C4×C11—212no—
134C22×C4×C11—48no—
135C22×C4×C11C22⋊C411yescharacteristic
136C22×C4×C11C22⋊C416yes—
137C22×C4×C11C22⋊C416yes—
138C22×C4×C11C22⋊C411yescharacteristic
139C22×C4×C11C22⋊C416yes—
140C22×C4×C11C22⋊C416yes—
141C22×C4×C11C22⋊C4124yes—
142C22×C4×C11C22⋊C416yes—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C416yes—
145C22×C4×C11C22×C413yes—
146C22×C4×C11C22×C416yes—
147C22×C4×C11C22×C4112yes—
148C22×C4×C11C2×D413yes—
149C22×C4×C11C2×D416yes—
150C22×C4×C11C2×D4112yes—
151C22×C4×C11C2×D416yes—
152C22×C4×C11C2×D416yes—
153C22×C4×C11C2×D413yes—
154C22×C4×C11C2×D4112yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2413yes—
157C22×C4×C11C2414yes—
158C11×M16—216no—
159C11×M16—212no—
160C11×M16C2418yescomplemented
161C2×C8×C11—212no—
162C2×C8×C11—216no—
163C11×C4⋊C4—216no—
164C11×C22⋊C4—216no—
165C42×C11—212no—
166C42×C11C2418yescomplemented
167C23×#41C2×C1111yescharacteristic
168C23×M16C2×C1111yescharacteristic, complemented
169C22×#117C2×C1111yescharacteristic, complemented
170C2×#421C2×C11124yesdirect product factor
171C22×#104C2×C1114yescomplemented
172C23×C11—24no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—212no—
176C23×C11—216no—
177C23×C11—412no—
178C23×C11—412no—
179C23×C11—448no—
180C23×C11—48no—
181C23×C11C2×C22⋊C416yes—
182C23×C11C2×C22⋊C413yes—
183C23×C11C2×C22⋊C416yes—
184C23×C11C2×C22⋊C4112yes—
185C23×C11C2×C22⋊C411yescharacteristic
186C23×C11C22×D413yes—
187C23×C11C22×D414yes—
188Q8×C11—212no—
189Q8×C11—216no—
190Q8×C11C23×C418yes—
191D4×C11—224no—
192D4×C11—232no—
193D4×C11—28no—
194D4×C11—212no—
195D4×C11—216no—
196D4×C11C23×C418yes—
197C2×C4×C11—212no—
198C2×C4×C11—216no—
199C2×C4×C11—224no—
200C2×C4×C11—232no—
201C2×C4×C11—28no—
202C2×C4×C11—28no—
203C2×C4×C11—424no—
204C2×C4×C11C2×C22⋊C4112yes—
205C2×C4×C11C2×C22⋊C416yes—
206C2×C4×C11C2×C22⋊C413yes—
207C2×C4×C11C2×C22⋊C4112yes—
208C2×C4×C11C2×C22⋊C413yes—
209C2×C4×C11C2×C22⋊C416yes—
210C2×C4×C11C2×C22⋊C416yes—
211C2×C4×C11C2×C22⋊C4112yes—
212C2×C4×C11C2×C22⋊C4112yes—
213C2×C4×C11C2×C22⋊C4112yes—
214C2×C4×C11C23×C413yes—
215C2×C4×C11C23×C414yes—
216C2×C4×C11C23×C413yes—
217C2×C4×C11C23×C414yes—
218C2×C4×C11C22×D413yes—
219C2×C4×C11C22×D414yes—
220C2×C4×C11C22×D413yes—
221C2×C4×C11C22×D414yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11C22×D413yes—
224C2×C4×C11C2511yescharacteristic
225C8×C11—28no—
226C22×#41—21no—
227C22×#41—26no—
228C22×#41—21no—
229C22×#41—26no—
230C22×#41C4×C1112yescomplemented
231C22×#41C4×C11112yescomplemented
232C22×#41C22×C1112yes—
233C22×#41C22×C11112yes—
234C23×Q8C4×C1111yescharacteristic, complemented
235C23×D4—21no—
236C23×D4C4×C1111yescharacteristic, complemented
237C24×C4—21no—
238C24×C4C22×C1111yescharacteristic
