Finite Group Databasebeta

← C2×#13072264 #14921847

Subgroups — C2×#13072264 #14921847

Order 2816.

7606 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
1C23×D4×D11C211yesmaximal, characteristic
2C22×#67000C211yesmaximal, characteristic, complemented
3C22×#66999C211yesmaximal, characteristic, complemented
4#13072264C2116yesmaximal, direct product factor
5C2×#10622572C214yesmaximal, complemented
6C2×#10622834C211yesmaximal, characteristic, complemented
7C2×#10622552C211yesmaximal, characteristic, complemented
8C2×#10622568C214yesmaximal, complemented
9C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10C22×C11×#124C211yesmaximal, characteristic, complemented
11C25×D11C2212yes—
12C23×Q8×C11C2211yescharacteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C22×D4×D11—28no—
16C22×D4×D11—28no—
17C22×D4×D11—28no—
18C22×D4×D11C2218yes—
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C2×C11×#124—28no—
22C2×C11×#124C2218yescomplemented
23C22×C11×C22⋊C4C2214yescomplemented
24C22×C42×C11C2211yescharacteristic, complemented
25C22×C22⋊Dic11C2214yescomplemented
26C2×#67000—28no—
27C2×#67000C2218yescomplemented
28C2×#66999—28no—
29C2×#66999C2218yescomplemented
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2214yescomplemented
33C22×(C2×D11)⋊C4C2214yescomplemented
34C22×C4⋊Dic11C2211yescharacteristic, complemented
35C22×Dic11⋊C4C2212yescomplemented
36C22×C4×Dic11C2211yescharacteristic, complemented
37#10622834C2218yescomplemented
38C2×C11⋊#95C2212yescomplemented
39#10622572C22132yescomplemented
40#10622568C22132yescomplemented
41#10622552C2218yescomplemented
42C4×(C2×D11)⋊C4C2218yescomplemented
43C25×C11C2312yes—
44C24×D11—28no—
45C24×D11—28no—
46C24×D11—28no—
47C24×D11—216no—
48C24×D11—48no—
49C24×D11C2312yes—
50C24×D11C2318yes—
51C24×D11C2311yescharacteristic
52C22×Q8×C11—24no—
53C22×Q8×C11—24no—
54C22×Q8×C11—24no—
55C22×Q8×C11C2314yescomplemented
56C22×D4×C11—24no—
57C22×D4×C11—24no—
58C22×D4×C11D418yes—
59C22×D4×C11C2314yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—28no—
66C22×C22⋊D11C2318yes—
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C2×D4×D11—2128no—
71C2×D4×D11—232no—
72C2×D4×D11—232no—
73C2×D4×D11—232no—
74C22×D44—24no—
75C22×D44—24no—
76C22×D44D418yes—
77C22×D44C2314yes—
78C22×C4×D11—24no—
79C22×C4×D11—24no—
80C22×C4×D11D418yes—
81C22×C4×D11C2314yes—
82C11×#124—232no—
83C2×C11×C22⋊C4—216no—
84C2×C11×C22⋊C4C23116yescomplemented
85C2×C42×C11—24no—
86C2×C42×C11C2314yescomplemented
87C2×C22⋊Dic11—48no—
88C2×C22⋊Dic11C23116yescomplemented
89#67000—232no—
90#66999—232no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—216no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—48no—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C23116yescomplemented
98C2×(C2×D11)⋊C4C23116yescomplemented
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2314yescomplemented
101C2×Dic11⋊C4—28no—
102C2×Dic11⋊C4C2318yescomplemented
103C2×C4×Dic11—24no—
104C2×C4×Dic11C2314yescomplemented
105C11⋊#95C2318yescomplemented
106C2×#2435—111nomaximal, Sylow
107C24×C11—24no—
108C24×C11—24no—
109C24×C11—28no—
110C24×C11—28no—
111C24×C11C2×D418yes—
112C24×C11C2414yes—
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—264no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—216no—
121C23×D11—28no—
122C23×D11—28no—
123C23×D11—216no—
124C23×D11—216no—
125C23×D11—232no—
126C23×D11—416no—
127C23×D11—464no—
128C23×D11—464no—
129C23×D11—432no—
130C23×D11—432no—
131C23×D11C2×D418yes—
132C23×D11C2×D414yes—
