Finite Group Databasebeta

← C2×#19135662 #25123615

Subgroups — C2×#19135662 #25123615

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×#14583699C211yesmaximal, characteristic, complemented
2C2×#14583410C212yesmaximal, complemented
3C2×#14582915C212yesmaximal, complemented
4#19135662C218yesmaximal, direct product factor
5C2×#14582656C211yesmaximal, characteristic, complemented
6C2×C43×#407C211yesmaximal, characteristic, complemented
7C22×#10621898C2212yes—
8#14583699—24no—
9#14583699—22no—
10#14583699C2214yescomplemented
11C2×#13063358—22no—
12C2×#13063353—22no—
13C2×#13063347—22no—
14#14583410—24no—
15#14583410—24no—
16#14583410—24no—
17#14583410C2218yescomplemented
18C2×#13063308—22no—
19C2×#13063304—22no—
20C2×#13063299—22no—
21C2×#13063294—22no—
22C2×C4×C22⋊D43—24no—
23C2×#13063284C2212yes—
24#14582915—24no—
25#14582915C2218yescomplemented
26C2×#13063251—24no—
27#14582656C2214yescomplemented
28C24×C4×C43C2211yescharacteristic
29C22×M16×C43C2211yescharacteristic
30C22×M16×C43C2211yescharacteristic
31C43×#407—22no—
32C43×#407C2214yescomplemented
33C2×C22⋊C8×C43—22no—
34C2×#10621898—22no—
35C2×#10621898—22no—
36C2×#10621898—22no—
37C2×#10621898—22no—
38C2×#10621898—22no—
39C2×#10621898—22no—
40C2×#10621898—22no—
41C2×#10621898—22no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898D414yescomplemented
45C2×#10621898C2314yes—
46C22×Dic86D412yescomplemented
47C22×D172D412yescomplemented
48C22×C22⋊D43—24no—
49C22×C22⋊D43—22no—
50C22×C4×D43—22no—
51#13063358—28no—
52#13063358—28no—
53#13063353—28no—
54#13063353—28no—
55#13063347—28no—
56#13063347—28no—
57C2×Dic172—22no—
58C2×#10621873—24no—
59C2×D344—22no—
60#13063308—28no—
61#13063308—28no—
62#13063304—28no—
63#13063304—28no—
64#13063299—28no—
65#13063299—28no—
66#13063294—28no—
67#13063294—28no—
68C4×C22⋊D43—216no—
69C4×C22⋊D43—216no—
70#13063284—22no—
71#13063284—22no—
72#13063284D414yescomplemented
73#13063284C2314yes—
74C2×C4⋊Dic43—22no—
75C2×Dic43⋊C4—24no—
76C2×C22⋊Dic43—24no—
77C2×C22⋊Dic43—22no—
78C2×(C2×D43)⋊C4—24no—
79C2×C4×Dic43D414yescomplemented
80#13063251—216no—
81C25×C43D411yescharacteristic
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—22no—
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C23×C4×C43—21no—
89C23×C4×C43—21no—
90C23×C4×C43D411yescharacteristic
91C23×C4×C43D412yes—
92C23×C4×C43C2312yes—
93C23×C4×C43C2311yescharacteristic
94C2×M16×C43—22no—
95C2×M16×C43—22no—
96C2×M16×C43—21no—
97C2×M16×C43—22no—
98C2×M16×C43—22no—
99C2×M16×C43D412yescomplemented
100C2×M16×C43C2312yes—
101C2×M16×C43C2312yes—
102C22×C8×C43—21no—
103C22×C8×C43D412yescomplemented
104C22⋊C8×C43—28no—
105C24×C43—22no—
106C24×C43—21no—
107C24×C43—22no—
108C24×C43—21no—
109C24×C43—44no—
110C24×C43C2×D412yes—
111C24×C43C2×D411yescharacteristic
112C23×D43—22no—
113C22×C4×C43—24no—
114C22×C4×C43—24no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—24no—
119C22×C4×C43—24no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43—41no—
133C22×C4×C43—42no—
134C22×C4×C43—41no—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43#4111yescharacteristic
144C22×C4×C43#4111yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—216no—
