Finite Group Databasebeta

← C2×#19135615 #25123487

Subgroups — C2×#19135615 #25123487

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063350C211yesmaximal, characteristic
2C22×#13063314C211yesmaximal, characteristic, complemented
3C22×#13063252C211yesmaximal, characteristic, complemented
4C2×#14582903C211yesmaximal, characteristic, complemented
5C22×#13063244C211yesmaximal, characteristic, complemented
6#19135615C218yesmaximal, direct product factor
7C2×#14582658C211yesmaximal, characteristic, complemented
8C2×C43×#536C211yesmaximal, characteristic, complemented
9C23×D172C2211yescharacteristic
10C2×#13063350—24no—
11C2×#13063350—24no—
12C2×#13063350—22no—
13C2×#13063350C2214yes—
14C22×#10621884—21no—
15C22×#10621882—21no—
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×#13063314—24no—
19C2×#13063314—24no—
20C2×#13063314—22no—
21C2×#13063314C2214yescomplemented
22C22×(C2×D43)⋊C4—22no—
23C22×C4×Dic43C2211yescharacteristic
24C2×#13063252—24no—
25C2×#13063252C2214yescomplemented
26#14582903—22no—
27#14582903C2214yescomplemented
28C2×#13063245—22no—
29C2×#13063244—24no—
30C2×#13063244C2214yescomplemented
31#14582658C2214yescomplemented
32C22×#41×C43C2211yescharacteristic
33C23×Q8×C43C2211yescharacteristic
34C43×#536—22no—
35C43×#536—22no—
36C43×#536—22no—
37C43×#536C2214yescomplemented
38C2×C4⋊Q8×C43—21no—
39C2×#124×C43—21no—
40C2×#123×C43—22no—
41C2×C22⋊Q8×C43—22no—
42C2×#117×C43C2211yescharacteristic
43C24×D43—21no—
44C22×D172—21no—
45C22×D172—21no—
46C22×D172—21no—
47C22×D172—22no—
48C22×D172—21no—
49C22×D172—22no—
50C22×D172—22no—
51C22×D172—21no—
52C22×D172D414yes—
53C22×D172C2312yes—
54C23×Dic43—21no—
55#13063350—216no—
56#13063350—28no—
57#13063350—28no—
58C2×#10621884—28no—
59C2×#10621884—24no—
60C2×#10621882—28no—
61C2×#10621882—24no—
62C2×#10621877—22no—
63C2×#10621877—21no—
64C2×#10621877—21no—
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877D414yes—
68C2×#10621877C2312yes—
69C2×#10621877C2312yes—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72#13063314—216no—
73#13063314—28no—
74#13063314—28no—
75C2×(C2×D43)⋊C4—216no—
76C2×(C2×D43)⋊C4—28no—
77C2×C4×Dic43—22no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43D414yes—
80C2×C4×Dic43C2312yes—
81#13063252—28no—
82#13063245—28no—
83#13063244—28no—
84C2×#41×C43—21no—
85C2×#41×C43—21no—
86C2×#41×C43—22no—
87C2×#41×C43—22no—
88C2×#41×C43—22no—
89C2×#41×C43—22no—
90C2×#41×C43D412yes—
91C2×#41×C43C2312yes—
92C22×Q8×C43—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43—21no—
95C22×Q8×C43—21no—
96C22×Q8×C43—22no—
97C22×Q8×C43—22no—
98C22×Q8×C43—22no—
99C22×Q8×C43—22no—
100C22×Q8×C43D411yescharacteristic
101C22×Q8×C43D412yes—
102C22×Q8×C43C2312yes—
103C22×D4×C43—21no—
104C22×D4×C43D411yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43D412yes—
107C23×C4×C43C2311yescharacteristic
108C4⋊Q8×C43—24no—
109C4⋊Q8×C43—24no—
