Finite Group Databasebeta

← C22⋊C4×#4325 #14769607

Subgroups — C22⋊C4×#4325 #14769607

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4325C211yesmaximal, characteristic
2C2×C4×#4325C212yesmaximal, complemented
3C22⋊C4×D44C211yesmaximal, characteristic
4#13069473C212yesmaximal, complemented
5#13068971C212yesmaximal, complemented
6#13068953C212yesmaximal, complemented
7#13068639C211yesmaximal, characteristic, complemented
8#13068551C211yesmaximal, characteristic, complemented
9#13068546C211yesmaximal, characteristic
10C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C2×C4×Q8×C11C2212yescomplemented
15C22×#4325—28no—
16C22×#4325C418yescomplemented
17C22×#4325C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C22⋊C4×D11—21no—
23C2×C4×D44C2212yes—
24C11×#391—22no—
25C11×#391C2212yescomplemented
26C11×#380—21no—
27C11×#380C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66899C2212yescomplemented
31C2×#66899C2212yescomplemented
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C4×#4325—28no—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×#66872C2212yescomplemented
38#10622568—21no—
39#10622552C2212yes—
40C2×C4×C11⋊C8C2212yescomplemented
41#10622278—22no—
42#10622167C2212yescomplemented
43#10622162C2212yescomplemented
44C24×D11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—24no—
48C22×Q8×C11—42no—
49C22×Q8×C11C2×C414yescomplemented
50C22×Q8×C11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×D44—24no—
55C22×D44—21no—
56C22×D44—22no—
57C22×D44—42no—
58C22×D44C2×C414yes—
59C22×D44C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—22no—
62C4×Q8×C11—24no—
63C4×Q8×C11—42no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C42×C11—22no—
70C2×C42×C11C2312yes—
71C2×C22⋊Dic11—21no—
72C2×#4325—24no—
73C2×#4325—24no—
74C2×#4325—232no—
75C2×#4325—24no—
76C2×#4325C2×C414yes—
77C2×#4325C2×C414yes—
78C2×#4325C2×C414yescomplemented
79C2×#4325C2×C414yescomplemented
80C2×#4325D418yes—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×C4⋊Dic11C2312yes—
85C22×C11⋊C8—24no—
86C22×C11⋊C8C2×C414yescomplemented
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22⋊C4×D11—44no—
91C4×D44—24no—
92C4×D44—42no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—21no—
96C11×#95D412yes—
97#66899—24no—
98#66899—42no—
99C11⋊#95—21no—
100C22⋊(C11⋊C8)—22no—
101#66873—24no—
102#66873—42no—
103#66872—24no—
104C4×C11⋊C8—24no—
105C22⋊C4×SD16—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—24no—
110C23×D11—44no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11—82no—
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—44no—
122C2×Q8×C11—44no—
123C2×Q8×C11—48no—
124C2×Q8×C11C22×C412yes—
125C2×Q8×C11C22×C412yes—
126C2×Q8×C11C2×D414yes—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—44no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—22no—
141C2×D44—28no—
142C2×D44—24no—
143C2×D44—22no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—44no—
149C2×D44—44no—
150C2×D44—48no—
151C2×D44C22×C412yes—
152C2×D44C22×C412yes—
153C2×D44C2×D414yes—
154C2×C4×D11—44no—
155C2×C4×D11—44no—
156C2×C4×D11—82no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—44no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4SD1614yescomplemented
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—44no—
166C22⋊Dic11—42no—
167#4325—28no—
168#4325—28no—
169#4325—28no—
170#4325C22⋊C4116yesdirect product factor
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—82no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C2×C11⋊C8—28no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8C22×C412yes—
182C2×C11⋊C8C22×C412yes—
183C2×C11⋊C8C2×D414yes—
184C23×SD16—111no—
185C2×C4×SD16—112no—
186Q8×C22⋊C4D1111yescharacteristic, complemented
187D4×C22⋊C4—111no—
188#1968—112no—
189#1880—112no—
190#1877—112no—
191#1807—111no—
192#1787—111no—
193#1786—111no—
194C8×C22⋊C4—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11C4×D412yes—
