Finite Group Databasebeta

← C2×#19135020 #25098263

Subgroups — C2×#19135020 #25098263

Order 11008.

2438 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D43C211yesmaximal, characteristic, complemented
2C22×#13063296C211yesmaximal, characteristic
3C22×#13063246C211yesmaximal, characteristic, complemented
4C2×#14582756C211yesmaximal, characteristic, complemented
5#19135020C218yesmaximal, direct product factor
6C2×#14582662C211yesmaximal, characteristic, complemented
7C2×#14582661C211yesmaximal, characteristic, complemented
8C22×#102×C43C211yesmaximal, characteristic, complemented
9C23×C22⋊D43—21no—
10C23×C4×D43C2211yescharacteristic
11C23×C43⋊C8C2211yescharacteristic
12C22×C8×D43—24no—
13C22×C8×D43—24no—
14C22×C8×D43—24no—
15C22×C8×D43C2214yescomplemented
16C2×#13063296—24no—
17C2×#13063296—22no—
18C2×#13063296C418yescomplemented
19C2×#13063296C2214yes—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43—21no—
23C22×(C2×D43)⋊C4—21no—
24C2×#13063246—24no—
25C2×#13063246C2214yescomplemented
26#14582756—22no—
27#14582756C2214yescomplemented
28C2×C43⋊#95—21no—
29#14582662C2214yescomplemented
30#14582661C2214yescomplemented
31C23×D4×C43C2211yescharacteristic
32C23×C8×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C2×#102×C43—24no—
35C2×#102×C43C2214yescomplemented
36C24×D43D411yescharacteristic
37C22×C22⋊D43—28no—
38C22×C22⋊D43—24no—
39C22×C22⋊D43—44no—
40C22×C22⋊D43—44no—
41C23×Dic43—21no—
42C23×Dic43—21no—
43C23×Dic43D411yescharacteristic
44C22×C4×D43—22no—
45C22×C4×D43—22no—
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43C2×C414yes—
49C22×C4×D43D412yes—
50C22×C4×D43D414yes—
51C22×C4×D43C2312yes—
52C22×C43⋊C8—22no—
53C22×C43⋊C8—22no—
54C22×C43⋊C8D414yescomplemented
55C22×C43⋊C8C2312yes—
56C2×C8×D43—232no—
57C2×C8×D43—28no—
58C2×C8×D43—28no—
59C2×C8×D43—28no—
60#13063296—216no—
61#13063296—28no—
62#13063296C2×C4116yescomplemented
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2×C414yes—
69C2×C4⋊Dic43C2312yes—
70C2×C4⋊Dic43C2312yes—
71C2×C22⋊Dic43—28no—
72C2×C22⋊Dic43—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—44no—
75#13063246—28no—
76C43⋊#95—24no—
77C25×C43—21no—
78C22×D4×C43—22no—
79C22×D4×C43—22no—
80C22×D4×C43—22no—
81C22×D4×C43—21no—
82C22×D4×C43—22no—
83C22×D4×C43—22no—
84C22×D4×C43C2×C414yes—
85C22×D4×C43C2312yes—
86C23×C4×C43—21no—
87C23×C4×C43C2311yescharacteristic
88C22×C8×C43—22no—
89C22×C8×C43—22no—
90C22×C8×C43D414yescomplemented
91C22×C8×C43C2312yes—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43C2312yes—
96#102×C43—28no—
97C24×C43—24no—
98C24×C43—22no—
99C24×C43—42no—
100C24×C43—42no—
101C24×C43—42no—
102C24×C43—42no—
103C24×C43—42no—
104C24×C43—42no—
105C24×C43C2×D411yescharacteristic
106C23×D43—22no—
107C23×D43—22no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43C22⋊C414yes—
111C23×D43D814yes—
112C23×D43SD1614yes—
113C23×D43C2×D412yes—
114C2×D4×C43—24no—
115C2×D4×C43—22no—
116C2×D4×C43—28no—
117C2×D4×C43—28no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—44no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—44no—
126C2×D4×C43C22×C414yes—
127C22×C4×C43—22no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43#4112yes—
137C22×C4×C43#4112yes—
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—216no—
140C2×C22⋊D43—432no—
141C2×C22⋊D43—48no—
142C2×C22⋊D43—48no—
143C22×Dic43—24no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43C22⋊C414yes—