239C22×M16—21no—
240C22×M16—26no—
241C22×M16C22×C1112yescomplemented
242C22×M16C22×C11112yescomplemented
243C23×C8—21no—
244C2×#117—26no—
245C2×#117C22×C11112yescomplemented
246C22×C4⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C42C22×C1112yescomplemented
249#421C22×C11164yesdirect product factor
250C2×#104C22×C11148yescomplemented
251C22×C11—26no—
252C22×C11—212no—
253C22×C11—26no—
254C22×C11—212no—
255C22×C11—28no—
256C22×C11—412no—
257C22×C11—44no—
258C22×C11—432no—
259C22×C11—424no—
260C22×C11#42114yesdirect product factor
261C22×C11C22×C22⋊C414yes—
262C22×C11C22×C22⋊C413yes—
263C22×C11C22×C22⋊C414yes—
264C22×C11C22×C22⋊C413yes—
265C22×C11C23×D411yescharacteristic
266C4×C11—28no—
267C4×C11—48no—
268C4×C11C22×C22⋊C413yes—
269C4×C11C22×C22⋊C414yes—
270C4×C11C22×C22⋊C413yes—
271C4×C11C22×C22⋊C414yes—
272C4×C11C24×C411yescharacteristic
273C4×C11C23×D411yescharacteristic
274C25—21no—
275C25D4×C1111yescharacteristic
276C2×#41—212no—
277C2×#41—212no—
278C2×#41—212no—
279C2×#41—248no—
280C2×#41—26no—
281C2×#41—212no—
282C2×#41—224no—
283C2×#41—212no—
284C2×#41—26no—
285C2×#41—224no—
286C2×#41C2×C4×C11112yes—
287C2×#41C2×C4×C11124yescomplemented
288C2×#41C2×C4×C11148yescomplemented
289C2×#41C23×C11112yes—
290C2×#41C23×C11116yes—
291C22×Q8—21no—
292C22×Q8—26no—
293C22×Q8C2×C4×C1112yes—
294C22×Q8C2×C4×C11112yescomplemented
295C22×D4—22no—
296C22×D4—212no—
297C22×D4—22no—
298C22×D4—212no—
299C22×D4—26no—
300C22×D4—21no—
301C22×D4C2×C4×C1112yes—
302C22×D4C2×C4×C11112yescomplemented
303C23×C4—21no—
304C23×C4—22no—
305C23×C4—212no—
306C23×C4—22no—
307C23×C4—212no—
308C23×C4—22no—
309C23×C4C2×C4×C1111yescharacteristic
310C23×C4C2×C4×C1111yescharacteristic
311C23×C4C2×C4×C1116yes—
312C23×C4D4×C1111yescharacteristic
313C23×C4D4×C1116yes—
314C23×C4D4×C1111yescharacteristic
315C23×C4D4×C1111yescharacteristic
316C23×C4D4×C1116yes—
317C23×C4C23×C1116yes—
318C23×C4C23×C1111yescharacteristic
319C2×M16—212no—
320C2×M16—26no—
321C2×M16—224no—
322C2×M16C23×C11112yescomplemented
323C2×M16C23×C11116yescomplemented
324C22×C8—22no—
325C22×C8—212no—
326#117—224no—
327#117C23×C11116yescomplemented
328C2×C4⋊C4—212no—
329C2×C22⋊C4—212no—
330C2×C42—26no—
331C2×C42C23×C11112yescomplemented
332#104C23×C11164yescomplemented
333C2×C11—21no—
334C2×C11—24no—
335C2×C11—23no—
336C2×C11—24no—
337C2×C11—48no—
338C2×C11C2×#42116yesdirect product factor
339C2×C11C23×C22⋊C411yescharacteristic
340C24—22no—
341C24—212no—
342C24—44no—
343C24—48no—
344C24C11×C22⋊C411yescharacteristic
345C24C11×C22⋊C411yescharacteristic
346C24C11×C22⋊C416yes—
347C24C2×D4×C1111yescharacteristic
348C24C2×D4×C1116yes—
349#41—224no—
350#41—248no—
351#41—248no—
352#41—248no—