198C23×C11C2×SD1612yes—
199C23×C11#13512yes—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—24no—
203C22×D11—22no—
204C22×D11—48no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—42no—
212C22×D11—48no—
213C22×D11—84no—
214C22×D11—88no—
215C22×D11—88no—
216Q8×C11—22no—
217Q8×C11—24no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—48no—
221Q8×C11—42no—
222Q8×C11C2×C22⋊C414yescomplemented
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—48no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11C4×D412yes—
241C2×C4×C11C2×SD1614yescomplemented
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D412yes—
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)12yes—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249D44—22no—
250D44—22no—
251D44—22no—
252D44—24no—
253D44—48no—
254D44—42no—
255D44C2×C22⋊C414yes—
256C4×D11—88no—
257C11⋊C8—22no—
258C11⋊C8—42no—
259C11⋊C8C2×C22⋊C414yescomplemented
260C23×Q8C2×D1111yescharacteristic
261C23×D4—111no—
262C22×SD16—111no—
263C22×SD16—111no—
264C22×SD16—111no—
265C22×SD16—111no—
266C22×SD16—118no—
267C22×SD16—228no—
268C23×C8—111no—
269C2×C4×Q8C2×D1112yescomplemented
270C2×C4×D4—112no—
271C22×C22⋊C4—221no—
272C4×SD16—228no—
273C2×#106—112no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#102—112no—
277C2×#102—112no—
278C2×C22⋊C8—111no—
279C2×C4×C8—112no—
280#391—22no—
281#391C2×D1112yescomplemented
282#390—112no—
283#386—222no—
284#380—21no—
285#380—111no—
286#380C2×D1111yescharacteristic
287#379—221no—
288C4×C22⋊C4—21no—
289C4×C22⋊C4C2×D1111yescharacteristic
290#340—112no—
291#336—112no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11C4×SD1614yescomplemented
297C22×C11C2×C4×D411yescharacteristic
298C22×C11D4212yes—
299C22×C11C22×SD1611yescharacteristic
300C22×C11C2×#13511yescharacteristic
301C22×C11#57712yes—
302C2×D11—24no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—44no—
306C2×D11—44no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—816no—
311C2×D11—82no—
312C2×D11—82no—
313C4×C11—22no—
314C4×C11—24no—
315C4×C11—24no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—82no—
319C4×C11C22×C22⋊C411yescharacteristic
320C4×C11#51811yescharacteristic
321C4×C11#54612yes—
322Dic11—82no—
323C25—221no—
324C22×Q8—22no—
325C22×Q8—21no—
326C22×Q8—24no—
327C22×Q8—42no—
328C22×Q8C4×D1114yescomplemented
329C22×Q8C22×D1111yescharacteristic
330C22×Q8C22×D1111yescharacteristic
331C22×D4—114no—
332C22×D4—111no—
333C22×D4—111no—
334C22×D4—224no—
335C22×D4—222no—
336C22×D4—221no—
337C22×D4—442no—
338C23×C4—21no—
339C23×C4—222no—
340C23×C4C22×D1111yescharacteristic
341C2×SD16—114no—
342C2×SD16—118no—
343C2×SD16—114no—
344C2×SD16—114no—
345C2×SD16—114no—
346C2×SD16—224no—
347C2×SD16—2232no—
348C2×SD16—224no—
349C2×SD16—224no—
350C22×C8—111no—
351C22×C8—114no—
352C22×C8—111no—
353C22×C8—112no—
354C22×C8—224no—
355C4×Q8—24no—
356C4×Q8—42no—
357C4×D4—224no—
358C4×D4—442no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4C22×D1112yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—444no—
368C2×C22⋊C4C22⋊D1111yescharacteristic
369C2×C22⋊C4C22⋊D1111yescharacteristic
370C2×C42—22no—
371C2×C42C22×D1112yes—
372#106—224no—
373#103—224no—
374#103—442no—
375#102—224no—
376#102—442no—
377C22⋊C8—222no—
378C4×C8—224no—
379#95—22no—
380#95—22no—
381#95—21no—
382#95—221no—
383#95C22⋊D1112yes—
384C2×C11—24no—
385C2×C11D4×C22⋊C411yescharacteristic
386C2×C11C2×C4×SD1611yescharacteristic
387C2×C11#294911yescharacteristic
388C2×C11D4×SD1612yes—
389C2×C11#328212yes—
390D11—44no—
391D11—82no—
392C24—221no—
393C24—221no—
394C24—224no—
395C24—444no—
396C24—442no—
397C24—442no—
398C24—882no—
399C24C2×C22⋊D1111yescharacteristic
400C2×Q8—24no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—28no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—48no—
410C2×Q8C2×C4×D1112yes—
411C2×Q8C2×C4×D1112yes—
412C2×Q8D4×D1114yes—
413C2×D4—112no—
414C2×D4—112no—
415C2×D4—114no—
416C2×D4—228no—
