Finite Group Databasebeta

← C2×#19135017 #25098259

Subgroups — C2×#19135017 #25098259

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D43C211yesmaximal, characteristic
2C22×#13063305C211yesmaximal, characteristic
3C22×#13063250C211yesmaximal, characteristic, complemented
4C22×#13063248C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic
6#19135017C218yesmaximal, direct product factor
7C2×#14582661C211yesmaximal, characteristic, complemented
8C2×C43×#340C211yesmaximal, characteristic, complemented
9C23×Dic86C2211yescharacteristic
10C23×C4×D43C2211yescharacteristic
11C23×C43⋊C8C2211yescharacteristic
12C22×C8×D43—24no—
13C22×C8×D43—24no—
14C22×C8×D43—24no—
15C22×C8×D43C2214yes—
16C2×#13063305—24no—
17C2×#13063305—22no—
18C2×#13063305C418yescomplemented
19C2×#13063305C2214yes—
20C22×C4⋊Dic43—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×(C2×D43)⋊C4—21no—
23C22×(C2×D43)⋊C4—21no—
24C2×#13063250—24no—
25C2×#13063250C2214yescomplemented
26C2×#13063248—24no—
27C2×#13063248C2214yescomplemented
28#14582756—22no—
29#14582756C2214yes—
30C2×C43⋊#95—21no—
31#14582661C2214yescomplemented
32C23×C8×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#340C2214yescomplemented
36C24×D43D411yescharacteristic
37C22×Dic86—22no—
38C22×Dic86—22no—
39C22×Dic86—22no—
40C22×Dic86—22no—
41C22×Dic86—21no—
42C22×Dic86—22no—
43C22×Dic86C2×C414yes—
44C22×Dic86C2312yes—
45C23×Dic43—21no—
46C23×Dic43—21no—
47C23×Dic43D411yescharacteristic
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43C2×C414yes—
53C22×C4×D43D412yes—
54C22×C4×D43D414yes—
55C22×C4×D43C2312yes—
56C22×C43⋊C8—22no—
57C22×C43⋊C8—22no—
58C22×C43⋊C8D414yes—
59C22×C43⋊C8C2312yes—
60C2×C8×D43—232no—
61C2×C8×D43—28no—
62C2×C8×D43—28no—
63C2×C8×D43—28no—
64#13063305—216no—
65#13063305—28no—
66#13063305C2×C4116yescomplemented
67C2×C4⋊Dic43—28no—
68C2×C4⋊Dic43—24no—
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2312yes—
73C2×(C2×D43)⋊C4—28no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4—24no—
76C2×(C2×D43)⋊C4—44no—
77#13063250—28no—
78#13063248—28no—
79C43⋊#95—24no—
80C23×C4×C43—21no—
81C23×C4×C43—21no—
82C23×C4×C43C2311yescharacteristic
83C22×C8×C43—22no—
84C22×C8×C43—22no—
85C22×C8×C43D414yes—
86C22×C8×C43C2312yes—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—22no—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43C2×C414yes—
93C2×C4⋊C4×C43C2312yes—
94C2×C4⋊C4×C43C2312yes—
95C24×C43C2×D411yescharacteristic
96C23×D43—22no—
97C23×D43—22no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43C22⋊C414yes—
101C23×D43SD1614yes—
102C23×D43Q1614yes—
103C23×D43C2×D412yes—
104C22×C4×C43—24no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—42no—
108C22×C4×C43—42no—
109C22×C4×C43—42no—
110C22×C4×C43—42no—
111C22×C4×C43—42no—
112C22×C4×C43C22×C412yes—
113C22×C4×C43C2×D412yes—
114C22×C4×C43C2×D412yes—
115C22×C4×C43C2×D412yes—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43#4112yes—
118C22×C4×C43#4112yes—
119C22×C4×C43C2411yescharacteristic
120C22×Dic43—24no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—42no—
126C22×Dic43—42no—
127C22×Dic43—42no—
128C22×Dic43—42no—
129C22×Dic43—42no—
130C22×Dic43C22⋊C414yes—
131C22×Dic43C2×D412yes—
132C2×C4×D43—28no—
133C2×C4×D43—28no—
134C2×C4×D43—28no—
135C2×C4×D43—24no—
136C2×C4×D43—24no—
137C2×C4×D43—28no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43C22⋊C418yes—
143C2×C4×D43C22×C414yes—
144C2×C4×D43C2×D414yes—
145C2×Dic86—28no—
146C2×Dic86—28no—
147C2×Dic86—22no—
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—24no—
152C2×Dic86—22no—
153C2×Dic86—44no—
154C2×Dic86—42no—