154C22×Dic43C2×D412yes—
155C2×C4×D43—28no—
156C2×C4×D43—28no—
157C2×C4×D43—28no—
158C2×C4×D43—24no—
159C2×C4×D43—24no—
160C2×C4×D43—28no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43C22⋊C418yes—
166C2×C4×D43C22×C414yes—
167C2×C4×D43C2×D414yes—
168C2×C8×C43—28no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43C2×D414yescomplemented
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—42no—
175C22⋊Dic43—216no—
176(C2×D43)⋊C4—48no—
177C4⋊Dic43—24no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—42no—
182C4⋊Dic43C22×C414yes—
183C2×C43⋊C8—28no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8C2×D414yescomplemented
187C8×D43—232no—
188C23×C43—24no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—48no—
196C23×C43—48no—
197C23×C43—48no—
198C23×C43—84no—
199C23×C43—84no—
200C23×C43—84no—
201C23×C43—84no—
202C23×C43C2×C22⋊C412yes—
203C23×C43#12112yes—
204C23×C43#12112yes—
205C23×C43C2×D812yes—
206C23×C43C2×SD1612yes—
207C23×C43#13512yes—
208C23×C43#13512yes—
209C23×C43C22×D411yescharacteristic
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—28no—
215C22×D43—28no—
216C22×D43—28no—
217C22×D43—28no—
218C22×D43—28no—
219C22×D43—28no—
220C22×D43#102116yescomplemented
221C22×D43C2×C22⋊C414yes—
222C22×D43C2×D814yes—
223C22×D43C2×SD1614yes—
224D4×C43—24no—
225D4×C43—24no—
226D4×C43—42no—
227D4×C43—42no—
228D4×C43—48no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—84no—
233C2×C4×C43C2×C22⋊C412yes—
234C2×C4×C43C4×D414yes—
235C2×C4×C43C4×D414yes—
236C2×C4×C43#12014yes—
237C2×C4×C43#12112yes—
238C2×C4×C43#12112yes—
239C2×C4×C43#12314yes—
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C22⋊D43—432no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—28no—
250C2×Dic43—24no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—48no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—84no—
258C2×Dic43C2×C22⋊C414yes—
259C4×D43—24no—
260C4×D43—24no—
261C4×D43—24no—
262C4×D43—24no—
263C4×D43—216no—
264C8×C43—24no—
265C43⋊C8—24no—
266C2×#1893—431nomaximal, Sylow
267C22×C43—44no—
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—816no—
271C22×C43—82no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43—82no—
275C22×C43#38614yes—
276C22×C43C2×#10214yes—
277C22×C43#41614yes—
278C22×C43#46514yes—
279C22×C43#46514yes—
280C22×C43#46614yes—
281C22×C43#46614yes—
282C22×C43C22×C22⋊C411yescharacteristic
283C22×C43C2×#12111yescharacteristic
284C22×C43C2×#12111yescharacteristic
285C22×C43C22×D811yescharacteristic
286C22×C43C22×SD1611yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C2×D43—24no—
290C2×D43—232no—
291C2×D43—24no—
292C2×D43—24no—
293C2×D43—24no—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43C2×#10218yescomplemented
297C4×C43—82no—
298C4×C43#38614yes—
299C4×C43C2×C4×D411yescharacteristic
300C4×C43C2×C4×D411yescharacteristic
301C4×C43C2×#12011yescharacteristic
302C4×C43C2×#12311yescharacteristic
303Dic43—24no—
304Dic43—44no—
305Dic43—82no—
306C24×C8—431no—
307C22×#121—431no—
308C22×#102—431no—
309C22×#102D4311yescharacteristic, complemented
310C2×#380—431no—
311#1893—438no—
312C2×#340—431no—
313C2×#340—431no—
314C2×C43—84no—
315C2×C43#189318yescomplemented
316C2×C43C2×#38611yescharacteristic
317C2×C43C22×#10211yescharacteristic
318C2×C43C2×#41611yescharacteristic
319C2×C43C2×#46511yescharacteristic
