Finite Group Databasebeta

← C2×#13074303 #14924623

Subgroups — C2×#13074303 #14924623

Order 2816.

3286 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic, complemented
2#13074303C2116yesmaximal, direct product factor
3C2×#10622592C211yesmaximal, characteristic, complemented
4C2×#10622604C211yesmaximal, characteristic, complemented
5C2×#10622560C211yesmaximal, characteristic, complemented
6C2×#10622573C211yesmaximal, characteristic
7C2×#10622570C212yesmaximal, complemented
8C2×#10622553C212yesmaximal, complemented
9C2×#10622603C212yesmaximal, complemented
10C2×#10622826C212yesmaximal, complemented
11C2×#10622545C211yesmaximal, characteristic, complemented
12C22×C11×#117C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×D44C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#117—28no—
18C2×C11×#117C2218yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2212yes—
33C2×#66928—28no—
34C2×#66928C2218yescomplemented
35#10622826C22116yescomplemented
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622604C2218yescomplemented
42#10622603C22116yescomplemented
43#10622592C2218yescomplemented
44#10622573C2218yes—
45#10622570C22116yescomplemented
46#10622560C2218yescomplemented
47#10622553C22116yescomplemented
48#10622545C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—28no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11C2318yes—
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C22×D44—24no—
69C22×D44—44no—
70C22×D44C2314yes—
71C22×Dic22—24no—
72C22×Dic22—44no—
73C22×Dic22C2314yes—
74C11×#117—232no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C42×C11—24no—
84C2×C42×C11D418yescomplemented
85C2×C42×C11C2314yes—
86C2×C42×C11C2314yes—
87C2×C22⋊Dic11—44no—
88C2×C22⋊Dic11C2318yes—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—44no—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×Dic11⋊C4—44no—
100C2×Dic11⋊C4C2318yes—
101C2×C4×Dic11—28no—
102C2×C4×Dic11C2318yes—
103#66928—232no—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2610—111nomaximal, Sylow
110C24×C11—22no—
111C24×C11—24no—
112C24×C11—22no—
113C24×C11—24no—
114C24×C11#4114yes—
115C24×C11C2412yes—
116C24×C11C2411yescharacteristic
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11C2414yes—
125C22×C4×C11—232no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—28no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—28no—
134C22×C4×C11—28no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D414yes—
142C22×C4×C11#4114yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C2×C22⋊D11—216no—
150C2×C22⋊D11—216no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—432no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11#4118yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C2×D44—28no—
166C2×D44—48no—
167C2×D44—416no—
168C2×Dic22—28no—
169C2×Dic22—48no—
170C2×Dic22—416no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—28no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C42×C11—28no—
176C42×C11C2×D4116yescomplemented
177C22⋊Dic11—48no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—48no—
183Dic11⋊C4—48no—
184C4×Dic11—216no—
185C22×#124—111no—
186C22×#117D1111yescharacteristic, complemented
187#2610—1116no—
188C2×#395—111no—
189C2×#394—111no—
190C2×#393—111no—
191C2×#392—111no—
192C2×#390—112no—
193C2×#388—112no—
194C2×#388—112no—
195C2×#386—112no—
196C2×#376—111no—
197C23×C11—28no—
198C23×C11—216no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—48no—
