Finite Group Databasebeta

← C2×#19135846 #25124357

Subgroups — C2×#19135846 #25124357

Order 11008.

2046 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583461C211yesmaximal, characteristic
2C22×#13063239C212yesmaximal, complemented
3C2×#14582778C212yesmaximal, complemented
4#19135846C218yesmaximal, direct product factor
5C2×#14582666C211yesmaximal, characteristic, complemented
6C2×C43×#385C211yesmaximal, characteristic, complemented
7C23×C22⋊D43C2212yes—
8#14583461—24no—
9#14583461—22no—
10#14583461C2214yes—
11C2×#13063309—22no—
12C2×#13063299—21no—
13C2×#13063299—21no—
14C2×#13063295—22no—
15C22×C22⋊Dic43C2212yes—
16C22×(C2×D43)⋊C4—22no—
17C2×#13063239—28no—
18C2×#13063239C2218yescomplemented
19#14582778—24no—
20#14582778C2218yescomplemented
21C2×C43⋊#95—22no—
22#14582666C2214yescomplemented
23C24×C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43—21no—
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C43×#385—22no—
28C43×#385C2214yescomplemented
29C2×#95×C43—21no—
30C24×D43D412yes—
31C22×D172—21no—
32C22×D172—21no—
33C22×C22⋊D43—24no—
34C22×C22⋊D43—22no—
35C22×C22⋊D43—22no—
36C22×C22⋊D43—22no—
37C22×C22⋊D43—22no—
38C22×C22⋊D43—24no—
39C22×C22⋊D43—24no—
40C22×C22⋊D43—24no—
41C22×C22⋊D43D414yes—
42C22×C22⋊D43C2314yes—
43C23×Dic43—22no—
44C23×Dic43D412yes—
45#13063309—28no—
46#13063309—28no—
47#13063299—24no—
48#13063299—24no—
49#13063299—24no—
50#13063299—24no—
51#13063295—28no—
52#13063295—28no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C22⋊Dic43—24no—
56C2×C22⋊Dic43—24no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43C2314yes—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—28no—
62C2×(C2×D43)⋊C4—48no—
63#13063239—216no—
64C43⋊#95—28no—
65C25×C43C2311yescharacteristic
66C23×C4×C43—21no—
67C23×C4×C43—21no—
68C23×C4×C43—22no—
69C23×C4×C43—21no—
70C23×C4×C43—22no—
71C23×C4×C43—44no—
72C23×C4×C43D411yescharacteristic
73C23×C4×C43D411yescharacteristic
74C23×C4×C43C2312yes—
75C2×C4⋊C4×C43—24no—
76C2×C4⋊C4×C43—44no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43D412yes—
82C2×C22⋊C4×C43D414yescomplemented
83C2×C22⋊C4×C43C2312yes—
84C2×C22⋊C4×C43C2312yes—
85#95×C43—24no—
86C24×C43—42no—
87C24×C43—42no—
88C24×C43C2×D412yes—
89C24×C43C2×D411yescharacteristic
90C24×C43C2×D412yes—
91C24×C43C2×D411yescharacteristic
92C24×C43C2×D412yes—
93C24×C43#4112yes—
94C24×C43#4114yes—
95C24×C43C2411yescharacteristic
96C23×D43—22no—
97C23×D43—24no—
98C23×D43—22no—
99C23×D43—24no—
100C23×D43—44no—
101C23×D43—44no—
102C23×D43C2×D414yes—
103C22×C4×C43—24no—
104C22×C4×C43—28no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—24no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—24no—
113C22×C4×C43—42no—
114C22×C4×C43—42no—
115C22×C4×C43—44no—
116C22×C4×C43—42no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43—44no—
120C22×C4×C43—48no—
121C22×C4×C43—44no—
122C22×C4×C43—42no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D412yes—
127C2×C22⋊D43—24no—
128C2×C22⋊D43—24no—
129C2×C22⋊D43—28no—
130C2×C22⋊D43—28no—
131C2×C22⋊D43—24no—