320C2×C43C2×#46511yescharacteristic
321C2×C43C2×#46611yescharacteristic
322C2×C43C2×#46611yescharacteristic
323D43—28no—
324C23×D4—861no—
325C23×D4C2×D4311yescharacteristic
326C24×C4—431no—
327C23×C8—431no—
328C23×C8—434no—
329C23×C8—864no—
330C23×C8—864no—
331C23×C8—864no—
332C23×C8C2×D4311yescharacteristic
333C2×#121—434no—
334C2×#121—438no—
335C2×#121—864no—
336C2×#121—862no—
337C22×C4⋊C4—431no—
338C22×C4⋊C4—431no—
339C22×C4⋊C4C2×D4311yescharacteristic
340C22×C22⋊C4—861no—
341C22×C22⋊C4—861no—
342C2×#102—24no—
343C2×#102—434no—
344C2×#102—864no—
345C2×#102C2×D4314yescomplemented
346#380—434no—
347#380—862no—
348C2×#95—861no—
349#340—434no—
350#340—434no—
351C43C2×#189311yescharacteristic, complemented, Sylow
352C25—21no—
353C25—431no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—868no—
361C22×D4—864no—
362C22×D4—1724no—
363C22×D4—1724no—
364C22×D4C4×D4314yes—
365C22×D4C22×D4312yes—
366C23×C4—21no—
367C23×C4—431no—
368C23×C4—434no—
369C23×C4—434no—
370C23×C4—432no—
371C23×C4—432no—
372C23×C4—862no—
373C23×C4—862no—
374C23×C4—862no—
375C23×C4—862no—
376C23×C4—861no—
377C23×C4—861no—
378C23×C4C22×D4311yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—434no—
382C22×C8—432no—
383C22×C8—868no—
384C22×C8—868no—
385C22×C8—8632no—
386C22×C8—862no—
387C22×C8—862no—
388C22×C8—868no—
389C22×C8C22⋊D4314yescomplemented
390C22×C8C22×D4312yes—
391#121—4316no—
392#121—8616no—
393#121—868no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—434no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—432no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4C22×D4312yes—
406C2×C22⋊C4—868no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—1724no—
410#102—28no—
411#102—868no—
412#95—864no—
413C24—24no—
414C24—22no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—434no—
422C24—434no—
423C24—434no—
424C24—432no—
425C24—862no—
426C24—862no—
427C24—862no—
428C24—862no—
429C24D4×D4311yescharacteristic
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—44no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—8616no—
443C2×D4—17232no—
444C2×D4—1728no—
445C2×D4—1728no—
446C2×D4C2×C4×D4314yes—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—434no—
452C22×C4—432no—
453C22×C4—438no—
454C22×C4—434no—
455C22×C4—434no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—868no—
459C22×C4—868no—
460C22×C4—868no—
461C22×C4—864no—
462C22×C4—864no—
463C22×C4—868no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—864no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4C2×C4×D4312yes—
477C22×C4#1062189812yes—
478C22×C4D4×D4311yescharacteristic
479C22×C4D4×D4312yes—
480C22×C4D4×D4312yes—
481C22×C4#1062190012yes—
482C22×C4C2×C22⋊D4312yes—
483C22×C4C23×D4311yescharacteristic
484C2×C8—28no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—434no—
488C2×C8—8632no—
489C2×C8—868no—
490C2×C8—862no—
491C2×C8—862no—
492C2×C8C2×C22⋊D4314yescomplemented
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—42no—
496C4⋊C4—434no—
497C4⋊C4—864no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—1722no—
502C22⋊C4—8616no—
503C22⋊C4—1728no—
504C23—24no—
505C23—42no—
506C23—42no—
507C23—48no—
508C23—48no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—48no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23—84no—
518C23—434no—
519C23—4316no—
520C23—434no—
521C23—434no—
522C23—868no—
523C23—868no—