133C23×D11#4118yes—
134C23×D11C2414yes—
135C23×D11C2412yes—
136C2×Q8×C11—28no—
137C2×Q8×C11—28no—
138C2×Q8×C11—28no—
139C2×Q8×C11—416no—
140C2×D4×C11—232no—
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11C2×D4116yes—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2412yes—
156C2×C22⋊D11—264no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—216no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—28no—
166C22×Dic11—24no—
167C22×Dic11C2×D414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171D4×D11—2256no—
172C2×D44—232no—
173C2×D44—28no—
174C2×D44—28no—
175C2×D44C2×D4116yes—
176C2×C4×D11—232no—
177C2×C4×D11—28no—
178C2×C4×D11—28no—
179C2×C4×D11C2×D4116yes—
180C11×C22⋊C4—232no—
181C42×C11—28no—
182C22⋊Dic11—416no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—232no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—416no—
187C4⋊Dic11—28no—
188Dic11⋊C4—216no—
189C4×Dic11—28no—
190C24×D4—111no—
191C22×#124—111no—
192C22×#124D1111yescharacteristic, complemented
193C22×C22⋊Q8—111no—
194#2435—1116no—
195C2×#394—114no—
196C2×#390—111no—
197C2×#390—111no—
198C2×#379—114no—
199C2×C4×C22⋊C4—111no—
200C23×C11—216no—
201C23×C11—232no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—416no—
209C23×C11C22×D412yes—
210C23×C11C22×D412yes—
211C23×C11C22×D418yes—
212C23×C11C22×D412yes—
213C23×C11C2×#4114yes—
214C23×C11H(5,𝔽2)14yes—
215C23×C11C2511yescharacteristic
216C22×D11—28no—
217C22×D11—28no—
218C22×D11—216no—
219C22×D11—216no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—264no—
224C22×D11—216no—
225C22×D11—232no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—28no—
229C22×D11—28no—
230C22×D11—464no—
231C22×D11—464no—
232C22×D11—432no—
233C22×D11—4256no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—416no—
237C22×D11—432no—
238C22×D11#124116yescomplemented
239C22×D11C22×D418yes—
240C22×D11C22×D414yes—
241C22×D11C2×#4118yes—
242Q8×C11—416no—
243D4×C11—232no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—48no—
251C2×C4×C11—48no—
252C2×C4×C11#120116yes—
253C2×C4×C11C22×D414yes—
254C2×C4×C11C22×D414yes—
255C2×C4×C11C22×D414yes—
256C22⋊D11—264no—
257C2×Dic11—28no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—28no—
264C2×Dic11—24no—
265C2×Dic11—48no—
266C2×Dic11—48no—
267C2×Dic11C22×D414yes—
268D44—232no—
269C4×D11—232no—
270C26—112no—
271C23×Q8C2×D1111yescharacteristic, complemented
272C23×D4—112no—
273C23×D4—118no—
274C23×D4—111no—
275C23×D4—228no—
276C23×D4—228no—
277C23×D4—228no—
278C23×D4C2×D1111yescharacteristic
279C24×C4—111no—
280C2×#124—28no—
281C2×#124—118no—
282C2×#124—228no—
283C2×#124C2×D1118yescomplemented
284C2×C22⋊Q8—118no—
285C2×C22⋊Q8—228no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4—111no—
288C22×C22⋊C4—114no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—114no—
292C22×C22⋊C4—114no—
293C22×C22⋊C4C2×D1114yescomplemented
294C22×C42—111no—
295C22×C42C2×D1111yescharacteristic, complemented
296#394—1132no—
297#390—118no—
298#390—118no—
299#379—1132no—
300C4×C22⋊C4—118no—
301C2×#95—112no—
302C22×C11—28no—
303C22×C11—216no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—432no—
307C22×C11—48no—
308C22×C11C2×#12014yes—
309C22×C11C2×#12414yes—
310C22×C11#53514yes—
311C22×C11#54618yes—
312C22×C11#54618yes—
313C22×C11C23×D411yescharacteristic
314C22×C11C23×D411yescharacteristic
315C22×C11C23×D411yescharacteristic
316C22×C11C22×#4112yes—
317C22×C11C2×H(5,𝔽2)12yes—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—232no—
