Finite Group Databasebeta

← C2×#13076610 #14959888

Subgroups — C2×#13076610 #14959888

Order 2816.

4438 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66990C212yesmaximal, complemented
2#13076610C2116yesmaximal, direct product factor
3C2×#10622288C212yesmaximal, complemented
4C2×#10622566C211yesmaximal, characteristic, complemented
5C2×#10622574C212yesmaximal, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622835C212yesmaximal, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622568C211yesmaximal, characteristic, complemented
10C2×C11×#392C211yesmaximal, characteristic, complemented
11C25×D11C2211yescharacteristic
12C23×D4×C11C2212yes—
13C23×D4×C11C2211yescharacteristic, complemented
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yescomplemented
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yescomplemented
21C22×C22⋊Dic11C2212yescomplemented
22C2×#66990—216no—
23C2×#66990C22116yescomplemented
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic, complemented
29C22×Dic11⋊C4C2212yescomplemented
30C11×#392C2218yescomplemented
31C2×C11×#95C2211yescharacteristic, complemented
32#10622836C22116yescomplemented
33#10622835C22116yescomplemented
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2211yescharacteristic, complemented
37#10622574C22116yescomplemented
38#10622572C22116yescomplemented
39#10622568C2218yescomplemented
40#10622566C2218yescomplemented
41#10622288C22116yescomplemented
42C25×C11C2312yes—
43C25×C11C2311yescharacteristic
44C24×D11—44no—
45C24×D11—44no—
46C24×D11—42no—
47C24×D11—42no—
48C24×D11D418yescomplemented
49C24×D11C2312yes—
50C24×D11C2314yes—
51C22×D4×C11—28no—
52C22×D4×C11—44no—
53C22×D4×C11—44no—
54C22×D4×C11—44no—
55C22×D4×C11—42no—
56C22×D4×C11C2318yes—
57C22×D4×C11C2314yescomplemented
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—28no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11C2318yes—
68C22×C22⋊D11C2318yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4—44no—
74C2×C11×C22⋊C4C2314yes—
75C2×C11×C22⋊C4C2318yescomplemented
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—44no—
79C2×C22⋊Dic11—44no—
80C2×C22⋊Dic11C2318yes—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2318yescomplemented
83C2×C22⋊Dic11C2318yescomplemented
84#66990—264no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×C4⋊Dic11—42no—
94C2×C4⋊Dic11C2314yescomplemented
95C2×Dic11⋊C4—44no—
96C2×Dic11⋊C4C2318yescomplemented
97C11×#95C2314yescomplemented
98C11⋊#95C2318yescomplemented
99C11⋊#95C2318yescomplemented
100C11⋊#95C2314yescomplemented
101C2×#2812—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—24no—
105C24×C11—24no—
106C24×C11—24no—
107C24×C11—24no—
108C24×C11—24no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11C2×D414yes—
114C24×C11C2414yes—
115C24×C11C2412yes—
116C24×C11C2411yescharacteristic
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—416no—
124C23×D11—432no—
125C23×D11—48no—
126C23×D11—48no—
127C23×D11—44no—
128C23×D11—44no—
129C23×D11—416no—
130C23×D11—432no—
131C23×D11—416no—
132C23×D11C2×D418yes—
133C23×D11C2×D4116yescomplemented
134C23×D11C2414yes—
135C2×D4×C11—216no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—44no—
140C2×D4×C11—432no—
141C2×D4×C11—416no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11C2412yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2412yes—
152C2×C22⋊D11—216no—
153C2×C22⋊D11—216no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—432no—
159C2×C22⋊D11—432no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2414yes—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—48no—
174C22⋊Dic11—216no—
175C22⋊Dic11—44no—
176C22⋊Dic11—48no—
177C22⋊Dic11—48no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182C4⋊Dic11—44no—
183Dic11⋊C4—48no—
184C22×#120—112no—
185#2812—1116no—
186C2×#397—112no—
187C2×#397—111no—
188C2×#394—112no—
