Finite Group Databasebeta

← C2×#19135659 #25123612

Subgroups — C2×#19135659 #25123612

Order 11008.

2190 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C212yesmaximal, complemented
2C2×#14582916C212yesmaximal, complemented
3C2×#14582862C211yesmaximal, characteristic, complemented
4#19135659C218yesmaximal, direct product factor
5C2×#14582656C211yesmaximal, characteristic, complemented
6C2×C43×#575C211yesmaximal, characteristic, complemented
7C23×C4×D43C2211yescharacteristic
8C22×#10621877C2211yescharacteristic
9#14583406—24no—
10#14583406—24no—
11#14583406—24no—
12#14583406C2218yescomplemented
13C2×#13063306—22no—
14C2×#13063301—22no—
15C2×#13063296—22no—
16C2×#13063293—22no—
17C2×C4×C22⋊D43—24no—
18C2×#13063284C2212yes—
19#14582916—24no—
20#14582916C2218yescomplemented
21C2×#13063252—24no—
22#14582862—22no—
23#14582862C2214yescomplemented
24C2×(C2×D43)⋊C8—22no—
25#14582656C2214yescomplemented
26C22×#41×C43C2212yes—
27C43×#575—24no—
28C43×#575—22no—
29C43×#575C2214yescomplemented
30C2×#137×C43—22no—
31C2×AGL(1,ℤ/8)×C43—22no—
32C2×#135×C43—22no—
33C22×M16×C43C2211yescharacteristic
34C24×D43D411yescharacteristic
35C22×C22⋊D43—24no—
36C23×Dic43D411yescharacteristic
37C22×C4×D43—22no—
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—22no—
41C22×C4×D43—22no—
42C22×C4×D43—22no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43D412yes—
46C22×C4×D43C2312yes—
47C2×#10621877—21no—
48C2×#10621877—22no—
49C2×#10621877—22no—
50C2×#10621877C2312yes—
51C22×C43⋊C8—21no—
52#13063306—28no—
53#13063306—28no—
54#13063301—28no—
55#13063301—28no—
56#13063296—28no—
57#13063296—28no—
58#13063293—28no—
59#13063293—28no—
60C4×C22⋊D43—216no—
61C4×C22⋊D43—216no—
62#13063284—22no—
63#13063284—22no—
64#13063284D414yescomplemented
65#13063284C2314yes—
66C2×C4⋊Dic43—22no—
67C2×Dic43⋊C4—24no—
68C2×C22⋊Dic43—24no—
69C2×C22⋊Dic43—22no—
70C2×(C2×D43)⋊C4—24no—
71C2×C4×Dic43D414yescomplemented
72#13063252—216no—
73(C2×D43)⋊C8—28no—
74C2×#41×C43—22no—
75C2×#41×C43—22no—
76C2×#41×C43—22no—
77C2×#41×C43—22no—
78C2×#41×C43—22no—
79C2×#41×C43—22no—
80C2×#41×C43—22no—
81C2×#41×C43—22no—
82C2×#41×C43—22no—
83C2×#41×C43—22no—
84C2×#41×C43D414yescomplemented
85C2×#41×C43C2314yes—
86C22×Q8×C43D412yescomplemented
87C22×D4×C43—22no—
88C22×D4×C43D412yescomplemented
89C23×C4×C43—22no—
90C23×C4×C43C2311yescharacteristic
91#137×C43—28no—
92#137×C43—28no—
93AGL(1,ℤ/8)×C43—28no—
94AGL(1,ℤ/8)×C43—28no—
95#135×C43—28no—
96#135×C43—28no—
97C2×Q16×C43—22no—
98C2×SD16×C43—24no—
99C2×D8×C43—22no—
100C2×M16×C43—22no—
101C2×M16×C43—22no—
102C2×M16×C43D412yescomplemented
103C2×M16×C43C2312yes—
104C22×C8×C43D412yescomplemented
105C24×C43—22no—
106C24×C43C2×D411yescharacteristic
107C23×D43—22no—
108C23×D43—21no—
109C23×D43—22no—
110C23×D43—21no—
111C23×D43—44no—
112C23×D43C2×D412yes—
113#41×C43—24no—
114#41×C43—24no—
115#41×C43—24no—
116#41×C43—24no—
117#41×C43—24no—
118#41×C43—24no—
119#41×C43—24no—
120#41×C43—24no—
121#41×C43—42no—
122#41×C43—42no—
123#41×C43—42no—
124#41×C43—42no—
125#41×C43—42no—
126#41×C43—42no—
127#41×C43—42no—
128#41×C43—42no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—22no—
132C2×Q8×C43—22no—
133C2×Q8×C43—22no—
134C2×Q8×C43C2×D414yescomplemented
135C2×D4×C43—22no—
136C2×D4×C43—24no—
137C2×D4×C43—24no—
138C2×D4×C43—22no—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—42no—
143C2×D4×C43—42no—
144C2×D4×C43—42no—
145C2×D4×C43—42no—
146C2×D4×C43C2×D414yescomplemented