321C2×D11—28no—
322C2×D11—28no—
323C2×D11—28no—
324C2×D11—216no—
325C2×D11—4128no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—432no—
329C2×D11—48no—
330C2×D11C2×#12418yescomplemented
331C4×C11—44no—
332C4×C11—44no—
333C4×C11C2×#12018yes—
334Dic11—24no—
335Dic11—44no—
336Dic11—44no—
337C25—111no—
338C25—112no—
339C25—118no—
340C25—228no—
341C25—228no—
342C25—2216no—
343C25—228no—
344C25—448no—
345C25C22×D1112yes—
346C22×Q8—24no—
347C22×Q8—24no—
348C22×Q8—24no—
349C22×Q8C22×D1114yescomplemented
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—118no—
353C22×D4—118no—
354C22×D4—114no—
355C22×D4—2232no—
356C22×D4—228no—
357C22×D4—2232no—
358C22×D4—22128no—
359C22×D4—228no—
360C22×D4—228no—
361C22×D4—2232no—
362C22×D4—224no—
363C22×D4—224no—
364C22×D4C22⋊D1118yes—
365C22×D4C22×D1114yes—
366C23×C4—111no—
367C23×C4—118no—
368C23×C4—114no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—224no—
372C23×C4—224no—
373C23×C4C22×D1112yes—
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376#124—232no—
377#124—2232no—
378C22⋊Q8—2232no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—228no—
382C2×C4⋊C4—224no—
383C2×C22⋊C4—216no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—1116no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—1116no—
388C2×C22⋊C4—1116no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—2216no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—448no—
393C2×C22⋊C4—448no—
394C2×C22⋊C4C22×D11116yescomplemented
395C2×C42—24no—
396C2×C42—114no—
397C2×C42—224no—
398C2×C42C22×D1114yescomplemented
399#95—118no—
400C2×C11—48no—
401C2×C11#243518yescomplemented
402C2×C11C22×#12011yescharacteristic
403C2×C11C22×#12411yescharacteristic
404C2×C11C2×#53511yescharacteristic
405C2×C11C2×#54612yes—
406C2×C11C2×#54612yes—
407D11—28no—
408D11—48no—
409C24—24no—
410C24—24no—
411C24—28no—
412C24—28no—
413C24—114no—
414C24—118no—
415C24—112no—
416C24—118no—
417C24—114no—
418C24—2216no—
419C24—2216no—
420C24—2232no—
421C24—2264no—
422C24—222no—
423C24—224no—
424C24—222no—
425C24—224no—
426C24—228no—
427C24—228no—
428C24—2216no—
429C24—224no—
430C24—4416no—
431C24—4464no—
432C24—4432no—
433C24—4464no—
434C24—4432no—
435C24C2×C22⋊D1118yes—
436C24C23×D1114yes—
437C24C23×D1111yescharacteristic
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—416no—
442C2×D4—232no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—1116no—
446C2×D4—2216no—
447C2×D4—22256no—
448C2×D4—2216no—
449C2×D4—2264no—
450C2×D4—2216no—
451C2×D4—2232no—
452C2×D4—228no—
453C2×D4—228no—
454C2×D4C2×C22⋊D11116yes—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—114no—
462C22×C4—112no—
463C22×C4—1116no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—2232no—
469C22×C4—228no—
470C22×C4—228no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—228no—
475C22×C4—224no—
476C22×C4D4×D1114yes—
477C22×C4D4×D1114yes—
478C22×C4C2×C22⋊D1114yes—
479C22×C4C23×D1114yes—
480C22×C4C23×D1114yes—
481C22×C4C23×D1112yes—
482C4⋊C4—2216no—
483C4⋊C4—228no—
484C22⋊C4—232no—
485C22⋊C4—2216no—
486C22⋊C4—2232no—
487C22⋊C4—2216no—
488C22⋊C4—4416no—
489C22⋊C4—4416no—
490C42—28no—
491C42—228no—
492C11C2×#243511yescharacteristic, complemented, Sylow
493C23—216no—
494C23—232no—
495C23—24no—
496C23—24no—
497C23—28no—
498C23—28no—
499C23—48no—
500C23—48no—
501C23—416no—
502C23—114no—
503C23—118no—
504C23—1116no—
505C23—118no—
506C23—2264no—
507C23—228no—
508C23—2216no—
509C23—222no—
510C23—224no—
511C23—222no—
512C23—228no—
513C23—2216no—