132C2×C22⋊D43—24no—
133C2×C22⋊D43—24no—
134C2×C22⋊D43—24no—
135C2×C22⋊D43—24no—
136C2×C22⋊D43—24no—
137C2×C22⋊D43—44no—
138C2×C22⋊D43—44no—
139C2×C22⋊D43—44no—
140C2×C22⋊D43—44no—
141C2×C22⋊D43—44no—
142C2×C22⋊D43—44no—
143C2×C22⋊D43—44no—
144C2×C22⋊D43—44no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—24no—
148C22×Dic43—24no—
149C22×Dic43—24no—
150C22×Dic43—44no—
151C22×Dic43—44no—
152C22×Dic43—44no—
153C22×Dic43C2×D414yes—
154C2×D172—24no—
155C2×D172—24no—
156C2×D172—82no—
157C2×D172—82no—
158C4⋊C4×C43—48no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43C2×D414yescomplemented
164C22⋊Dic43—24no—
165C22⋊Dic43—24no—
166C22⋊Dic43—44no—
167(C2×D43)⋊C4—28no—
168(C2×D43)⋊C4—28no—
169(C2×D43)⋊C4—416no—
170C4⋊Dic43—24no—
171C4⋊Dic43—24no—
172C23×C43—24no—
173C23×C43—22no—
174C23×C43—24no—
175C23×C43—22no—
176C23×C43—42no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—44no—
180C23×C43—42no—
181C23×C43—41no—
182C23×C43—44no—
183C23×C43—48no—
184C23×C43—41no—
185C23×C43#12012yes—
186C23×C43#12011yescharacteristic
187C23×C43#12011yescharacteristic
188C23×C43#12112yes—
189C23×C43#12112yes—
190C23×C43#12114yes—
191C23×C43#12114yes—
192C23×C43#12314yes—
193C23×C43#12314yes—
194C23×C43#12412yes—
195C23×C43#12412yes—
196C23×C43C22×D412yes—
197C23×C43C22×D411yescharacteristic
198C23×C43C22×D411yescharacteristic
199C23×C43C2×#4111yescharacteristic
200C23×C43C2×#4112yes—
201C22×D43—24no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—44no—
205C22×D43—44no—
206C22×D43—416no—
207C22×D43—44no—
208C22×D43—44no—
209C22×D43—44no—
210C22×D43—44no—
211C22×D43—82no—
212C22×D43—82no—
213C22×D43—88no—
214C2×C4×C43—28no—
215C2×C4×C43—24no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—24no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—48no—
222C2×C4×C43—44no—
223C2×C4×C43—48no—
224C2×C4×C43—44no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—44no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—81no—
233C2×C4×C43—81no—
234C22⋊D43—44no—
235C22⋊D43—44no—
236C22⋊D43—44no—
237C22⋊D43—44no—
238C22⋊D43—48no—
239C22⋊D43—48no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—44no—
244C2×Dic43—44no—
245C2×Dic43—44no—
246C2×Dic43—44no—
247C2×Dic43—44no—
248C2×Dic43—88no—
249D172—84no—
250D172—84no—
251C2×#2044—431nomaximal, Sylow
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—28no—
261C22×C43—28no—
262C22×C43—24no—
263C22×C43—24no—
264C22×C43—42no—
265C22×C43—44no—
266C22×C43—44no—
267C22×C43—42no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—42no—
271C22×C43#39414yes—
272C22×C43#39412yes—
273C22×C43#39412yes—
274C22×C43B(4,𝔽2)12yes—
275C22×C43#45812yes—
276C22×C43C2×#12011yescharacteristic
277C22×C43C2×#12111yescharacteristic
278C22×C43C2×#12112yes—
279C22×C43C2×#12312yes—
280C22×C43C2×#12411yescharacteristic
281C2×D43—48no—
282C2×D43—44no—
283C2×D43—44no—
284C2×D43—44no—
285C2×D43—88no—
286C2×D43—88no—
287C2×D43—84no—
288C4×C43—44no—
289C4×C43—42no—
290C4×C43—44no—
291C4×C43—42no—
292Dic43—44no—
293Dic43—84no—
294C2×#534—431no—