206C23×C11C22×D412yes—
207C23×C11C2×#4114yes—
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210C23×C11C2×#4114yes—
211C23×C11H(5,𝔽2)14yes—
212C23×C11C2511yescharacteristic
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11—48no—
223C22×D11—48no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11—48no—
227C2×C4×C11—232no—
228C2×C4×C11—28no—
229C2×C4×C11—28no—
230C2×C4×C11—28no—
231C2×C4×C11—28no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11C22×D414yes—
245C2×C4×C11C22×D414yes—
246C2×C4×C11C22×D414yes—
247C2×C4×C11C2×#4114yes—
248C22⋊D11—432no—
249C2×Dic11—216no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—48no—
259C2×Dic11—48no—
260C2×Dic11C2×#4118yes—
261D44—416no—
262Dic22—416no—
263C23×Q8—111no—
264C23×D4—112no—
265C23×D4—111no—
266C24×C4C2×D1111yescharacteristic
267C2×#124—118no—
268C2×#124—228no—
269C2×#117—28no—
270C2×#117C2×D1118yescomplemented
271C22×C4⋊C4—112no—
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4C2×D1111yescharacteristic
281C22×C22⋊C4C2×D1111yescharacteristic
282C22×C42—112no—
283C22×C42C2×D1111yescharacteristic
284C22×C42C2×D1111yescharacteristic
285#395—118no—
286#394—118no—
287#393—118no—
288#392—118no—
289#390—1116no—
290#388—1116no—
291#388—1116no—
292#386—1116no—
293#376—118no—
294C2×#95—111no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C22×C11—24no—
300C22×C11—28no—
301C22×C11—416no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11#52514yes—
306C22×C11#53214yes—
307C22×C11#53514yes—
308C22×C11#55118yes—
309C22×C11#55518yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C22×#4111yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4112yes—
314C22×C11C2×H(5,𝔽2)12yes—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—816no—
323C4×C11—24no—
324C4×C11—24no—
325C4×C11—24no—
326C4×C11—24no—
327C4×C11—42no—
328C4×C11—42no—
329Dic11—28no—
330Dic11—44no—
331Dic11—44no—
332C25—112no—
333C25C22×D1111yescharacteristic
334C22×Q8—114no—
335C22×Q8—224no—
336C22×Q8—444no—
337C22×D4—118no—
338C22×D4—114no—
339C22×D4—228no—
340C22×D4—228no—
341C22×D4—224no—
342C22×D4—444no—
343C22×D4—444no—
344C23×C4—24no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4C22×D1114yes—
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357#124—2232no—
358#117—232no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—444no—
363C2×C4⋊C4C22×D1114yes—
364C2×C4⋊C4C22×D1114yes—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—444no—
378C2×C22⋊C4—444no—
379C2×C22⋊C4C22×D1114yes—
380C2×C22⋊C4C22×D1114yes—
381C2×C42—24no—
382C2×C42—118no—
383C2×C42—228no—
384C2×C42C22⋊D1118yescomplemented
385C2×C42C22×D1114yes—
386C2×C42C22×D1114yes—
387#95—118no—
388#95—114no—
389#95—114no—
390#95—118no—
391#95—118no—
392C2×C11—44no—
393C2×C11#261018yescomplemented
394C2×C11C2×#52511yescharacteristic
395C2×C11C2×#53211yescharacteristic
396C2×C11C2×#53511yescharacteristic
397C2×C11C2×#55112yes—
398C2×C11C2×#55512yes—
399D11—84no—
400C24—22no—
401C24—24no—
402C24—24no—
403C24—22no—
404C24—114no—
405C24—224no—
406C24—224no—
407C24—224no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24—224no—
412C24#433914yes—
413C24C23×D1112yes—
414C24C23×D1111yescharacteristic
415C2×Q8—228no—
416C2×Q8—448no—
417C2×Q8—4416no—
418C2×D4—2216no—
419C2×D4—2216no—
420C2×D4—228no—
421C2×D4—448no—
422C2×D4—4416no—
423C2×D4—448no—
424C2×D4—4432no—
425C22×C4—232no—
426C22×C4—28no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—118no—