514C23—2216no—
515C23—224no—
516C23—228no—
517C23—228no—
518C23—224no—
519C23—2232no—
520C23—4464no—
521C23—4432no—
522C23—4464no—
523C23—4432no—
524C23—44256no—
525C23—4416no—
526C23—448no—
527C23—448no—
528C23C2×D4×D1112yes—
529C23C2×D4×D1112yes—
530C23#41×D1114yes—
531C23#6704214yes—
532C23C22×C22⋊D1118yes—
533C23C22×C22⋊D1112yes—
534C23C24×D1111yescharacteristic
535Q8—416no—
536D4—232no—
537D4—2264no—
538D4—2232no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—48no—
546C2×C4—48no—
547C2×C4—114no—
548C2×C4—228no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—2232no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—228no—
556C2×C4—224no—
557C2×C4—448no—
558C2×C4—448no—
559C2×C4#66990116yes—
560C2×C4C2×D4×D1114yes—
561C2×C4C2×D4×D1114yes—
562C2×C4C22×C22⋊D1114yes—
563C22—216no—
564C22—28no—
565C22—44no—
566C22—44no—
567C22—432no—
568C22—48no—
569C22—118no—
570C22—224no—
571C22—2232no—
572C22—228no—
573C22—228no—
574C22—224no—
575C22—2216no—
576C22—228no—
577C22—44128no—
578C22—444no—
579C22—444no—
580C22—4432no—
581C22—448no—
582C22D11×#12414yes—
583C22#1062320514yes—
584C22#1062320718yes—
585C22C2×#6699014yes—
586C22#1062336018yes—
587C22C22×D4×D1111yescharacteristic
588C22C22×D4×D1111yescharacteristic
589C22C2×#41×D1112yes—
590C22C2×#6704212yes—
591C22C23×C22⋊D1111yescharacteristic
592C4—44no—
593C4—44no—
594C4—224no—
595C4—444no—
596C4—444no—
597C4C2×#6699018yes—
598C2—48no—
599C2—228no—
600C2—448no—
601C2#1307226418yesdirect product factor
602C2C22×#6699011yescharacteristic
603C2C2×D11×#12411yescharacteristic
604C2C2×#1062320511yescharacteristic
605C2C2×#1062336012yes—
606C2C2×#1062320712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#124C2
socleC24×C11C24
prime radicalC23×D4×D11C2
hypercenterC22×#124D11
hypocenterC11C2×#2435
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
2. C22×#67000C2semidirect
3. C22×#66999C2semidirect
4. #13072264C2direct (N × H)
5. C2×#10622572C2semidirect
6. C2×#10622834C2semidirect
7. C2×#10622552C2semidirect
8. C2×#10622568C2semidirect
9. C2×C4×(C2×D11)⋊C4C2semidirect
10. C22×C11×#124C2semidirect
12. C23×Q8×C11C22semidirect
22. C2×C11×#124C22semidirect
23. C22×C11×C22⋊C4C22semidirect
24. C22×C42×C11C22semidirect
25. C22×C22⋊Dic11C22semidirect
27. C2×#67000C22semidirect
29. C2×#66999C22semidirect
32. C22×(C2×D11)⋊C4C22semidirect
33. C22×(C2×D11)⋊C4C22semidirect
34. C22×C4⋊Dic11C22semidirect
35. C22×Dic11⋊C4C22semidirect
36. C22×C4×Dic11C22semidirect
37. #10622834C22semidirect
38. C2×C11⋊#95C22semidirect
39. #10622572C22semidirect
40. #10622568C22semidirect
41. #10622552C22semidirect
42. C4×(C2×D11)⋊C4C22semidirect
55. C22×Q8×C11C23semidirect
84. C2×C11×C22⋊C4C23semidirect
86. C2×C42×C11C23semidirect
88. C2×C22⋊Dic11C23semidirect
97. C2×(C2×D11)⋊C4C23semidirect
98. C2×(C2×D11)⋊C4C23semidirect
100. C2×C4⋊Dic11C23semidirect
102. C2×Dic11⋊C4C23semidirect
104. C2×C4×Dic11C23semidirect
105. C11⋊#95C23semidirect
192. C22×#124D11semidirect
238. C22×D11#124semidirect
271. C23×Q8C2×D11semidirect
283. C2×#124C2×D11semidirect
293. C22×C22⋊C4C2×D11semidirect
295. C22×C42C2×D11semidirect
330. C2×D11C2×#124semidirect
349. C22×Q8C22×D11semidirect
394. C2×C22⋊C4C22×D11semidirect
398. C2×C42C22×D11semidirect
401. C2×C11#2435semidirect
492. C11C2×#2435semidirect
601. C2#13072264direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×D112
C22×#670002
C22×#669992
#130722642
C2×#106225722
C2×#106228342
C2×#106225522
C2×#106225682
C2×C4×(C2×D11)⋊C42
C22×C11×#1242
C2×#243511