147C22×C4×C43—24no—
148C22×C4×C43—24no—
149C22×C4×C43—22no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—216no—
165C2×C22⋊D43—416no—
166C22×Dic43—24no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D412yes—
172C2×C4×D43—24no—
173C2×C4×D43—24no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—24no—
178C2×C4×D43—24no—
179C2×C4×D43—22no—
180C2×C4×D43—41no—
181C2×C4×D43—41no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—41no—
188C2×C4×D43—42no—
189C2×C4×D43—41no—
190Q16×C43—28no—
191SD16×C43—216no—
192D8×C43—28no—
193M16×C43—24no—
194M16×C43—24no—
195C2×C8×C43—22no—
196C2×C8×C43—22no—
197C2×C8×C43C2×D414yescomplemented
198C22⋊Dic43—216no—
199C22⋊Dic43—24no—
200C22⋊Dic43—24no—
201(C2×D43)⋊C4—216no—
202C4⋊Dic43—24no—
203C4⋊Dic43—24no—
204Dic43⋊C4—216no—
205C4×Dic43—24no—
206C4×Dic43C2×D418yescomplemented
207#10621877—24no—
208#10621877—42no—
209C2×C43⋊C8—22no—
210C2×C43⋊C8—41no—
211C2×C43⋊C8—41no—
212C23×C43—24no—
213C23×C43—42no—
214C23×C43—48no—
215C23×C43—42no—
216C23×C43—42no—
217C23×C43#12012yes—
218C23×C43#12012yes—
219C23×C43#12111yescharacteristic
220C23×C43#12111yescharacteristic
221C23×C43C22×D411yescharacteristic
222C22×D43—28no—
223C22×D43—24no—
224C22×D43—24no—
225C22×D43—22no—
226C22×D43—44no—
227C22×D43—44no—
228C22×D43—48no—
229C22×D43—44no—
230C22×D43—42no—
231C22×D43—42no—
232C22×D43—41no—
233C22×D43—41no—
234Q8×C43—24no—
235Q8×C43—24no—
236Q8×C43—42no—
237Q8×C43—42no—
238D4×C43—24no—
239D4×C43—24no—
240D4×C43—44no—
241D4×C43—44no—
242D4×C43—44no—
243D4×C43—44no—
244D4×C43—42no—
245D4×C43—42no—
246C2×C4×C43—24no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—44no—
250C2×C4×C43—44no—
251C2×C4×C43—44no—
252C2×C4×C43—44no—
253C2×C4×C43#12012yes—
254C2×C4×C43#12012yes—
255C2×C4×C43#12011yescharacteristic
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43#12012yes—
258C2×C4×C43#12111yescharacteristic
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12112yes—
261C2×C4×C43#12112yes—
262C2×C4×C43#12112yes—
263C2×C4×C43#12112yes—
264C2×C4×C43#12711yescharacteristic
265C2×C4×C43#12712yes—
266C2×C4×C43#12711yescharacteristic
267C2×C4×C43C22×D412yes—
268C2×C4×C43C22×D412yes—
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C22⋊D43—432no—
272C2×Dic43—28no—
273C2×Dic43—24no—
274C2×Dic43—22no—
275C2×Dic43—48no—
276C2×Dic43—42no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C4×D43—42no—
280C4×D43—44no—
281C4×D43—42no—
282C4×D43—42no—
283C4×D43—44no—
284C4×D43—42no—
285C8×C43—24no—
286C43⋊C8—42no—
287C2×#2010—431nomaximal, Sylow
288C22×C43—24no—
289C22×C43—22no—
290C22×C43—42no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—48no—
294C22×C43—44no—
295C22×C43—84no—
296C22×C43—84no—
297C22×C43#39212yes—
298C22×C43#39211yescharacteristic
299C22×C43#39211yescharacteristic
300C22×C43C2×#12012yes—
301C22×C43C2×#12111yescharacteristic
302C2×D43—24no—
303C2×D43—28no—
304C2×D43—44no—
305C2×D43—42no—
306C2×D43—48no—
307C2×D43—44no—
308C2×D43—42no—
309C2×D43—44no—
310C4×C43—44no—
311C4×C43#39211yescharacteristic
312C4×C43#39212yes—
313C4×C43#39211yescharacteristic
314C4×C43C2×#12011yescharacteristic
315C4×C43C2×#12112yes—
316C4×C43C2×#12711yescharacteristic
317Dic43—48no—
318Dic43—42no—
319C2×#575D4311yescharacteristic, complemented
320C2×#525—432no—
321C2×#421—432no—
322C2×#407—431no—
323#2010—438no—
324C2×H(3,ℤ/4)—431no—
325C2×C43—22no—
326C2×C43—21no—
327C2×C43—22no—
328C2×C43—21no—
329C2×C43—84no—
