Finite Group Databasebeta

← C2×#13074425 #14920116

Subgroups — C2×#13074425 #14920116

Order 2816.

4142 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic11C211yesmaximal, characteristic
3#13074425C2116yesmaximal, direct product factor
4C2×#10622562C212yesmaximal, complemented
5C2×#10622561C212yesmaximal, complemented
6C2×#10622561C212yesmaximal, complemented
7C2×#10622560C212yesmaximal, complemented
8C2×#10622563C211yesmaximal, characteristic, complemented
9C2×#10622559C211yesmaximal, characteristic, complemented
10C2×#10622555C211yesmaximal, characteristic, complemented
11C2×#10622860C211yesmaximal, characteristic
12C2×C11×#379C211yesmaximal, characteristic
13C26×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic, complemented
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11—28no—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2218yes—
27C22×C22⋊Dic11C2212yes—
28C22×C22⋊Dic11C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic, complemented
30C22×C4⋊Dic11C2212yescomplemented
31C22×Dic11⋊C4C2211yescharacteristic, complemented
32C22×Dic11⋊C4C2211yescharacteristic, complemented
33C22×Dic11⋊C4C2212yescomplemented
34C22×Dic11⋊C4C2212yescomplemented
35C2×#66931—28no—
36C2×#66931C2218yescomplemented
37C11×#379C2218yes—
38#10622860C2218yes—
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42#10622563C2218yescomplemented
43#10622562C22116yescomplemented
44#10622561C22116yescomplemented
45#10622561C22116yescomplemented
46#10622560C22116yescomplemented
47#10622559C2218yescomplemented
48#10622555C2218yescomplemented
49C25×C11—24no—
50C25×C11—24no—
51C25×C11—44no—
52C25×C11—44no—
53C25×C11Q818yescomplemented
54C25×C11C2312yes—
55C25×C11C2311yescharacteristic
56C25×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—24no—
61C23×Dic11—44no—
62C23×Dic11—44no—
63C23×Dic11D418yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2314yes—
71C23×Dic11C2314yes—
72C22×Dic22—24no—
73C22×Dic22—44no—
74C22×Dic22C2314yescomplemented
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—44no—
78C2×C11×C22⋊C4—44no—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11—232no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11—44no—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—44no—
98C2×C4⋊Dic11C2314yescomplemented
99C2×C4⋊Dic11C2318yescomplemented
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4—44no—
104C2×Dic11⋊C4C2314yescomplemented
105C2×Dic11⋊C4C2314yescomplemented
106C2×Dic11⋊C4C2318yescomplemented
107C2×Dic11⋊C4C2318yescomplemented
108#66931—232no—
109C11⋊#95C2318yescomplemented
110C11⋊#95C2318yescomplemented
111C11⋊#95C2318yescomplemented
112C2×#2626—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—232no—
116C24×C11—24no—
117C24×C11—28no—
118C24×C11—24no—
119C24×C11—28no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—432no—
125C24×C11—48no—
126C24×C11—48no—
127C24×C11—416no—
128C24×C11—416no—
129C24×C11—432no—
130C24×C11C2×D414yes—
131C24×C11C2×Q818yes—
132C24×C11C2×Q814yes—
133C24×C11C2×Q8116yescomplemented
134C24×C11#4114yes—
135C24×C11C2414yes—
136C24×C11C2412yes—
137C24×C11C2411yescharacteristic
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—28no—
151C22×Dic11—24no—
152C22×Dic11—24no—
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—416no—
162C22×Dic11—48no—
163C22×Dic11—48no—
164C22×Dic11—416no—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×D414yes—
167C22×Dic11C2×D4116yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C2×Dic22—28no—
175C2×Dic22—48no—
176C2×Dic22—416no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—48no—
180C11×C22⋊C4—48no—
181C22⋊Dic11—216no—
182C22⋊Dic11—216no—
183C22⋊Dic11—28no—
184C22⋊Dic11—28no—
185C22⋊Dic11—48no—
186C22⋊Dic11—48no—
187C4⋊Dic11—28no—
188C4⋊Dic11—48no—
189Dic11⋊C4—28no—
190Dic11⋊C4—28no—
191Dic11⋊C4—48no—
192Dic11⋊C4—48no—
193C22×C22⋊Q8—111no—
194C23×C22⋊C4—111no—
195#2626—1116no—