110#124×C43—24no—
111#124×C43—24no—
112#123×C43—28no—
113#123×C43—28no—
114C22⋊Q8×C43—28no—
115C22⋊Q8×C43—28no—
116#117×C43—21no—
117#117×C43—21no—
118#117×C43D412yes—
119#117×C43C2312yes—
120C2×C4⋊C4×C43—24no—
121C2×C4⋊C4×C43D412yes—
122C2×C22⋊C4×C43—24no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125C24×C43—21no—
126C24×C43C2×D411yescharacteristic
127C23×D43—24no—
128C23×D43—22no—
129C23×D43—48no—
130C23×D43—41no—
131C23×D43—41no—
132C23×D43—42no—
133#41×C43—24no—
134#41×C43—24no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—42no—
140#41×C43—42no—
141#41×C43—42no—
142#41×C43—42no—
143C2×Q8×C43—22no—
144C2×Q8×C43—22no—
145C2×Q8×C43—21no—
146C2×Q8×C43—24no—
147C2×Q8×C43—24no—
148C2×Q8×C43—22no—
149C2×Q8×C43—22no—
150C2×Q8×C43—22no—
151C2×Q8×C43—22no—
152C2×Q8×C43—22no—
153C2×Q8×C43—22no—
154C2×Q8×C43—22no—
155C2×Q8×C43—22no—
156C2×Q8×C43—42no—
157C2×Q8×C43—42no—
158C2×Q8×C43—42no—
159C2×Q8×C43—42no—
160C2×Q8×C43—42no—
161C2×Q8×C43—42no—
162C2×Q8×C43—42no—
163C2×Q8×C43—42no—
164C2×Q8×C43C2×D412yes—
165C2×D4×C43—21no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43C2×D412yes—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—21no—
178C22×C4×C43—22no—
179C22×C4×C43—24no—
180C22×C4×C43—24no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43C2×D412yes—
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D412yes—
190C22×C4×C43C2×D414yes—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43#4112yes—
193C22×C4×C43C2411yescharacteristic
194C22×Dic43—24no—
195C22×Dic43—22no—
196C22×Dic43—44no—
197C2×D172—24no—
198C2×D172—22no—
199C2×D172—24no—
200C2×D172—24no—
201C2×D172—24no—
202C2×D172—24no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—41no—
208C2×D172—41no—
209C2×D172—42no—
210C2×D172—42no—
211C2×D172—42no—
212C2×D172—42no—
213C2×D172—42no—
214C2×D172C2×D414yes—
215C4⋊C4×C43—216no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43C2×D414yes—
218C22⋊C4×C43—216no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C42×C43—22no—
222C42×C43—22no—
223#10621884—216no—
224#10621882—216no—
225(C2×D43)⋊C4—232no—
226C4×Dic43—24no—
227C4×Dic43—22no—
228C4×Dic43C2×D414yes—
229#10621877—24no—
230#10621877—22no—
231#10621877—22no—
232#10621877—22no—
233#10621877—42no—
234#10621877C2×D414yes—
235C2×C43⋊C8—24no—
236C2×C43⋊C8—22no—
237C2×C43⋊C8—22no—
238C2×C43⋊C8—42no—
239C23×C43—24no—
240C23×C43—22no—
241C23×C43—42no—
242C23×C43—44no—
243C23×C43#12012yes—
244C23×C43#12011yescharacteristic
245C23×C43#12011yescharacteristic
246C23×C43#12112yes—
247C23×C43C22×D411yescharacteristic
248C22×D43—24no—
249C22×D43—48no—
250C22×D43—416no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—44no—
254C22×D43—44no—
255C22×D43—84no—
256C22×D43—88no—
257C22×D43—84no—
258Q8×C43—22no—
259Q8×C43—22no—
260Q8×C43—42no—
261Q8×C43—42no—
262Q8×C43—42no—
263Q8×C43—42no—
264Q8×C43—44no—
265Q8×C43—44no—