189C2×#394—112no—
190C2×#394—112no—
191C2×#392—112no—
192C2×#392D1111yescharacteristic, complemented
193C2×#379—111no—
194C23×C11—216no—
195C23×C11—28no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11C22×D414yes—
218C23×C11C22×D412yes—
219C23×C11H(5,𝔽2)14yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C11H(5,𝔽2)14yes—
222C23×C11H(5,𝔽2)12yes—
223C23×C11C2511yescharacteristic
224C22×D11—216no—
225C22×D11—216no—
226C22×D11—216no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—432no—
234C22×D11—416no—
235C22×D11—416no—
236C22×D11—432no—
237C22×D11—416no—
238C22×D11—4128no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11C22×D418yes—
244D4×C11—432no—
245D4×C11—416no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—48no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C22⋊D11—432no—
257C22⋊D11—432no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—48no—
268C2×Dic11—48no—
269C2×Dic11—48no—
270C26—111no—
271C23×D4—112no—
272C23×D4—112no—
273C23×D4C2×D1112yes—
274C23×D4C2×D1111yescharacteristic, complemented
275C2×#120—1116no—
276C2×#120—2216no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4C2×D1111yescharacteristic
288C22×C22⋊C4C2×D1112yescomplemented
289#397—118no—
290#397—1116no—
291#394—1116no—
292#394—1116no—
293#394—1116no—
294#392—1116no—
295#392C2×D1118yescomplemented
296#379—118no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—111no—
300C2×#95C2×D1111yescharacteristic, complemented
301C22×C11—28no—
302C22×C11—24no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—416no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—816no—
315C22×C11#53418yes—
316C22×C11#53414yes—
317C22×C11#56014yes—
318C22×C11#56018yes—
319C22×C11H(3,𝔽4)14yes—
320C22×C11C23×D411yescharacteristic
321C22×C11C2×H(5,𝔽2)12yes—
322C22×C11C2×H(5,𝔽2)11yescharacteristic
323C22×C11C2×H(5,𝔽2)12yes—
324C22×C11C2×H(5,𝔽2)11yescharacteristic
325C2×D11—28no—
326C2×D11—28no—
327C2×D11—28no—
328C2×D11—464no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—432no—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11—42no—
337Dic11—44no—
338Dic11—44no—
339Dic11—44no—
340C25—112no—
341C25—118no—
342C25—114no—
343C25—442no—
344C25—444no—
345C25—444no—
346C25—442no—
347C25C22×D1112yes—
348C25C22×D1111yescharacteristic
349C22×D4—28no—
350C22×D4—44no—
351C22×D4—44no—
352C22×D4—42no—
353C22×D4—44no—
354C22×D4—118no—
355C22×D4—118no—
356C22×D4—228no—
357C22×D4—228no—
358C22×D4—444no—
359C22×D4—444no—
360C22×D4—444no—
361C22×D4—444no—
362C22×D4C22×D1118yes—
363C22×D4C22×D1114yescomplemented
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—112no—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yes—
370#120—2264no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—444no—
374C2×C4⋊C4—442no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—228no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—444no—
389C2×C22⋊C4—444no—
390C2×C22⋊C4—444no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4—444no—
393C2×C22⋊C4C22×D1114yes—
394C2×C22⋊C4C22×D1118yescomplemented
395#95—118no—
396#95—114no—
397#95—118no—
398#95C22×D1114yescomplemented
399C2×C11—44no—
400C2×C11—84no—
401C2×C11#281218yescomplemented
402C2×C11C2×#53411yescharacteristic
403C2×C11C2×#53412yes—
404C2×C11C2×#56011yescharacteristic
405C2×C11C2×#56012yes—
406C2×C11C2×H(3,𝔽4)11yescharacteristic
407D11—48no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—24no—
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—118no—
420C24—114no—
421C24—1116no—
422C24—224no—
423C24—224no—
424C24—224no—
425C24—224no—
426C24—224no—
427C24—224no—
428C24—4432no—
429C24—4416no—
430C24—444no—
431C24—448no—
432C24—448no—
433C24—444no—
434C24—4416no—
435C24—4416no—
436C24—4432no—
437C24D4×D1114yes—
438C24C23×D1114yes—
439C24C23×D1112yes—
440C24C23×D1111yescharacteristic