353#41—212no—
354#41—216no—
355#41—216no—
356#41—212no—
357#41C22×C4×C11124yes—
358#41C22×C4×C11132yescomplemented
359#41C24×C1118yes—
360C2×Q8—26no—
361C2×Q8—212no—
362C2×Q8—224no—
363C2×Q8C22×C4×C11112yes—
364C2×Q8C22×C4×C11116yescomplemented
365C2×D4—212no—
366C2×D4—224no—
367C2×D4—248no—
368C2×D4—212no—
369C2×D4—216no—
370C2×D4—26no—
371C2×D4—224no—
372C2×D4—212no—
373C2×D4C22×C4×C11112yes—
374C2×D4C22×C4×C11116yescomplemented
375C22×C4—22no—
376C22×C4—212no—
377C22×C4—212no—
378C22×C4—224no—
379C22×C4—248no—
380C22×C4—212no—
381C22×C4—216no—
382C22×C4—212no—
383C22×C4—48no—
384C22×C4C11×C22⋊C416yes—
385C22×C4C11×C22⋊C411yescharacteristic
386C22×C4C11×C22⋊C416yes—
387C22×C4C11×C22⋊C411yescharacteristic
388C22×C4C11×C22⋊C416yes—
389C22×C4C11×C22⋊C416yes—
390C22×C4C11×C22⋊C416yes—
391C22×C4C11×C22⋊C4124yes—
392C22×C4C22×C4×C1111yescharacteristic
393C22×C4C22×C4×C1116yes—
394C22×C4C22×C4×C1113yes—
395C22×C4C22×C4×C1116yes—
396C22×C4C22×C4×C11112yes—
397C22×C4C2×D4×C1113yes—
398C22×C4C2×D4×C1116yes—
399C22×C4C2×D4×C11112yes—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1116yes—
402C22×C4C2×D4×C1116yes—
403C22×C4C2×D4×C1113yes—
404C22×C4C2×D4×C11112yes—
405C22×C4C24×C1113yes—
406C22×C4C24×C1114yes—
407M16—216no—
408M16—212no—
409M16C24×C1118yescomplemented
410C2×C8—212no—
411C2×C8—216no—
412C4⋊C4—216no—
413C22⋊C4—216no—
414C42—212no—
415C42C24×C1118yescomplemented
416C11C22×#42111yescharacteristic, direct product factor, Sylow
417C23—24no—
418C23—24no—
419C23—24no—
420C23—212no—
421C23—216no—
422C23—412no—
423C23—412no—
424C23—448no—
425C23—48no—
426C23C2×C11×C22⋊C416yes—
427C23C2×C11×C22⋊C413yes—
428C23C2×C11×C22⋊C416yes—
429C23C2×C11×C22⋊C4112yes—
430C23C2×C11×C22⋊C411yescharacteristic
431C23C22×D4×C1113yes—
432C23C22×D4×C1114yes—
433Q8—212no—
434Q8—216no—
435Q8C23×C4×C1118yes—
436D4—224no—
437D4—232no—
438D4—28no—
439D4—212no—
440D4—216no—
441D4C23×C4×C1118yes—
442C2×C4—212no—
443C2×C4—216no—
444C2×C4—224no—
445C2×C4—232no—
446C2×C4—28no—
447C2×C4—28no—
448C2×C4—424no—
449C2×C4C2×C11×C22⋊C4112yes—
450C2×C4C2×C11×C22⋊C416yes—
451C2×C4C2×C11×C22⋊C413yes—
452C2×C4C2×C11×C22⋊C4112yes—
453C2×C4C2×C11×C22⋊C413yes—
454C2×C4C2×C11×C22⋊C416yes—
455C2×C4C2×C11×C22⋊C416yes—
456C2×C4C2×C11×C22⋊C4112yes—
457C2×C4C2×C11×C22⋊C4112yes—
458C2×C4C2×C11×C22⋊C4112yes—
459C2×C4C23×C4×C1113yes—
460C2×C4C23×C4×C1114yes—
461C2×C4C23×C4×C1113yes—
462C2×C4C23×C4×C1114yes—
463C2×C4C22×D4×C1113yes—
464C2×C4C22×D4×C1114yes—
465C2×C4C22×D4×C1113yes—
466C2×C4C22×D4×C1114yes—
467C2×C4C22×D4×C1114yes—
468C2×C4C22×D4×C1113yes—
469C2×C4C25×C1111yescharacteristic
470C8—28no—
471C22—26no—
472C22—212no—
473C22—26no—
474C22—212no—
475C22—28no—
476C22—412no—