266Q8×C43—42no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—42no—
270D4×C43—42no—
271D4×C43—44no—
272D4×C43—42no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—24no—
276C2×C4×C43—22no—
277C2×C4×C43—24no—
278C2×C4×C43—44no—
279C2×C4×C43—44no—
280C2×C4×C43—42no—
281C2×C4×C43—44no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—44no—
285C2×C4×C43#12012yes—
286C2×C4×C43#12012yes—
287C2×C4×C43#12012yes—
288C2×C4×C43#12011yescharacteristic
289C2×C4×C43#12011yescharacteristic
290C2×C4×C43#12112yes—
291C2×C4×C43#12112yes—
292C2×C4×C43#12112yes—
293C2×C4×C43#12112yes—
294C2×C4×C43#12112yes—
295C2×C4×C43#12712yes—
296C2×C4×C43#12712yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×Dic43—24no—
304C2×Dic43—44no—
305C2×Dic43—48no—
306D172—24no—
307D172—24no—
308D172—42no—
309D172—42no—
310D172—44no—
311D172—44no—
312C43⋊C8—24no—
313C43⋊C8—42no—
314C2×#2003—431nomaximal, Sylow
315C22×C43—22no—
316C22×C43—22no—
317C22×C43—24no—
318C22×C43—24no—
319C22×C43—42no—
320C22×C43—44no—
321C22×C43—84no—
322C22×C43#39212yes—
323C22×C43#39212yes—
324C22×C43#45414yes—
325C22×C43C2×#12011yescharacteristic
326C22×C43C2×#12011yescharacteristic
327C22×C43C2×#12111yescharacteristic
328C2×D43—48no—
329C2×D43—44no—
330C2×D43—84no—
331C2×D43—88no—
332C2×D43—84no—
333C2×D43—88no—
334C4×C43—44no—
335C4×C43—42no—
336C4×C43—44no—
337C4×C43#39212yes—
338C4×C43#39212yes—
339C4×C43C2×#12011yescharacteristic
340C4×C43C2×#12111yescharacteristic
341C4×C43C2×#12111yescharacteristic
342C4×C43C2×#12711yescharacteristic
343Dic43—44no—
344C22×AGL(1,ℤ/8)—431no—
345C2×#536D4311yescharacteristic, complemented
346C22×#124—431no—
347C22×#104—431no—
348C2×#418—431no—
349C22×#101—431no—
350#2003—438no—
351C2×#339—431no—
352C2×C43—21no—
353C2×C43—21no—
354C2×C43—22no—
355C2×C43—82no—
356C2×C43#200314yescomplemented
357C2×C43C2×#39211yescharacteristic
358C2×C43C2×#45412yes—
359D43—84no—
360C22×#41C2×D4311yescharacteristic
361C23×Q8C2×D4311yescharacteristic
362C23×D4—431no—
363C2×AGL(1,ℤ/8)—434no—
364C2×AGL(1,ℤ/8)—864no—
365C2×AGL(1,ℤ/8)—864no—
366C2×AGL(1,ℤ/8)—862no—
367C22×SD16—861no—
368C22×D8—861no—
369C22×M16—431no—
370C22×M16—431no—
371#536—22no—
372#536—22no—
373#536—22no—
374#536C2×D4314yescomplemented
375C2×C4⋊Q8—21no—
376C2×#124—21no—
377C2×#124—434no—
378C2×#124—864no—
379C2×#124—864no—
380C2×#124—862no—
381C2×#123—22no—
382C2×C22⋊Q8—22no—
383C2×#117C2×D4311yescharacteristic
384C22×C22⋊C4—862no—
385C22×C42—431no—
386C2×#104—434no—
387C2×#104—864no—
388#418—434no—
389#418—862no—
390C2×#102—862no—
391C2×#101—434no—
392C2×#101—864no—
393#339—434no—
394C43C2×#200311yescharacteristic, complemented, Sylow
395C25—861no—
396C2×#41—21no—
397C2×#41—21no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41C22⋊D4312yes—
403C2×#41C22×D4312yes—
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—21no—
409C22×Q8—21no—
410C22×Q8—21no—
411C22×Q8—21no—