330C2×C43#201012yescomplemented
331C2×C43C2×#39211yescharacteristic
332D43—44no—
333C22×#41C2×D4312yes—
334C24×C4—431no—
335#575—24no—
336#575—22no—
337#575C2×D4314yescomplemented
338C2×#137—22no—
339C2×AGL(1,ℤ/8)—22no—
340C2×#135—22no—
341C22×M16—431no—
342C22×M16C2×D4311yescharacteristic
343#525—438no—
344#525—864no—
345#525—864no—
346#525—864no—
347C2×#123—862no—
348C2×C22⋊Q8—862no—
349C2×#121—862no—
350C2×#120—862no—
351C2×C4×D4—864no—
352C2×#117—432no—
353#421—438no—
354#421—864no—
355C2×#104—864no—
356#407—434no—
357#407—862no—
358C2×C22⋊C8—862no—
359H(3,ℤ/4)—434no—
360C43C2×#201011yescharacteristic, complemented, Sylow
361C25—431no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41C22⋊D4314yescomplemented
373C2×#41C22×D4314yes—
374C22×Q8C22⋊D4312yescomplemented
375C22×D4—22no—
376C22×D4—864no—
377C22×D4C22⋊D4312yescomplemented
378C23×C4—22no—
379C23×C4—431no—
380C23×C4—432no—
381C23×C4—432no—
382C23×C4—862no—
383C23×C4—862no—
384C23×C4—861no—
385C23×C4—861no—
386C23×C4—862no—
387C23×C4—862no—
388C23×C4—861no—
389C23×C4—861no—
390C23×C4C22×D4311yescharacteristic
391#137—28no—
392#137—28no—
393AGL(1,ℤ/8)—28no—
394AGL(1,ℤ/8)—28no—
395#135—28no—
396#135—28no—
397C2×Q16—22no—
398C2×SD16—24no—
399C2×D8—22no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—432no—
403C2×M16—861no—
404C2×M16—862no—
405C2×M16—862no—
406C2×M16C22⋊D4312yescomplemented
407C2×M16C22×D4312yes—
408C22×C8—861no—
409C22×C8C22⋊D4312yescomplemented
410#123—868no—
411#123—868no—
412C22⋊Q8—868no—
413C22⋊Q8—868no—
414#121—868no—
415#121—868no—
416#120—868no—
417#120—868no—
418C4×D4—8616no—
419C4×D4—8616no—
420#117—434no—
421#117—434no—
422#117—862no—
423#117—862no—
424C2×C4⋊C4—864no—
425C2×C4⋊C4—862no—
426C2×C22⋊C4—864no—
427C2×C22⋊C4—864no—
428C2×C22⋊C4—862no—
429C2×C42—434no—
430#104—8616no—
431C22⋊C8—868no—
432C24—22no—
433C24—432no—
434C24—862no—
435C24—861no—
436C24—862no—
437C24—861no—
438C24—1724no—
439C24D4×D4311yescharacteristic
440#41—24no—
441#41—24no—
442#41—24no—
443#41—24no—
444#41—24no—
445#41—24no—
446#41—24no—
447#41—24no—
448#41—42no—
449#41—42no—
450#41—42no—
451#41—42no—
452#41—42no—
453#41—42no—
454#41—42no—
455#41—42no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8C2×C22⋊D4314yescomplemented
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—8616no—
474C2×D4—17216no—
475C2×D4C2×C22⋊D4314yescomplemented
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—432no—
484C22×C4—864no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—864no—
490C22×C4—864no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—864no—
494C22×C4—862no—
495C22×C4—864no—
496C22×C4—862no—
497C22×C4—1721no—
498C22×C4—1721no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4—1721no—
505C22×C4—1722no—
506C22×C4—1721no—
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4312yes—
509C22×C4D4×D4312yes—
510C22×C4#1062190011yescharacteristic
511C22×C4#1062190011yescharacteristic
512C22×C4C2×C22⋊D4312yes—
513C22×C4C2×C22⋊D4312yes—
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517Q16—28no—
518SD16—216no—
519D8—28no—
520M16—24no—
521M16—24no—
522M16—864no—
523M16—1722no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—862no—
527C2×C8—1721no—
528C2×C8—1721no—
529C2×C8C2×C22⋊D4314yescomplemented
530C4⋊C4—8616no—
531C4⋊C4—864no—
532C4⋊C4—864no—
533C22⋊C4—8616no—
534C22⋊C4—8616no—
535C22⋊C4—864no—
536C22⋊C4—864no—
537C42—438no—
538C42—864no—
539C23—24no—
540C23—42no—