524C23—868no—
525C23—862no—
526C23—868no—
527C23—862no—
528C23—868no—
529C23—862no—
530C23—862no—
531C23—868no—
532C23C22⋊C4×D4312yes—
533C23#1306329612yes—
534C23#1306329812yes—
535C23D8×D4312yes—
536C23SD16×D4312yes—
537C23#1306334412yes—
538C23#1306334612yes—
539C23C2×D4×D4311yescharacteristic
540D4—24no—
541D4—24no—
542D4—42no—
543D4—42no—
544D4—48no—
545D4—17232no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—84no—
550C2×C4—434no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—868no—
554C2×C4—864no—
555C2×C4—864no—
556C2×C4—864no—
557C2×C4—864no—
558C2×C4—8616no—
559C2×C4—864no—
560C2×C4—3444no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1728no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4C22⋊C4×D4312yes—
568C2×C4(C22⋊D43)⋊C414yes—
569C2×C4C4×C22⋊D4314yes—
570C2×C4#1306329314yes—
571C2×C4#1306329612yes—
572C2×C4#1306329812yes—
573C2×C4#1306330714yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C22×C22⋊D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C8—24no—
581C8—864no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—816no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—438no—
591C22—8632no—
592C22—864no—
593C22—864no—
594C22—864no—
595C22—864no—
596C22—864no—
597C22—864no—
598C22#1458277514yes—
599C22#102×D4314yes—
600C22#1458289214yes—
601C22#1458312514yes—
602C22#1458312714yes—
603C22#1458313214yes—
604C22#1458313414yes—
605C22C2×C22⋊C4×D4311yescharacteristic
606C22C2×#1306329611yescharacteristic
607C22C2×#1306329811yescharacteristic
608C22C2×D8×D4311yescharacteristic
609C22C2×SD16×D4311yescharacteristic
610C22C2×#1306334411yescharacteristic
611C22C2×#1306334611yescharacteristic
612C4—82no—
613C4—864no—
614C4—3442no—
615C4—1724no—
616C4#1458277514yes—
617C4C2×(C22⋊D43)⋊C411yescharacteristic
618C4C2×C4×C22⋊D4311yescharacteristic
619C4C2×#1306329311yescharacteristic
620C4C2×#1306330711yescharacteristic
621C2—84no—
622C2—868no—
623C2#1913502018yesdirect product factor
624C2C2×#1458277511yescharacteristic
625C2C2×#102×D4311yescharacteristic
626C2C2×#1458289211yescharacteristic
627C2C2×#1458312511yescharacteristic
628C2C2×#1458312711yescharacteristic
629C2C2×#1458313211yescharacteristic
630C2C2×#1458313411yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC24×C43C2×D4
prime radicalC22×#13063296C2
cosocleC22×C4×C43C24
hypercenterC22×#102D43
hypocenterC43C2×#1893
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C23×C8×D43C2semidirect
3. C22×#13063246C2semidirect
4. C2×#14582756C2semidirect
5. #19135020C2direct (N × H)
6. C2×#14582662C2semidirect
7. C2×#14582661C2semidirect
8. C22×#102×C43C2semidirect
15. C22×C8×D43C22semidirect
18. C2×#13063296C4semidirect
25. C2×#13063246C22semidirect
27. #14582756C22semidirect
29. #14582662C22semidirect
30. #14582661C22semidirect
35. C2×#102×C43C22semidirect
54. C22×C43⋊C8D4semidirect
62. #13063296C2×C4semidirect
90. C22×C8×C43D4semidirect
171. C2×C8×C43C2×D4semidirect
186. C2×C43⋊C8C2×D4semidirect
220. C22×D43#102semidirect
296. C2×D43C2×#102semidirect
309. C22×#102D43semidirect
315. C2×C43#1893semidirect
345. C2×#102C2×D43semidirect
351. C43C2×#1893semidirect
389. C22×C8C22⋊D43semidirect
492. C2×C8C2×C22⋊D43semidirect
623. C2#19135020direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D432
C22×#130632962
C22×#130632462
C2×#145827562
#191350202
C2×#145826622
C2×#145826612
C22×#102×C432
C2×#189343