441C2×D4—216no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—44no—
445C2×D4—48no—
446C2×D4—432no—
447C2×D4—416no—
448C2×D4—2216no—
449C2×D4—2216no—
450C2×D4—448no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—448no—
454C2×D4—4432no—
455C2×D4—4432no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4C23×D1112yes—
476C22×C4C23×D1114yes—
477C22×C4C23×D1112yes—
478C4⋊C4—448no—
479C4⋊C4—444no—
480C22⋊C4—44no—
481C22⋊C4—48no—
482C22⋊C4—2216no—
483C22⋊C4—2216no—
484C22⋊C4—2216no—
485C22⋊C4—448no—
486C22⋊C4—448no—
487C22⋊C4—448no—
488C22⋊C4—444no—
489C22⋊C4—448no—
490C11C2×#281211yescharacteristic, complemented, Sylow
491C23—216no—
492C23—28no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—44no—
505C23—44no—
506C23—48no—
507C23—48no—
508C23—48no—
509C23—48no—
510C23—48no—
511C23—48no—
512C23—48no—
513C23—48no—
514C23—118no—
515C23—2216no—
516C23—2216no—
517C23—2216no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—4416no—
525C23—4432no—
526C23—4416no—
527C23—4432no—
528C23—4416no—
529C23—44128no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23C2×D4×D1114yes—
535C23C2×D4×D1112yes—
536C23#6703714yes—
537C23#6703712yes—
538C23#6703714yes—
539C23#6704212yes—
540C23C24×D1111yescharacteristic
541D4—432no—
542D4—416no—
543D4—4432no—
544D4—4432no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—44no—
553C2×C4—48no—
554C2×C4—44no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—448no—
565C2×C4—448no—
566C2×C4—448no—
567C22—24no—
568C22—28no—
569C22—42no—
570C22—44no—
571C22—42no—
572C22—416no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—816no—
581C22—228no—
582C22—228no—
583C22—228no—
584C22—4464no—
585C22—444no—
586C22—444no—
587C22—444no—
588C22—444no—
589C22—4432no—
590C22#1062312018yes—
591C22#1062312514yes—
592C22#1062313614yes—
593C22#1062315118yes—
594C22#1062325114yes—
595C22C22×D4×D1111yescharacteristic
596C22C2×#6703711yescharacteristic
597C22C2×#6703712yes—
598C22C2×#6703712yes—
599C22C2×#6704211yescharacteristic
600C4—44no—
601C4—42no—
602C4—42no—
603C4—444no—
604C4—444no—
605C4—444no—
606C2—44no—
607C2—84no—
608C2—448no—
609C2#1307661018yesdirect product factor
610C2C2×#1062313611yescharacteristic
611C2C2×#1062312012yes—
612C2C2×#1062325111yescharacteristic
613C2C2×#1062315112yes—
614C2C2×#1062312511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66990C2semidirect
2. #13076610C2direct (N × H)
3. C2×#10622288C2semidirect
4. C2×#10622566C2semidirect
5. C2×#10622574C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622568C2semidirect
10. C2×C11×#392C2semidirect
13. C23×D4×C11C22semidirect
17. C22×C11×C22⋊C4C22semidirect
20. C22×C22⋊Dic11C22semidirect
21. C22×C22⋊Dic11C22semidirect
23. C2×#66990C22semidirect
28. C22×C4⋊Dic11C22semidirect
29. C22×Dic11⋊C4C22semidirect
30. C11×#392C22semidirect
31. C2×C11×#95C22semidirect
32. #10622836C22semidirect
33. #10622835C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. #10622574C22semidirect
38. #10622572C22semidirect
39. #10622568C22semidirect
40. #10622566C22semidirect
41. #10622288C22semidirect
48. C24×D11D4semidirect
57. C22×D4×C11C23semidirect
75. C2×C11×C22⋊C4C23semidirect
82. C2×C22⋊Dic11C23semidirect
83. C2×C22⋊Dic11C23semidirect
94. C2×C4⋊Dic11C23semidirect
96. C2×Dic11⋊C4C23semidirect
97. C11×#95C23semidirect
98. C11⋊#95C23semidirect
99. C11⋊#95C23semidirect
100. C11⋊#95C23semidirect
133. C23×D11C2×D4semidirect
192. C2×#392D11semidirect
274. C23×D4C2×D11semidirect
288. C22×C22⋊C4C2×D11semidirect
295. #392C2×D11semidirect
300. C2×#95C2×D11semidirect
363. C22×D4C22×D11semidirect
394. C2×C22⋊C4C22×D11semidirect
398. #95C22×D11semidirect
401. C2×C11#2812semidirect
490. C11C2×#2812semidirect
609. C2#13076610direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669902
#130766102
C2×#106222882
C2×#106225662
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225682
C2×C11×#3922
C2×#281211