541C23—48no—
542C23—42no—
543C23—42no—
544C23—868no—
545C23—864no—
546C23—864no—
547C23—862no—
548C23—1724no—
549C23—1722no—
550C23—1724no—
551C23—1728no—
552C23—1724no—
553C23—1722no—
554C23—1721no—
555C23—1721no—
556C23#1306329312yes—
557C23#1306329312yes—
558C23#1306329611yescharacteristic
559C23#1306329611yescharacteristic
560C23C2×D4×D4311yescharacteristic
561Q8—24no—
562Q8—24no—
563Q8—42no—
564Q8—42no—
565D4—24no—
566D4—24no—
567D4—44no—
568D4—44no—
569D4—44no—
570D4—44no—
571D4—42no—
572D4—42no—
573D4—17232no—
574C2×C4—24no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—868no—
582C2×C4—864no—
583C2×C4—862no—
584C2×C4—1728no—
585C2×C4—1722no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1722no—
589C2×C4—1724no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1724no—
593C2×C4—1722no—
594C2×C4#1306329312yes—
595C2×C4#1306329312yes—
596C2×C4#1306329411yescharacteristic
597C2×C4#1306329411yescharacteristic
598C2×C4#1306329412yes—
599C2×C4#1306329611yescharacteristic
600C2×C4#1306329611yescharacteristic
601C2×C4#1306329712yes—
602C2×C4#1306329712yes—
603C2×C4#1306329712yes—
604C2×C4#1306329712yes—
605C2×C4#1306332111yescharacteristic
606C2×C4#1306332112yes—
607C2×C4#1306332111yescharacteristic
608C2×C4C2×D4×D4312yes—
609C2×C4C22×C22⋊D4312yes—
610C2×C4C22×C22⋊D4311yescharacteristic
611C2×C4C2×#1062190011yescharacteristic
612C8—24no—
613C8—1722no—
614C22—24no—
615C22—22no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—48no—
620C22—44no—
621C22—84no—
622C22—84no—
623C22—868no—
624C22—864no—
625C22—1724no—
626C22—1728no—
627C22—1722no—
628C22—1724no—
629C22—1724no—
630C22—1722no—
631C22#1458280712yes—
632C22#1458280711yescharacteristic
633C22#1458280711yescharacteristic
634C22C2×#1306329312yes—
635C22C2×#1306329611yescharacteristic
636C4—44no—
637C4—1728no—
638C4—1722no—
639C4#1458280711yescharacteristic
640C4#1458280712yes—
641C4#1458280711yescharacteristic
642C4C2×#1306329411yescharacteristic
643C4C2×#1306329712yes—
644C4C2×#1306332111yescharacteristic
645C2—22no—
646C2—22no—
647C2—21no—
648C2—21no—
649C2—84no—
650C2—1724no—
651C2#1913565912yesdirect product factor
652C2C2×#1458280711yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#575C2
socleC22×C43#392
hypercenterC2×#575D43
hypocenterC43C2×#2010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#14583406C2semidirect
2. C2×#14582916C2semidirect
3. C2×#14582862C2semidirect
4. #19135659C2direct (N × H)
5. C2×#14582656C2semidirect
6. C2×C43×#575C2semidirect
12. #14583406C22semidirect
20. #14582916C22semidirect
23. #14582862C22semidirect
25. #14582656C22semidirect
29. C43×#575C22semidirect
64. #13063284D4semidirect
71. C2×C4×Dic43D4semidirect
84. C2×#41×C43D4semidirect
86. C22×Q8×C43D4semidirect
88. C22×D4×C43D4semidirect
102. C2×M16×C43D4semidirect
104. C22×C8×C43D4semidirect
134. C2×Q8×C43C2×D4semidirect
146. C2×D4×C43C2×D4semidirect
197. C2×C8×C43C2×D4semidirect
206. C4×Dic43C2×D4semidirect
319. C2×#575D43semidirect
330. C2×C43#2010semidirect
337. #575C2×D43semidirect
360. C43C2×#2010semidirect
372. C2×#41C22⋊D43semidirect
374. C22×Q8C22⋊D43semidirect
377. C22×D4C22⋊D43semidirect
406. C2×M16C22⋊D43semidirect
409. C22×C8C22⋊D43semidirect
461. C2×Q8C2×C22⋊D43semidirect
475. C2×D4C2×C22⋊D43semidirect
529. C2×C8C2×C22⋊D43semidirect
651. C2#19135659direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#145829162
C2×#145828622
#191356592
C2×#145826562
C2×C43×#5752
C2×#201043