196C2×#399—112no—
197C2×#396—112no—
198C2×#396—112no—
199C2×#393—112no—
200C2×#385—111no—
201C2×#385—111no—
202C2×#380—111no—
203C2×#379—111no—
204C2×#379D1111yescharacteristic
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—216no—
208C23×C11—216no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—216no—
212C23×C11—232no—
213C23×C11—216no—
214C23×C11—216no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—432no—
222C23×C11—4128no—
223C23×C11—416no—
224C23×C11—416no—
225C23×C11—432no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11C22⋊Q8116yes—
231C23×C11C22×D414yes—
232C23×C11C22×D412yes—
233C23×C11C22×Q818yes—
234C23×C11C22×Q814yes—
235C23×C11C22×Q812yes—
236C23×C11C2×#4114yes—
237C23×C11C2×#4112yes—
238C23×C11H(5,𝔽2)14yes—
239C23×C11H(5,𝔽2)14yes—
240C23×C11C2511yescharacteristic
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—48no—
251C2×Dic11—28no—
252C2×Dic11—28no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—416no—
266C2×Dic11—416no—
267C2×Dic11—44no—
268C2×Dic11—44no—
269C2×Dic11—48no—
270C2×Dic11—48no—
271C2×Dic11C22×D414yes—
272C2×Dic11C22×D414yes—
273Dic22—416no—
274C26C2×D1111yescharacteristic
275C23×Q8—111no—
276C24×C4—111no—
277C24×C4—111no—
278C2×C22⋊Q8—118no—
279C2×C22⋊Q8—228no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—112no—
286C22×C22⋊C4—118no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—228no—
294C22×C22⋊C4C2×D1111yescharacteristic
295C22×C22⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4C2×D1112yes—
297C22×C22⋊C4C2×D1112yes—
298#399—1116no—
299#396—1116no—
300#396—1116no—
301#393—1116no—
302#385—118no—
303#385—118no—
304#380—118no—
305#379—118no—
306#379C2×D1118yes—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—112no—
310C22×C11—232no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—28no—
314C22×C11—28no—
315C22×C11—28no—
316C22×C11—28no—
317C22×C11—28no—
318C22×C11—464no—
319C22×C11—432no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11C2×C22⋊Q818yes—
325C22×C11C2×C22⋊Q814yes—
326C22×C11#53414yes—
327C22×C11#53514yes—
328C22×C11#53818yes—
329C22×C11#54318yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C23×Q811yescharacteristic
332C22×C11C22×#4111yescharacteristic
333C22×C11C2×H(5,𝔽2)12yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—44no—
338Dic11—24no—
339Dic11—24no—
340Dic11—42no—
341Dic11—42no—
342Dic11—44no—
343Dic11—44no—
344C25—24no—
345C25—24no—
346C25—44no—
347C25—44no—
348C25Dic2218yescomplemented
349C25C22×D1112yes—
350C25C22×D1111yescharacteristic
351C25C22×D1114yes—
352C22×Q8—114no—
353C22×Q8—224no—
354C22×Q8—444no—
355C23×C4—111no—
356C23×C4—111no—
357C23×C4—118no—
358C23×C4—114no—
359C23×C4—111no—
360C23×C4—112no—
361C23×C4—111no—
362C23×C4—112no—
363C23×C4—114no—
364C23×C4—224no—
365C23×C4—444no—
366C23×C4—444no—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1112yes—
369C23×C4C22×D1111yescharacteristic
370C22⋊Q8—2232no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—118no—
375C2×C4⋊C4—118no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—444no—
381C2×C4⋊C4—444no—
382C2×C4⋊C4—444no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—228no—
394C2×C22⋊C4—228no—
395C2×C22⋊C4—2232no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—444no—
399C2×C22⋊C4—444no—
400C2×C22⋊C4C22×D1114yes—
401C2×C22⋊C4C22×D1114yes—
402C2×C22⋊C4C22×D1118yes—
403C2×C22⋊C4C22×D1118yes—
404#95—118no—
405#95—118no—
406#95—118no—
407C2×C11—28no—
408C2×C11—48no—
409C2×C11#262618yescomplemented
410C2×C11C22×C22⋊Q811yescharacteristic
411C2×C11C2×#53411yescharacteristic
412C2×C11C2×#53511yescharacteristic
413C2×C11C2×#53812yes—
414C2×C11C2×#54312yes—
415C24—24no—
416C24—24no—
417C24—232no—
418C24—24no—
419C24—28no—
420C24—24no—
421C24—28no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—48no—
427C24—48no—
428C24—432no—
429C24—416no—
430C24—416no—
431C24—432no—
432C24C2×Dic2218yes—
433C24C2×Dic2214yes—