147C2×C22⋊D43—24no—
148C2×C22⋊D43—24no—
149C2×C22⋊D43—416no—
150C2×C22⋊D43—42no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C2×C22⋊D43—42no—
154C22×Dic43—24no—
155C22×Dic43—22no—
156#10621898—24no—
157#10621898—24no—
158#10621898—24no—
159#10621898—24no—
160#10621898—24no—
161#10621898—24no—
162#10621898—24no—
163#10621898—24no—
164#10621898—42no—
165#10621898—42no—
166#10621898—42no—
167#10621898—42no—
168#10621898—42no—
169#10621898—42no—
170#10621898—42no—
171#10621898—42no—
172C2×D172—22no—
173C2×D172—22no—
174C2×D172—22no—
175C2×D172—22no—
176C2×D172—22no—
177C2×D172C2×D414yescomplemented
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×Dic86—22no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—22no—
188C2×Dic86—22no—
189C2×Dic86C2×D414yescomplemented
190M16×C43—24no—
191M16×C43—24no—
192M16×C43—24no—
193M16×C43—42no—
194C2×C8×C43—22no—
195C2×C8×C43—22no—
196C2×C8×C43—22no—
197C2×C8×C43—41no—
198C2×C8×C43—41no—
199C2×C8×C43C2×D414yescomplemented
200C22⋊Dic43—216no—
201C22⋊Dic43—24no—
202C22⋊Dic43—24no—
203(C2×D43)⋊C4—216no—
204C4⋊Dic43—24no—
205C4⋊Dic43—24no—
206Dic43⋊C4—216no—
207C4×Dic43—24no—
208C4×Dic43C2×D418yescomplemented
209Dic172—28no—
210D344—28no—
211#10621873—216no—
212C23×C43—28no—
213C23×C43—24no—
214C23×C43—24no—
215C23×C43—22no—
216C23×C43—42no—
217C23×C43—44no—
218C23×C43—44no—
219C23×C43—42no—
220C23×C43—44no—
221C23×C43—48no—
222C23×C43—42no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43#12012yes—
226C23×C43#12012yes—
227C23×C43#12111yescharacteristic
228C23×C43#12111yescharacteristic
229C23×C43C22×D411yescharacteristic
230C22×D43—24no—
231C22×D43—48no—
232C22×D43—42no—
233C22×D43—42no—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—44no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—44no—
244C2×C4×C43—42no—
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12012yes—
248C2×C4×C43#12012yes—
249C2×C4×C43#12012yes—
250C2×C4×C43#12112yes—
251C2×C4×C43#12112yes—
252C2×C4×C43#12112yes—
253C2×C4×C43#12112yes—
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43#12711yescharacteristic
257C2×C4×C43#12712yes—
258C2×C4×C43#12711yescharacteristic
259C2×C4×C43C22×D412yes—
260C2×C4×C43C22×D412yes—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C22⋊D43—432no—
264C22⋊D43—44no—
265C22⋊D43—44no—
266C22⋊D43—44no—
267C22⋊D43—44no—
268C2×Dic43—28no—
269C2×Dic43—24no—
270C2×Dic43—48no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273D172—24no—
274D172—24no—
275D172—42no—
276D172—42no—
277C4×D43—44no—
278C4×D43—44no—
279C4×D43—44no—
280C4×D43—44no—
281Dic86—24no—
282Dic86—24no—
283Dic86—42no—
284Dic86—42no—
285C8×C43—24no—
286C8×C43—42no—
287C2×#2010—431nomaximal, Sylow
288C22×C43—24no—
289C22×C43—22no—
290C22×C43—24no—
291C22×C43—28no—
292C22×C43—42no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—44no—
296C22×C43—48no—
297C22×C43—42no—
298C22×C43—44no—
299C22×C43—42no—
300C22×C43—44no—
301C22×C43#39212yes—
302C22×C43#39211yescharacteristic
303C22×C43#39211yescharacteristic
304C22×C43C2×#12012yes—
305C22×C43C2×#12111yescharacteristic
306C2×D43—48no—
307C2×D43—44no—
308C2×D43—84no—
309C2×D43—84no—
310C4×C43—42no—