412C22×Q8C22⋊D4311yescharacteristic
413C22×Q8C22⋊D4312yes—
414C22×Q8C22×D4312yes—
415C22×D4—21no—
416C22×D4—434no—
417C22×D4—432no—
418C22×D4—862no—
419C22×D4—862no—
420C22×D4—862no—
421C22×D4—861no—
422C22×D4—861no—
423C22×D4—861no—
424C22×D4—861no—
425C22×D4—861no—
426C22×D4C22⋊D4311yescharacteristic
427C23×C4—21no—
428C23×C4—861no—
429C23×C4C22⋊D4312yes—
430C23×C4C22×D4311yescharacteristic
431AGL(1,ℤ/8)—868no—
432AGL(1,ℤ/8)—868no—
433AGL(1,ℤ/8)—8616no—
434C2×SD16—868no—
435C2×SD16—864no—
436C2×D8—868no—
437C2×D8—864no—
438C2×M16—434no—
439C2×M16—432no—
440C2×M16—432no—
441C2×M16—862no—
442C2×M16—861no—
443C2×M16—861no—
444C2×M16—862no—
445C2×M16—862no—
446C22×C8—861no—
447C22×C8—861no—
448C4⋊Q8—24no—
449C4⋊Q8—24no—
450#124—24no—
451#124—24no—
452#124—868no—
453#124—868no—
454#124—8616no—
455#123—28no—
456#123—28no—
457C22⋊Q8—28no—
458C22⋊Q8—28no—
459#117—21no—
460#117—21no—
461#117C22⋊D4312yes—
462#117C22×D4312yes—
463C2×C4⋊C4—24no—
464C2×C4⋊C4C22⋊D4312yes—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—8616no—
468C2×C22⋊C4—868no—
469C2×C42—21no—
470C2×C42—434no—
471C2×C42—432no—
472C2×C42—862no—
473C2×C42—861no—
474#104—868no—
475#102—868no—
476#101—868no—
477C24—21no—
478C24—864no—
479C24—862no—
480C24—1728no—
481C24—1721no—
482C24—1721no—
483C24—1722no—
484C24C2×C22⋊D4311yescharacteristic
485#41—24no—
486#41—24no—
487#41—22no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—42no—
492#41—42no—
493#41—42no—
494#41—42no—
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—21no—
499C2×Q8—24no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8C2×C22⋊D4312yes—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—22no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—434no—
525C2×D4—864no—
526C2×D4—864no—
527C2×D4—864no—
528C2×D4—864no—
529C2×D4—864no—
530C2×D4—862no—
531C2×D4—862no—
532C2×D4—862no—
533C2×D4—862no—
534C2×D4—862no—
535C2×D4—1721no—
536C2×D4—1721no—
537C2×D4—1722no—
538C2×D4—1722no—
539C2×D4—1722no—
540C2×D4—1722no—
541C2×D4—1722no—
542C2×D4C2×C22⋊D4312yes—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—864no—
554C22×C4—862no—
555C22×C4—1724no—
556C22×C4D4×D4312yes—
557C22×C4D4×D4312yes—
558C22×C4D4×D4312yes—
559C22×C4#1062190012yes—
560C22×C4C2×C22⋊D4314yes—
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C2×C22⋊D4311yescharacteristic
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C23×D4311yescharacteristic
567SD16—8616no—
568D8—8616no—
569M16—434no—
570M16—864no—
571M16—862no—
572M16—862no—
573M16—862no—
574M16—1722no—
575C2×C8—864no—
576C2×C8—862no—
577C2×C8—862no—
578C2×C8—1722no—
579C4⋊C4—216no—
580C4⋊C4—22no—
581C4⋊C4C2×C22⋊D4314yes—
582C22⋊C4—216no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—8632no—
586C42—22no—
587C42—22no—
588C42—434no—
589C42—864no—
590C42—862no—
591C23—24no—
592C23—22no—
593C23—42no—
594C23—44no—
595C23—864no—
596C23—3448no—