295C22×#99—432no—
296C2×#386—432no—
297C2×#385D4311yescharacteristic, complemented
298#2044—438no—
299C2×#342—431no—
300C2×C43—22no—
301C2×C43—21no—
302C2×C43—22no—
303C2×C43—24no—
304C2×C43—21no—
305C2×C43—22no—
306C2×C43#204414yescomplemented
307C2×C43C2×#39411yescharacteristic
308C2×C43C2×B(4,𝔽2)11yescharacteristic
309C2×C43C2×#45811yescharacteristic
310D43—84no—
311C23×D4—432no—
312C24×C4C2×D4311yescharacteristic
313#534—434no—
314#534—864no—
315#534—862no—
316C2×#123—862no—
317C2×#121—861no—
318C2×#121—861no—
319C2×#120—862no—
320C22×C4⋊C4—21no—
321C22×C22⋊C4—432no—
322C22×C22⋊C4—862no—
323C22×C22⋊C4C2×D4311yescharacteristic
324C22×C22⋊C4C2×D4311yescharacteristic
325C2×#99—438no—
326C2×#99—868no—
327#386—438no—
328#386—864no—
329#385—22no—
330#385C2×D4314yescomplemented
331C2×#95—21no—
332C2×#95—862no—
333#342—434no—
334C43C2×#204411yescharacteristic, complemented, Sylow
335C25—432no—
336C25C22×D4311yescharacteristic
337C22×D4—434no—
338C22×D4—434no—
339C22×D4—861no—
340C22×D4—861no—
341C22×D4—864no—
342C22×D4—864no—
343C22×D4—862no—
344C22×D4—862no—
345C22×D4—864no—
346C22×D4—864no—
347C22×D4—862no—
348C22×D4—862no—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—22no—
353C23×C4—21no—
354C23×C4—44no—
355C23×C4—432no—
356C23×C4—862no—
357C23×C4C22⋊D4311yescharacteristic
358C23×C4C22⋊D4311yescharacteristic
359C23×C4C22×D4312yes—
360#123—868no—
361#123—868no—
362#121—864no—
363#121—864no—
364#121—864no—
365#121—864no—
366#120—868no—
367#120—868no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—434no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4—862no—
379C2×C22⋊C4—864no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4—868no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4—1728no—
384C2×C22⋊C4D17214yescomplemented
385C2×C22⋊C4C22⋊D4312yes—
386C2×C22⋊C4C22×D4312yes—
387C2×C22⋊C4C22×D4312yes—
388#99—8616no—
389#95—24no—
390#95—868no—
391C24—42no—
392C24—42no—
393C24—434no—
394C24—862no—
395C24—864no—
396C24—862no—
397C24—864no—
398C24—1724no—
399C24—1724no—
400C24C2×D17212yes—
401C24#1062189812yes—
402C24D4×D4312yes—
403C24D4×D4312yes—
404C24#1062190214yes—
405C24C2×C22⋊D4311yescharacteristic
406C24C2×C22⋊D4311yescharacteristic
407C24C23×D4311yescharacteristic
408C2×D4—864no—
409C2×D4—864no—
410C2×D4—864no—
411C2×D4—864no—
412C2×D4—868no—
413C2×D4—868no—
414C2×D4—864no—
415C2×D4—864no—
416C2×D4—864no—
417C2×D4—864no—
418C2×D4—864no—
419C2×D4—864no—
420C2×D4—3442no—
421C2×D4—3442no—
422C2×D4—1724no—
423C2×D4—1724no—
424C2×D4—1724no—
425C2×D4—1724no—
426C2×D4—1724no—
427C2×D4—1724no—
428C2×D4—1724no—
429C2×D4—1724no—
430C22×C4—28no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—44no—
441C22×C4—48no—
442C22×C4—44no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—434no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—864no—
456C22×C4—864no—
457C22×C4—864no—
458C22×C4—1724no—
459C22×C4—1724no—
460C22×C4—1724no—
461C22×C4C2×C22⋊D4312yes—
462C22×C4C2×C22⋊D4312yes—
463C4⋊C4—48no—
464C4⋊C4—864no—