434C24C2×Dic22116yescomplemented
435C24D4×D1114yes—
436C24#434114yes—
437C24C23×D1114yes—
438C24C23×D1112yes—
439C24C23×D1111yescharacteristic
440C2×Q8—228no—
441C2×Q8—448no—
442C2×Q8—4416no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—112no—
453C22×C4—112no—
454C22×C4—1116no—
455C22×C4—114no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—4416no—
473C22×C4—448no—
474C22×C4—448no—
475C22×C4—4416no—
476C22×C4C23×D1114yes—
477C22×C4C23×D1112yes—
478C22×C4C23×D1112yes—
479C4⋊C4—228no—
480C4⋊C4—228no—
481C4⋊C4—228no—
482C4⋊C4—448no—
483C4⋊C4—448no—
484C4⋊C4—448no—
485C22⋊C4—28no—
486C22⋊C4—28no—
487C22⋊C4—48no—
488C22⋊C4—48no—
489C22⋊C4—2216no—
490C22⋊C4—2216no—
491C22⋊C4—228no—
492C22⋊C4—228no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C11C2×#262611yescharacteristic, complemented, Sylow
496C23—216no—
497C23—28no—
498C23—28no—
499C23—216no—
500C23—24no—
501C23—24no—
502C23—216no—
503C23—232no—
504C23—216no—
505C23—216no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—432no—
513C23—416no—
514C23—416no—
515C23—432no—
516C23—4128no—
517C23—48no—
518C23—48no—
519C23—48no—
520C23—48no—
521C23#66931116yes—
522C23C22×Dic2218yes—
523C23C22×Dic2214yes—
524C23C22×Dic2212yes—
525C23C2×D4×D1114yes—
526C23C2×D4×D1112yes—
527C23C2×#434114yes—
528C23C2×#434112yes—
529C23#6703714yes—
530C23#6703714yes—
531C23C24×D1111yescharacteristic
532Q8—4416no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—48no—
543C2×C4—114no—
544C2×C4—114no—
545C2×C4—228no—
546C2×C4—228no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—4416no—
560C2×C4—4416no—
561C2×C4—444no—
562C2×C4—448no—
563C2×C4—444no—
564C2×C4—448no—
565C22—24no—
566C22—24no—
567C22—28no—
568C22—28no—
569C22—232no—
570C22—28no—
571C22—28no—
572C22—28no—
573C22—464no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—432no—
579C22C2×#6693118yes—
580C22C2×#6693114yes—
581C22#1062301418yes—
582C22#1062312014yes—
583C22#1062312314yes—
584C22#1062312418yes—
585C22C23×Dic2211yescharacteristic
586C22C22×D4×D1111yescharacteristic
587C22C22×#434111yescharacteristic
588C22C2×#6703712yes—
589C22C2×#6703712yes—
590C4—42no—
591C4—42no—
592C4—44no—
593C4—224no—
594C4—224no—
595C4—442no—
596C4—444no—
597C4—442no—
598C4—444no—
599C2—28no—
600C2—48no—
601C2#1307442518yesdirect product factor
602C2C22×#6693111yescharacteristic
603C2C2×#1062312011yescharacteristic
604C2C2×#1062312311yescharacteristic
605C2C2×#1062312412yes—
606C2C2×#1062301412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#379C2
socleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11C2×#2626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. #13074425C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622563C2semidirect
9. C2×#10622559C2semidirect
10. C2×#10622555C2semidirect
16. C23×Dic22C22semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×C4⋊Dic11C22semidirect
31. C22×Dic11⋊C4C22semidirect
32. C22×Dic11⋊C4C22semidirect
33. C22×Dic11⋊C4C22semidirect
34. C22×Dic11⋊C4C22semidirect
36. C2×#66931C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. #10622563C22semidirect
43. #10622562C22semidirect
44. #10622561C22semidirect
45. #10622561C22semidirect
46. #10622560C22semidirect
47. #10622559C22semidirect
48. #10622555C22semidirect
53. C25×C11Q8semidirect
74. C22×Dic22C23semidirect
98. C2×C4⋊Dic11C23semidirect
99. C2×C4⋊Dic11C23semidirect
104. C2×Dic11⋊C4C23semidirect
105. C2×Dic11⋊C4C23semidirect
106. C2×Dic11⋊C4C23semidirect
107. C2×Dic11⋊C4C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
111. C11⋊#95C23semidirect
133. C24×C11C2×Q8semidirect
348. C25Dic22semidirect
409. C2×C11#2626semidirect
434. C24C2×Dic22semidirect
495. C11C2×#2626semidirect
601. C2#13074425direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C23×C22⋊Dic112
#130744252
C2×#106225622
C2×#106225612
C2×#106225602
C2×#106225632
C2×#106225592
C2×#106225552
C2×#106228602
C2×C11×#3792
C2×#262611