Finite Group Databasebeta

← C2×#19135768 #25124022

Subgroups — C2×#19135768 #25124022

Order 11008.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583456C211yesmaximal, characteristic, complemented
2C2×#14582915C211yesmaximal, characteristic
3C22×#13063253C211yesmaximal, characteristic
4C2×#14582872C211yesmaximal, characteristic
5#19135768C218yesmaximal, direct product factor
6C2×#14582670C211yesmaximal, characteristic, complemented
7C2×#14582655C211yesmaximal, characteristic, complemented
8C2×C43×#339C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11#14583456—22no—
12#14583456—22no—
13#14583456—22no—
14#14583456C2214yescomplemented
15C2×#13063325—21no—
16C2×#13063317—21no—
17C2×#13063304—22no—
18C2×C4×Dic86—22no—
19C2×#13063284C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14582915—22no—
22#14582915C2214yes—
23C2×#13063253—21no—
24C2×#13063253—21no—
25C2×#13063253—22no—
26C2×#13063253C2214yes—
27C2×#13063251—22no—
28#14582872—22no—
29#14582872C2214yes—
30C2×#13063239—22no—
31#14582670C2214yescomplemented
32#14582655C2214yescomplemented
33C22×M16×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C22×C42×C43C2211yescharacteristic
36C43×#339C2214yescomplemented
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898Q812yescomplemented
48C2×#10621898C2312yes—
49C22×Dic86—22no—
50C22×Dic86Q811yescharacteristic, complemented
51C22×D172Q811yescharacteristic, complemented
52C22×C22⋊D43—21no—
53C22×C4×D43—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877C2312yes—
60C22×C43⋊C8—21no—
61#13063325—24no—
62#13063325—24no—
63#13063317—24no—
64#13063317—24no—
65#13063304—28no—
66#13063304—28no—
67C4×Dic86—28no—
68C4×Dic86—28no—
69#13063284—21no—
70#13063284—21no—
71#13063284—21no—
72#13063284—21no—
73#13063284D412yes—
74#13063284D412yes—
75#13063284C2312yes—
76#13063284C2312yes—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×Dic43⋊C4—24no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43D412yes—
83C2×C4×Dic43—21no—
84C2×C4×Dic43D412yes—
85#13063253—24no—
86#13063253—24no—
87#13063251—28no—
88#13063239—28no—
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43C2312yes—
97C22×C8×C43—21no—
98#117×C43—21no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43C2312yes—
102C2×C4⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C42×C43—21no—
105C2×C42×C43—21no—
106C2×C42×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43D411yescharacteristic
109C2×C42×C43D411yescharacteristic
110C2×C42×C43D412yes—
111C2×C42×C43C2312yes—
112C24×C43C2×D411yescharacteristic
113C23×D43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—44no—
119C22×C4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×Q811yescharacteristic
126C22×C4×C43C2×Q811yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—41no—
137C2×C22⋊D43—41no—
138C2×C22⋊D43—41no—
139C2×C22⋊D43—41no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143#10621898—22no—
144#10621898—22no—
145#10621898—22no—
146#10621898—22no—
147#10621898—22no—
148#10621898—22no—
149#10621898—22no—
150#10621898—22no—
151#10621898—41no—
152#10621898—41no—
153#10621898—41no—
154#10621898—41no—
155#10621898—41no—
156#10621898—41no—
157#10621898—41no—
158#10621898—41no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172C2×Q812yescomplemented
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—28no—
176C2×Dic86—21no—
177C2×Dic86—48no—
178C2×Dic86C2×Q812yescomplemented
179M16×C43—22no—
180M16×C43—22no—
181M16×C43—41no—
182M16×C43—41no—
183C2×C8×C43—22no—
184C2×C8×C43—41no—