465C4⋊C4—864no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—22no—
470C22⋊C4—868no—
471C22⋊C4—868no—
472C22⋊C4—864no—
473C22⋊C4—864no—
474C22⋊C4—17216no—
475C22⋊C4—1724no—
476C22⋊C4C2×D17214yescomplemented
477C23—22no—
478C23—24no—
479C23—22no—
480C23—24no—
481C23—42no—
482C23—41no—
483C23—41no—
484C23—44no—
485C23—44no—
486C23—42no—
487C23—48no—
488C23—41no—
489C23—41no—
490C23—864no—
491C23—864no—
492C23—864no—
493C23—3448no—
494C23—3442no—
495C23—3442no—
496C23—17216no—
497C23—1724no—
498C23—1724no—
499C23—1724no—
500C23—1724no—
501C23—1724no—
502C23—1724no—
503C23#1306329312yes—
504C23#1306329311yescharacteristic
505C23#1306329311yescharacteristic
506C23#1306329912yes—
507C23#1306329912yes—
508C23#1306330014yes—
509C23#1306330014yes—
510C23#1306331014yes—
511C23#1306331014yes—
512C23#1306331412yes—
513C23#1306331412yes—
514C23C2×D4×D4312yes—
515C23C22×C22⋊D4311yescharacteristic
516C23C22×D17211yescharacteristic
517C23C2×#1062189811yescharacteristic
518C23C2×#1062190212yes—
519D4—3444no—
520D4—3444no—
521D4—1728no—
522D4—1728no—
523D4—1724no—
524D4—1724no—
525D4—1724no—
526D4—1724no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—48no—
537C2×C4—42no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—864no—
548C2×C4—864no—
549C2×C4—864no—
550C2×C4—3448no—
551C2×C4—1724no—
552C2×C4—1724no—
553C2×C4—1724no—
554C2×C4—1724no—
555C2×C4—1724no—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—22no—
564C22—24no—
565C22—28no—
566C22—28no—
567C22—24no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—3444no—
576C22—3448no—
577C22—3448no—
578C22—1728no—
579C22—1724no—
580C22—1724no—
581C22—1724no—
582C22#1458281614yes—
583C22#1458281612yes—
584C22#1458281612yes—
585C22#1458308512yes—
586C22#1458308812yes—
587C22C2×#1306329311yescharacteristic
588C22C2×#1306329911yescharacteristic
589C22C2×#1306330012yes—
590C22C2×#1306331012yes—
591C22C2×#1306331411yescharacteristic
592C4—44no—
593C4—44no—
594C4—42no—
595C4—42no—
596C4—3444no—
597C4—1724no—
598C2—21no—
599C2—22no—
600C2—24no—
601C2—22no—
602C2—22no—
603C2—21no—
604C2—3444no—
605C2#1913584614yesdirect product factor
606C2C2×#1458281611yescharacteristic
607C2C2×#1458308511yescharacteristic
608C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC2×C43×#385C2
socleC23×C43#120
prime radicalC2×#14583461C2
hypercenterC2×#385D43
hypocenterC43C2×#2044
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#13063239C2semidirect
3. C2×#14582778C2semidirect
4. #19135846C2direct (N × H)
5. C2×#14582666C2semidirect
6. C2×C43×#385C2semidirect
18. C2×#13063239C22semidirect
20. #14582778C22semidirect
22. #14582666C22semidirect
28. C43×#385C22semidirect
82. C2×C22⋊C4×C43D4semidirect
163. C22⋊C4×C43C2×D4semidirect
297. C2×#385D43semidirect
306. C2×C43#2044semidirect
330. #385C2×D43semidirect
334. C43C2×#2044semidirect
384. C2×C22⋊C4D172semidirect
476. C22⋊C4C2×D172semidirect
605. C2#19135846direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834612
C22×#130632392
C2×#145827782
#191358462
C2×#145826662
C2×C43×#3852
C2×#204443