311C4×C43#39211yescharacteristic
312C4×C43#39212yes—
313C4×C43#39211yescharacteristic
314C4×C43C2×#12011yescharacteristic
315C4×C43C2×#12112yes—
316C4×C43C2×#12711yescharacteristic
317Dic43—48no—
318Dic43—44no—
319C2×#575—431no—
320C2×#525—432no—
321C2×#421—432no—
322C2×#407D4311yescharacteristic, complemented
323#2010—438no—
324C2×H(3,ℤ/4)—431no—
325C2×C43—22no—
326C2×C43—22no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—44no—
330C2×C43#201012yescomplemented
331C2×C43C2×#39211yescharacteristic
332D43—84no—
333C22×#41—432no—
334C24×C4C2×D4311yescharacteristic
335#575—434no—
336#575—864no—
337#575—862no—
338C2×#137—862no—
339C2×AGL(1,ℤ/8)—862no—
340C2×#135—862no—
341C22×M16C2×D4311yescharacteristic
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—22no—
357#407C2×D4314yescomplemented
358C2×C22⋊C8—22no—
359H(3,ℤ/4)—434no—
360C43C2×#201011yescharacteristic, complemented, Sylow
361C25D17211yescharacteristic
362C2×#41—434no—
363C2×#41—434no—
364C2×#41—862no—
365C2×#41—862no—
366C2×#41—862no—
367C2×#41—862no—
368C2×#41—862no—
369C2×#41—862no—
370C2×#41—862no—
371C2×#41—862no—
372C2×#41—862no—
373C2×#41—862no—
374C22×Q8—432no—
375C22×D4—432no—
376C22×D4—864no—
377C22×D4—862no—
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—862no—
387C23×C4D17211yescharacteristic
388C23×C4D17212yes—
389C23×C4C22×D4312yes—
390C23×C4C22×D4311yescharacteristic
391#137—868no—
392#137—868no—
393AGL(1,ℤ/8)—868no—
394AGL(1,ℤ/8)—868no—
395#135—868no—
396#135—868no—
397C2×Q16—862no—
398C2×SD16—864no—
399C2×D8—862no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—21no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16C22⋊D4312yescomplemented
406C2×M16C22×D4312yes—
407C2×M16C22×D4312yes—
408C22×C8—21no—
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—28no—
432C24—22no—
433C24—21no—
434C24—22no—
435C24—21no—
436C24—44no—
437C24—862no—
438C24C2×D17212yes—
439C24C2×D17211yescharacteristic
440#41—864no—
441#41—864no—
442#41—864no—
443#41—864no—
444#41—864no—
445#41—864no—
446#41—864no—
447#41—864no—
448#41—1722no—
449#41—1722no—
450#41—1722no—
451#41—1722no—
452#41—1722no—
453#41—1722no—
454#41—1722no—
455#41—1722no—
456C2×Q8—434no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×Q8—862no—
460C2×Q8—862no—
461C2×Q8—862no—
462C2×D4—434no—
463C2×D4—8616no—
464C2×D4—864no—
465C2×D4—864no—
466C2×D4—862no—
467C2×D4—862no—
468C2×D4—862no—
469C2×D4—862no—
470C2×D4—862no—
471C2×D4—17216no—
472C2×D4—1722no—
473C2×D4—1722no—
474C2×D4—1722no—
475C2×D4—1722no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—41no—
498C22×C4—864no—
499C22×C4—862no—
500C22×C4—864no—
501C22×C4—864no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4C2×D17212yes—
507C22×C4C2×D17211yescharacteristic
508C22×C4#1062189811yescharacteristic
509C22×C4#1062189811yescharacteristic
510C22×C4D4×D4312yes—
511C22×C4D4×D4312yes—
512C22×C4D4×D4312yes—
513C22×C4D4×D4312yes—
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517Q16—868no—
518SD16—8616no—
519D8—868no—
520M16—24no—
521M16—24no—
522M16—24no—
523M16—42no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—41no—
528C2×C8—41no—
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—28no—