597C23—3444no—
598C23—3444no—
599C23—17216no—
600C23—1728no—
601C23—1724no—
602C23—1724no—
603C23—1722no—
604C23—1722no—
605C23#1306329312yes—
606C23#1306329411yescharacteristic
607C23#1306329411yescharacteristic
608C23#1306329712yes—
609C23C22×C22⋊D4311yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—44no—
613Q8—44no—
614Q8—42no—
615Q8—42no—
616Q8—42no—
617Q8—42no—
618Q8—42no—
619D4—22no—
620D4—22no—
621D4—44no—
622D4—42no—
623D4—42no—
624D4—42no—
625D4—864no—
626D4—864no—
627D4—1724no—
628D4—1724no—
629D4—1722no—
630D4—1722no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—864no—
644C2×C4—1728no—
645C2×C4—1724no—
646C2×C4#1306329312yes—
647C2×C4#1306329312yes—
648C2×C4#1306329312yes—
649C2×C4#1306329411yescharacteristic
650C2×C4#1306329411yescharacteristic
651C2×C4#1306329612yes—
652C2×C4#1306329612yes—
653C2×C4#1306329712yes—
654C2×C4#1306329712yes—
655C2×C4#1306329712yes—
656C2×C4#1306332112yes—
657C2×C4#1306332112yes—
658C2×C4C2×D4×D4311yescharacteristic
659C2×C4C2×D4×D4311yescharacteristic
660C2×C4C2×D4×D4311yescharacteristic
661C2×C4C22×C22⋊D4311yescharacteristic
662C2×C4C22×C22⋊D4311yescharacteristic
663C2×C4C2×#1062190011yescharacteristic
664C8—864no—
665C8—1722no—
666C22—24no—
667C22—24no—
668C22—22no—
669C22—22no—
670C22—44no—
671C22—42no—
672C22—84no—
673C22—3448no—
674C22—3444no—
675C22—3448no—
676C22—3444no—
677C22—1728no—
678C22—1724no—
679C22#1458280712yes—
680C22#1458280712yes—
681C22#1458307214yes—
682C22C2×#1306329311yescharacteristic
683C22C2×#1306329411yescharacteristic
684C22C2×#1306329711yescharacteristic
685C4—44no—
686C4—44no—
687C4—42no—
688C4—1724no—
689C4#1458280712yes—
690C4#1458280712yes—
691C4C2×#1306329311yescharacteristic
692C4C2×#1306329611yescharacteristic
693C4C2×#1306329711yescharacteristic
694C4C2×#1306332111yescharacteristic
695C2—21no—
696C2—22no—
697C2—21no—
698C2—82no—
699C2—3444no—
700C2#1913561514yesdirect product factor
701C2C2×#1458280711yescharacteristic
702C2C2×#1458307212yes—
subgroupG/H
centerC23#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#536C2
socleC23×C43#120
prime radicalC22×#13063350C2
hypercenterC2×#536D43
hypocenterC43C2×#2003
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. C22×#13063314C2semidirect
3. C22×#13063252C2semidirect
4. C2×#14582903C2semidirect
5. C22×#13063244C2semidirect
6. #19135615C2direct (N × H)
7. C2×#14582658C2semidirect
8. C2×C43×#536C2semidirect
21. C2×#13063314C22semidirect
25. C2×#13063252C22semidirect
27. #14582903C22semidirect
30. C2×#13063244C22semidirect
31. #14582658C22semidirect
37. C43×#536C22semidirect
345. C2×#536D43semidirect
356. C2×C43#2003semidirect
374. #536C2×D43semidirect
394. C43C2×#2003semidirect
700. C2#19135615direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633502
C22×#130633142
C22×#130632522
C2×#145829032
C22×#130632442
#191356152
C2×#145826582
C2×C43×#5362
C2×#200343