185C2×C8×C43—41no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—41no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—41no—
190C42×C43—22no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—22no—
194C42×C43—22no—
195C42×C43—41no—
196C42×C43C2×D412yes—
197C42×C43C2×D412yes—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43C2×D414yes—
202C4⋊Dic43—28no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207Dic43⋊C4—216no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43C2×D414yes—
212#10621877—22no—
213#10621877—22no—
214#10621877—41no—
215#10621877—41no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—41no—
218C2×C43⋊C8—41no—
219C23×C43—42no—
220C23×C43#12011yescharacteristic
221C23×C43#12011yescharacteristic
222C23×C43C22⋊Q811yescharacteristic
223C23×C43C22⋊Q811yescharacteristic
224C23×C43#12411yescharacteristic
225C23×C43#12411yescharacteristic
226C23×C43C22×D411yescharacteristic
227C22×D43—22no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—82no—
231C2×C4×C43—24no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—44no—
235C2×C4×C43—44no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—82no—
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43#12011yescharacteristic
241C2×C4×C43C22⋊Q811yescharacteristic
242C2×C4×C43C22⋊Q811yescharacteristic
243C2×C4×C43C22⋊Q811yescharacteristic
244C2×C4×C43C22⋊Q811yescharacteristic
245C2×C4×C43C22⋊Q811yescharacteristic
246C2×C4×C43C22⋊Q811yescharacteristic
247C2×C4×C43C22⋊Q811yescharacteristic
248C2×C4×C43C22⋊Q811yescharacteristic
249C2×C4×C43C22⋊Q811yescharacteristic
250C2×C4×C43C22⋊Q811yescharacteristic
251C2×C4×C43#12411yescharacteristic
252C2×C4×C43#12411yescharacteristic
253C2×C4×C43#12411yescharacteristic
254C2×C4×C43#12411yescharacteristic
255C2×C4×C43#12411yescharacteristic
256C2×C4×C43#12411yescharacteristic
257C2×C4×C43#12411yescharacteristic
258C2×C4×C43#12411yescharacteristic
259C2×C4×C43#12411yescharacteristic
260C2×C4×C43#12411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×Q811yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C22⋊D43—42no—
268C22⋊D43—42no—
269C22⋊D43—42no—
270C22⋊D43—42no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—22no—
274C2×Dic43—44no—
275C2×Dic43—44no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278D172—22no—
279D172—22no—
280D172—41no—
281D172—41no—
282C4×D43—42no—
283C4×D43—42no—
284C4×D43—42no—
285C4×D43—42no—
286Dic86—22no—
287Dic86—22no—
288Dic86—416no—
289Dic86—41no—
290Dic86—41no—
291C8×C43—42no—
292C43⋊C8—42no—
293C2×#2031—431nomaximal, Sylow
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43#39311yescharacteristic
302C22×C43#39311yescharacteristic
303C22×C43#39311yescharacteristic
304C22×C43#39311yescharacteristic
305C22×C43C2×#12011yescharacteristic
306C22×C43C2×C22⋊Q811yescharacteristic
307C22×C43C2×#12411yescharacteristic
308C2×D43—42no—
309C2×D43—82no—
310C2×D43—82no—
311C2×D43—82no—
312C4×C43—24no—
313C4×C43—42no—
314C4×C43—82no—
315C4×C43#39311yescharacteristic
316C4×C43#39311yescharacteristic
317C4×C43#39311yescharacteristic
318C4×C43#39311yescharacteristic
319C4×C43C2×C22⋊Q811yescharacteristic
320C4×C43C2×C22⋊Q811yescharacteristic
321C4×C43C2×#12411yescharacteristic
322C4×C43C2×#12411yescharacteristic
323Dic43—44no—
324Dic43—44no—
325Dic43—42no—
326C2×#533—431no—
327C2×#421—431no—
328C22×#104—431no—
329C2×#410—431no—
330#2031—438no—
331C2×#344—431no—
332C2×#339D4311yescharacteristic, complemented
333C2×H(3,ℤ/4)—431no—
334C2×C43—21no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—21no—
340C2×C43#203112yescomplemented
341C2×C43C2×#39311yescharacteristic