477C22—44no—
478C22—432no—
479C22—424no—
480C22C11×#42114yesdirect product factor
481C22C22×C11×C22⋊C414yes—
482C22C22×C11×C22⋊C413yes—
483C22C22×C11×C22⋊C414yes—
484C22C22×C11×C22⋊C413yes—
485C22C23×D4×C1111yescharacteristic
486C4—28no—
487C4—48no—
488C4C22×C11×C22⋊C413yes—
489C4C22×C11×C22⋊C414yes—
490C4C22×C11×C22⋊C413yes—
491C4C22×C11×C22⋊C414yes—
492C4C24×C4×C1111yescharacteristic
493C4C23×D4×C1111yescharacteristic
494C2—21no—
495C2—24no—
496C2—23no—
497C2—24no—
498C2—48no—
499C2C2×C11×#42116yesdirect product factor
500C2C23×C11×C22⋊C411yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC4C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC23×C11C2×C22⋊C4
prime radicalC23×C11×#41C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C11×M16C2semidirect
3. C22×C11×#117C2semidirect
4. C2×C11×#421C2direct (N × H)
5. C22×C11×#104C2semidirect
10. C22×C11×#41C4semidirect
11. C22×C11×#41C4semidirect
14. C23×Q8×C11C4semidirect
16. C23×D4×C11C4semidirect
21. C22×C11×M16C22semidirect
22. C22×C11×M16C22semidirect
25. C2×C11×#117C22semidirect
28. C22×C42×C11C22semidirect
29. C11×#421C22direct (N × H)
30. C2×C11×#104C22semidirect
44. C2×C11×#41C2×C4semidirect
45. C2×C11×#41C2×C4semidirect
51. C22×Q8×C11C2×C4semidirect
59. C22×D4×C11C2×C4semidirect
79. C2×C11×M16C23semidirect
80. C2×C11×M16C23semidirect
84. C11×#117C23semidirect
88. C2×C42×C11C23semidirect
89. C11×#104C23semidirect
90. C22×#421C11direct (N × H)
109. C11×#41C22×C4semidirect
115. C2×Q8×C11C22×C4semidirect
125. C2×D4×C11C22×C4semidirect
160. C11×M16C24semidirect
166. C42×C11C24semidirect
168. C23×M16C2×C11semidirect
169. C22×#117C2×C11semidirect
170. C2×#421C2×C11direct (N × H)
171. C22×#104C2×C11semidirect
230. C22×#41C4×C11semidirect
231. C22×#41C4×C11semidirect
234. C23×Q8C4×C11semidirect
236. C23×D4C4×C11semidirect
241. C22×M16C22×C11semidirect
242. C22×M16C22×C11semidirect
245. C2×#117C22×C11semidirect
248. C22×C42C22×C11semidirect
249. #421C22×C11direct (N × H)
250. C2×#104C22×C11semidirect
260. C22×C11#421direct (N × H)
287. C2×#41C2×C4×C11semidirect
288. C2×#41C2×C4×C11semidirect
294. C22×Q8C2×C4×C11semidirect
302. C22×D4C2×C4×C11semidirect
322. C2×M16C23×C11semidirect
323. C2×M16C23×C11semidirect
327. #117C23×C11semidirect
331. C2×C42C23×C11semidirect
332. #104C23×C11semidirect
338. C2×C11C2×#421direct (N × H)
358. #41C22×C4×C11semidirect
364. C2×Q8C22×C4×C11semidirect
374. C2×D4C22×C4×C11semidirect
409. M16C24×C11semidirect
415. C42C24×C11semidirect
416. C11C22×#421direct (N × H)
480. C22C11×#421direct (N × H)
499. C2C2×C11×#421direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×#412
C23×C11×M162
C22×C11×#1172
C2×C11×#4212
C22×C11×#1042
C22×#42111