540C23—24no—
541C23—24no—
542C23—22no—
543C23—42no—
544C23—44no—
545C23—44no—
546C23—42no—
547C23—48no—
548C23—44no—
549C23—42no—
550C23—41no—
551C23—41no—
552C23—864no—
553C23—1728no—
554C23—1722no—
555C23—1722no—
556C23#1306329512yes—
557C23#1306329512yes—
558C23#1306329911yescharacteristic
559C23#1306329911yescharacteristic
560C23C22×D17211yescharacteristic
561Q8—864no—
562Q8—864no—
563Q8—1722no—
564Q8—1722no—
565D4—864no—
566D4—864no—
567D4—17232no—
568D4—1724no—
569D4—1724no—
570D4—1724no—
571D4—1724no—
572D4—1722no—
573D4—1722no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—868no—
586C2×C4—864no—
587C2×C4—1728no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1724no—
593C2×C4—1724no—
594C2×C4#1306329311yescharacteristic
595C2×C4#1306329311yescharacteristic
596C2×C4#1306329312yes—
597C2×C4#1306329512yes—
598C2×C4#1306329512yes—
599C2×C4#1306329812yes—
600C2×C4#1306329812yes—
601C2×C4#1306329812yes—
602C2×C4#1306329812yes—
603C2×C4#1306329911yescharacteristic
604C2×C4#1306329911yescharacteristic
605C2×C4#1306332111yescharacteristic
606C2×C4#1306332112yes—
607C2×C4#1306332111yescharacteristic
608C2×C4C2×D4×D4312yes—
609C2×C4C2×D4×D4312yes—
610C2×C4C22×C22⋊D4311yescharacteristic
611C2×C4C2×#1062189811yescharacteristic
612C8—24no—
613C8—42no—
614C22—24no—
615C22—22no—
616C22—28no—
617C22—24no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—44no—
622C22—42no—
623C22—48no—
624C22—44no—
625C22—44no—
626C22—42no—
627C22—3444no—
628C22—3444no—
629C22—1728no—
630C22—1724no—
631C22#1458280812yes—
632C22#1458280811yescharacteristic
633C22#1458280811yescharacteristic
634C22C2×#1306329512yes—
635C22C2×#1306329911yescharacteristic
636C4—42no—
637C4—1728no—
638C4—1724no—
639C4#1458280811yescharacteristic
640C4#1458280812yes—
641C4#1458280811yescharacteristic
642C4C2×#1306329311yescharacteristic
643C4C2×#1306329812yes—
644C4C2×#1306332111yescharacteristic
645C2—22no—
646C2—21no—
647C2—22no—
648C2—21no—
649C2—44no—
650C2—3444no—
651C2#1913566212yesdirect product factor
652C2C2×#1458280811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC22×C43#392
hypercenterC2×#407D43
hypocenterC43C2×#2010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#14583699C2semidirect
2. C2×#14583410C2semidirect
3. C2×#14582915C2semidirect
4. #19135662C2direct (N × H)
5. C2×#14582656C2semidirect
6. C2×C43×#407C2semidirect
10. #14583699C22semidirect
17. #14583410C22semidirect
25. #14582915C22semidirect
27. #14582656C22semidirect
32. C43×#407C22semidirect
44. C2×#10621898D4semidirect
46. C22×Dic86D4semidirect
47. C22×D172D4semidirect
72. #13063284D4semidirect
79. C2×C4×Dic43D4semidirect
99. C2×M16×C43D4semidirect
103. C22×C8×C43D4semidirect
177. C2×D172C2×D4semidirect
189. C2×Dic86C2×D4semidirect
199. C2×C8×C43C2×D4semidirect
208. C4×Dic43C2×D4semidirect
322. C2×#407D43semidirect
330. C2×C43#2010semidirect
357. #407C2×D43semidirect
360. C43C2×#2010semidirect
405. C2×M16C22⋊D43semidirect
409. C22×C8C22⋊D43semidirect
529. C2×C8C2×C22⋊D43semidirect
651. C2#19135662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836992
C2×#145834102
C2×#145829152
#191356622
C2×#145826562
C2×C43×#4072
C2×#201043