342D43—82no—
343C22×#41—431no—
344C22×M16—431no—
345C22×M16C2×D4311yescharacteristic
346#533—434no—
347#533—862no—
348#533—862no—
349#533—862no—
350C2×C4⋊Q8—861no—
351C2×#125—861no—
352C2×C22⋊Q8—862no—
353C2×C4×Q8—862no—
354C2×#117—431no—
355C2×#117—431no—
356C2×#117C2×D4311yescharacteristic
357C22×C42C2×D4311yescharacteristic
358#421—434no—
359#421—862no—
360C2×#104—434no—
361C2×#104—862no—
362C2×#104—861no—
363C2×#104—861no—
364C2×#104—862no—
365#410—434no—
366#410—862no—
367C2×#99—862no—
368#344—434no—
369#339C2×D4314yescomplemented
370H(3,ℤ/4)—434no—
371C43C2×#203111yescharacteristic, complemented, Sylow
372C2×#41—432no—
373C2×#41—432no—
374C2×#41—861no—
375C2×#41—861no—
376C2×#41—861no—
377C2×#41—861no—
378C2×#41—861no—
379C2×#41—861no—
380C2×#41—861no—
381C2×#41—861no—
382C2×#41—861no—
383C2×#41—861no—
384C22×Q8—431no—
385C22×Q8—862no—
386C22×D4—431no—
387C22×D4—861no—
388C23×C4—21no—
389C23×C4—861no—
390C23×C4C22×D4311yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—432no—
397C2×M16—861no—
398C2×M16—861no—
399C2×M16—861no—
400C2×M16—861no—
401C2×M16—861no—
402C2×M16C22×D4312yes—
403C22×C8—21no—
404C22×C8—861no—
405C4⋊Q8—864no—
406C4⋊Q8—864no—
407#125—864no—
408#125—864no—
409C22⋊Q8—868no—
410C22⋊Q8—868no—
411C4×Q8—868no—
412C4×Q8—868no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—432no—
417#117—432no—
418#117—432no—
419#117—432no—
420#117—861no—
421#117—861no—
422#117—861no—
423#117—861no—
424#117C22×D4312yes—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—864no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—432no—
432C2×C22⋊C4—861no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—432no—
438C2×C42—861no—
439C2×C42D17211yescharacteristic
440C2×C42D17211yescharacteristic
441C2×C42D17212yes—
442C2×C42C22×D4312yes—
443#104—868no—
444#104—864no—
445#104—864no—
446#99—868no—
447C24—861no—
448C24D4×D4311yescharacteristic
449#41—862no—
450#41—862no—
451#41—862no—
452#41—862no—
453#41—862no—
454#41—862no—
455#41—862no—
456#41—862no—
457#41—1721no—
458#41—1721no—
459#41—1721no—
460#41—1721no—
461#41—1721no—
462#41—1721no—
463#41—1721no—
464#41—1721no—
465C2×Q8—432no—
466C2×Q8—868no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—1728no—
473C2×D4—432no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—1721no—
482C2×D4—1721no—
483C2×D4—1721no—
484C2×D4—1721no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—41no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—861no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—1721no—
497C22×C4—1721no—
498C22×C4—1721no—
499C22×C4—1721no—
500C22×C4C2×D17211yescharacteristic
501C22×C4C2×D17211yescharacteristic
502C22×C4#1062189811yescharacteristic
503C22×C4#1062189811yescharacteristic
504C22×C4#1062189811yescharacteristic
505C22×C4#1062189811yescharacteristic
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4#1062190011yescharacteristic
510C22×C4#1062190011yescharacteristic
511C22×C4Q8×D4311yescharacteristic
512C22×C4Q8×D4311yescharacteristic
513C22×C4C23×D4311yescharacteristic
514M16—22no—
515M16—22no—
516M16—41no—
517M16—41no—
518M16—862no—
519M16—862no—
520M16—1721no—
521M16—1721no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—862no—
526C2×C8—1721no—
527C2×C8—1721no—
528C4⋊C4—22no—
529C4⋊C4—41no—
530C4⋊C4—8616no—
531C4⋊C4—868no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C22⋊C4—22no—
537C22⋊C4—41no—
538C22⋊C4—434no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C42—22no—
543C42—21no—
544C42—21no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—434no—