417C2×D4—224no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—444no—
424C2×D4—448no—
425C2×D4—444no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—222no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4—882no—
437C22×C4C2×C4×D1112yes—
438C22×C4#433912yes—
439C22×C4C2×C22⋊D1112yes—
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1112yes—
442C22×C4C23×D1111yescharacteristic
443SD16—1116no—
444SD16—228no—
445SD16—228no—
446SD16—228no—
447C2×C8—112no—
448C2×C8—114no—
449C2×C8—112no—
450C2×C8—228no—
451C2×C8—222no—
452C2×C8—222no—
453C2×C8—222no—
454C2×C8—222no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—44no—
458C4⋊C4—222no—
459C4⋊C4—222no—
460C22⋊C4—22no—
461C22⋊C4—42no—
462C22⋊C4—444no—
463C22⋊C4—442no—
464C22⋊C4—444no—
465C22⋊C4—882no—
466C22⋊C4#432514yesdirect product factor
467C42—22no—
468C42—22no—
469C42—44no—
470C11C22⋊C4×SD1611yescharacteristic, complemented, Sylow
471C23—22no—
472C23—22no—
473C23—222no—
474C23—224no—
475C23—222no—
476C23—448no—
477C23—441no—
478C23—441no—
479C23—442no—
480C23—442no—
481C23—441no—
482C23—441no—
483C23—442no—
484C23—448no—
485C23—884no—
486C23—888no—
487C23—888no—
488C23C4×C22⋊D1112yes—
489C23C2×#432512yes—
490C23#6700312yes—
491C23C22×C22⋊D1111yescharacteristic
492Q8—22no—
493Q8—24no—
494Q8—22no—
495Q8—22no—
496Q8—48no—
497Q8—42no—
498Q8C22⋊C4×D1114yescomplemented
499D4—114no—
500D4—222no—
501D4—222no—
502D4—222no—
503D4—224no—
504D4—448no—
505D4—442no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—48no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—888no—
527C2×C4C4×C22⋊D1112yes—
528C2×C4C2×#432514yescomplemented
529C2×C4C22×C4×D1111yescharacteristic
530C2×C4C2×#433911yescharacteristic
531C2×C4C2×D4×D1112yes—
532C2×C4#6703712yes—
533C8—114no—
534C8—222no—
535C8—442no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—24no—
540C22—224no—
541C22—444no—
542C22—442no—
543C22—442no—
544C22—444no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—8816no—
549C22—882no—
550C22—882no—
551C22C4×#432514yescomplemented
552C22C2×C4×C22⋊D1111yescharacteristic
553C22D4×C22⋊D1112yes—
554C22C22×#432511yescharacteristic
555C22C2×#6700311yescharacteristic
556C22#1062336812yes—
557C4—22no—
558C4—24no—
559C4—24no—
560C4—42no—
561C4—42no—
562C4—82no—
563C4—882no—
564C4C2×C22⋊C4×D1111yescharacteristic
565C4#1062301711yescharacteristic
566C4#1062302112yes—
567C2—24no—
568C2—444no—
569C2—882no—
570C2C22⋊C4×C22⋊D1111yescharacteristic
571C2C2×C4×#432511yescharacteristic
572C2#1307747511yescharacteristic
573C2D4×#432512yes—
574C2#1308032412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterQ8×C22⋊C4D11
hypocenterC11C22⋊C4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
4. #13069473C2semidirect
5. #13068971C2semidirect
6. #13068953C2semidirect
7. #13068639C2semidirect
8. #13068551C2semidirect
10. C22⋊C4×C11⋊C8C2semidirect
11. Q8×C11×C22⋊C4C2semidirect
14. C2×C4×Q8×C11C22semidirect
16. C22×#4325C4semidirect
25. C11×#391C22semidirect
30. C2×#66899C22semidirect
31. C2×#66899C22semidirect
37. C2×#66872C22semidirect
40. C2×C4×C11⋊C8C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
49. C22×Q8×C11C2×C4semidirect
78. C2×#4325C2×C4semidirect
79. C2×#4325C2×C4semidirect
86. C22×C11⋊C8C2×C4semidirect
162. C11×C22⋊C4SD16semidirect
170. #4325C22⋊C4direct (N × H)
186. Q8×C22⋊C4D11semidirect
222. Q8×C11C2×C22⋊C4semidirect
241. C2×C4×C11C2×SD16semidirect
259. C11⋊C8C2×C22⋊C4semidirect
269. C2×C4×Q8C2×D11semidirect
281. #391C2×D11semidirect
296. C22×C11C4×SD16semidirect
328. C22×Q8C4×D11semidirect
466. C22⋊C4#4325direct (N × H)
470. C11C22⋊C4×SD16semidirect
498. Q8C22⋊C4×D11semidirect
528. C2×C4C2×#4325semidirect
551. C22C4×#4325semidirect

Maximal subgroups

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

subgroupindex
C23×#43252
C2×C4×#43252
C22⋊C4×D442
#130694732
#130689712
#130689532
#130686392
#130685512
#130685462
C22⋊C4×C11⋊C82
Q8×C11×C22⋊C42
C22⋊C4×SD1611