440C22×C4—114no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4#433914yes—
452C22×C4C2×C22⋊D1114yes—
453C22×C4C2×C22⋊D1114yes—
454C22×C4C2×C22⋊D1114yes—
455C22×C4C23×D1112yes—
456C22×C4C23×D1112yes—
457C22×C4C23×D1112yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1112yes—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—448no—
464C22⋊C4—28no—
465C22⋊C4—28no—
466C22⋊C4—2216no—
467C22⋊C4—2216no—
468C22⋊C4—2216no—
469C22⋊C4—2216no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C42—28no—
473C42—2216no—
474C42C2×C22⋊D11116yescomplemented
475C11C2×#261011yescharacteristic, complemented, Sylow
476C23—216no—
477C23—28no—
478C23—22no—
479C23—24no—
480C23—24no—
481C23—22no—
482C23—48no—
483C23—44no—
484C23—44no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—224no—
489C23—224no—
490C23—224no—
491C23—224no—
492C23—448no—
493C23—448no—
494C23—448no—
495C23—448no—
496C23—448no—
497C23—448no—
498C23—448no—
499C23C2×#433914yes—
500C23C2×#433912yes—
501C23C2×#433912yes—
502C23#41×D1114yes—
503C23#6704214yes—
504C23C22×C22⋊D1112yes—
505C23C24×D1111yescharacteristic
506Q8—4416no—
507D4—4416no—
508D4—4432no—
509C2×C4—232no—
510C2×C4—28no—
511C2×C4—28no—
512C2×C4—28no—
513C2×C4—28no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—118no—
527C2×C4—2216no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—448no—
537C2×C4—448no—
538C2×C4C2×#433914yes—
539C2×C4C22×C22⋊D1114yes—
540C2×C4C22×C22⋊D1114yes—
541C2×C4C22×C22⋊D1114yes—
542C22—24no—
543C22—28no—
544C22—42no—
545C22—44no—
546C22—42no—
547C22—416no—
548C22—444no—
549C22—444no—
550C22—444no—
551C22—444no—
552C22—444no—
553C22—444no—
554C22—444no—
555C22—8816no—
556C22#1062305818yes—
557C22#1062306318yes—
558C22#1062332214yes—
559C22#1062336114yes—
560C22#1062336314yes—
561C22C22×#433911yescharacteristic
562C22C22×#433911yescharacteristic
563C22C2×#41×D1112yes—
564C22C2×#6704212yes—
565C22C23×C22⋊D1111yescharacteristic
566C4—24no—
567C4—24no—
568C4—24no—
569C4—24no—
570C4—42no—
571C4—42no—
572C4—228no—
573C4—444no—
574C4—444no—
575C2—44no—
576C2—884no—
577C2#1307430318yesdirect product factor
578C2C2×#1062332211yescharacteristic
579C2C2×#1062336311yescharacteristic
580C2C2×#1062336111yescharacteristic
581C2C2×#1062305812yes—
582C2C2×#1062306312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#117C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC22×#117D11
hypocenterC11C2×#2610
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#66928C2semidirect
2. #13074303C2direct (N × H)
3. C2×#10622592C2semidirect
4. C2×#10622604C2semidirect
5. C2×#10622560C2semidirect
7. C2×#10622570C2semidirect
8. C2×#10622553C2semidirect
9. C2×#10622603C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622545C2semidirect
12. C22×C11×#117C2semidirect
18. C2×C11×#117C22semidirect
34. C2×#66928C22semidirect
35. #10622826C22semidirect
41. #10622604C22semidirect
42. #10622603C22semidirect
43. #10622592C22semidirect
45. #10622570C22semidirect
46. #10622560C22semidirect
47. #10622553C22semidirect
48. #10622545C22semidirect
84. C2×C42×C11D4semidirect
176. C42×C11C2×D4semidirect
186. C22×#117D11semidirect
270. C2×#117C2×D11semidirect
384. C2×C42C22⋊D11semidirect
393. C2×C11#2610semidirect
474. C42C2×C22⋊D11semidirect
475. C11C2×#2610semidirect
577. C2#13074303direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
#130743032
C2×#106225922
C2×#106226042
C2×#106225602
C2×#106225732
C2×#106225702
C2×#106225532
C2×#106226032
C2×#106228262
C2×#106225452
C22×C11×#1172
C2×#261011