549C42—862no—
550C42—862no—
551C42—862no—
552C42C2×D17212yes—
553C42C2×D17212yes—
554C23—42no—
555C23—862no—
556C23—3442no—
557C23—1721no—
558C23—1721no—
559C23#1306329511yescharacteristic
560C23#1306329511yescharacteristic
561C23#1306330311yescharacteristic
562C23#1306330311yescharacteristic
563C23#1306331111yescharacteristic
564C23#1306331111yescharacteristic
565C23C2×D4×D4311yescharacteristic
566Q8—862no—
567Q8—862no—
568Q8—17216no—
569Q8—1721no—
570Q8—1721no—
571D4—862no—
572D4—862no—
573D4—1722no—
574D4—1722no—
575D4—1722no—
576D4—1722no—
577D4—1721no—
578D4—1721no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—82no—
587C2×C4—864no—
588C2×C4—864no—
589C2×C4—862no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4#1306329511yescharacteristic
599C2×C4#1306329511yescharacteristic
600C2×C4#1306330311yescharacteristic
601C2×C4#1306330311yescharacteristic
602C2×C4#1306330311yescharacteristic
603C2×C4#1306330311yescharacteristic
604C2×C4#1306330311yescharacteristic
605C2×C4#1306330311yescharacteristic
606C2×C4#1306330511yescharacteristic
607C2×C4#1306330511yescharacteristic
608C2×C4#1306330511yescharacteristic
609C2×C4#1306330511yescharacteristic
610C2×C4#1306331111yescharacteristic
611C2×C4#1306331111yescharacteristic
612C2×C4#1306331111yescharacteristic
613C2×C4#1306331111yescharacteristic
614C2×C4#1306331111yescharacteristic
615C2×C4#1306331111yescharacteristic
616C2×C4#1306331311yescharacteristic
617C2×C4#1306331311yescharacteristic
618C2×C4#1306331311yescharacteristic
619C2×C4#1306331311yescharacteristic
620C2×C4C2×D4×D4311yescharacteristic
621C2×C4C22×D17211yescharacteristic
622C2×C4C2×Q8×D4311yescharacteristic
623C2×C4C2×#1062190011yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4C2×#1062189811yescharacteristic
626C8—42no—
627C8—1722no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—3442no—
636C22—3442no—
637C22—3442no—
638C22—1722no—
639C22#1458281211yescharacteristic
640C22#1458281211yescharacteristic
641C22#1458281211yescharacteristic
642C22#1458281211yescharacteristic
643C22C2×#1306329511yescharacteristic
644C22C2×#1306330311yescharacteristic
645C22C2×#1306331111yescharacteristic
646C4—24no—
647C4—42no—
648C4—82no—
649C4—1724no—
650C4—1724no—
651C4—1722no—
652C4#1458281211yescharacteristic
653C4#1458281211yescharacteristic
654C4#1458281211yescharacteristic
655C4#1458281211yescharacteristic
656C4C2×#1306330311yescharacteristic
657C4C2×#1306330511yescharacteristic
658C4C2×#1306331111yescharacteristic
659C4C2×#1306331311yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—3442no—
667C2#1913576812yesdirect product factor
668C2C2×#1458281211yescharacteristic
subgroupG/H
centerC2×C4#13063311
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#339C2
socleC22×C43#393
prime radicalC22×#10621898C22
hypercenterC2×#339D43
hypocenterC43C2×#2031
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#14583456C2semidirect
5. #19135768C2direct (N × H)
6. C2×#14582670C2semidirect
7. C2×#14582655C2semidirect
8. C2×C43×#339C2semidirect
14. #14583456C22semidirect
31. #14582670C22semidirect
32. #14582655C22semidirect
36. C43×#339C22semidirect
47. C2×#10621898Q8semidirect
50. C22×Dic86Q8semidirect
51. C22×D172Q8semidirect
164. C2×D172C2×Q8semidirect
178. C2×Dic86C2×Q8semidirect
332. C2×#339D43semidirect
340. C2×C43#2031semidirect
369. #339C2×D43semidirect
371. C43C2×#2031semidirect
667. C2#19135768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834562
C2×#145829152
C22×#130632532
C2×#145828722
#191357682
C2×#145826702
C2×#145826552
C2×C43×#3392
C2×#203143