155C2×Dic86—42no—
156C2×Dic86—44no—
157C2×Dic86C22×C414yes—
158C2×C8×C43—28no—
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C2×C8×C43C2×D414yes—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43C22×C414yes—
168(C2×D43)⋊C4—216no—
169(C2×D43)⋊C4—48no—
170C4⋊Dic43—216no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—42no—
174C2×C43⋊C8—28no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8C2×D414yes—
178C8×D43—232no—
179C23×C43C2×C22⋊C412yes—
180C23×C43#12112yes—
181C23×C43#12112yes—
182C23×C43C2×SD1612yes—
183C23×C43C2×Q1612yes—
184C23×C43#13512yes—
185C23×C43#13512yes—
186C23×C43C22×D411yescharacteristic
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—28no—
192C22×D43—28no—
193C22×D43—28no—
194C22×D43—28no—
195C22×D43—28no—
196C22×D43—28no—
197C22×D43#103116yescomplemented
198C22×D43C2×C22⋊C414yes—
199C22×D43C2×SD1614yes—
200C22×D43C2×Q1614yes—
201C2×C4×C43—24no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—48no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—84no—
209C2×C4×C43C2×C22⋊C412yes—
210C2×C4×C43C4×D414yes—
211C2×C4×C43C4×D414yes—
212C2×C4×C43#12014yes—
213C2×C4×C43#12112yes—
214C2×C4×C43#12112yes—
215C2×C4×C43#12314yes—
216C2×C4×C43C23×C411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—28no—
225C2×Dic43—24no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—48no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—84no—
233C2×Dic43C2×C22⋊C414yes—
234C4×D43—24no—
235C4×D43—24no—
236C4×D43—24no—
237C4×D43—24no—
238C4×D43—216no—
239Dic86—24no—
240Dic86—24no—
241Dic86—42no—
242Dic86—42no—
243Dic86—48no—
244C8×C43—24no—
245C43⋊C8—24no—
246C2×#1892—431nomaximal, Sylow
247C22×C43#38614yes—
248C22×C43C2×#10314yes—
249C22×C43#41614yes—
250C22×C43#46514yes—
251C22×C43#46514yes—
252C22×C43#46714yes—
253C22×C43#46714yes—
254C22×C43C22×C22⋊C411yescharacteristic
255C22×C43C2×#12111yescharacteristic
256C22×C43C2×#12111yescharacteristic
257C22×C43C22×SD1611yescharacteristic
258C22×C43C22×Q1611yescharacteristic
259C22×C43C2×#13511yescharacteristic
260C22×C43C2×#13511yescharacteristic
261C2×D43—24no—
262C2×D43—232no—
263C2×D43—24no—
264C2×D43—24no—
265C2×D43—24no—
266C2×D43—24no—
267C2×D43—24no—
268C2×D43C2×#10318yescomplemented
269C4×C43—44no—
270C4×C43—82no—
271C4×C43#38614yes—
272C4×C43C2×C4×D411yescharacteristic
273C4×C43C2×C4×D411yescharacteristic
274C4×C43C2×#12011yescharacteristic
275C4×C43C2×#12311yescharacteristic
276Dic43—24no—
277Dic43—44no—
278Dic43—82no—
279C24×C8—431no—
280C22×C22⋊Q8—431no—
281C22×#103—431no—
282C22×#103—431no—
283C2×#380—431no—
284#1892—438no—
285C2×#340—431no—
286C2×#340D4311yescharacteristic, complemented
287C2×C43#189218yescomplemented
288C2×C43C2×#38611yescharacteristic
289C2×C43C22×#10311yescharacteristic
290C2×C43C2×#41611yescharacteristic
291C2×C43C2×#46511yescharacteristic
292C2×C43C2×#46511yescharacteristic
293C2×C43C2×#46711yescharacteristic
294C2×C43C2×#46711yescharacteristic
295D43—28no—
296C23×Q8—431no—
297C24×C4—431no—
298C23×C8—431no—
299C23×C8—434no—
300C23×C8—864no—
301C23×C8—864no—
302C23×C8—864no—
303C23×C8C2×D4311yescharacteristic
304C2×C22⋊Q8—434no—
305C2×C22⋊Q8—438no—
306C2×C22⋊Q8—864no—
307C2×C22⋊Q8—862no—
308C22×C4⋊C4—431no—
309C22×C4⋊C4—861no—
310C22×C4⋊C4C2×D4311yescharacteristic
311C22×C4⋊C4C2×D4311yescharacteristic
312C22×C22⋊C4—861no—
313C22×C22⋊C4—861no—
314C2×#103—434no—
315C2×#103—434no—
316C2×#103—864no—
317C2×#103—864no—
318#380—434no—
319#380—862no—
320C2×#95—861no—
321#340—434no—
322#340C2×D4314yescomplemented
323C43C2×#189211yescharacteristic, complemented, Sylow
324C25—431no—
325C22×Q8—434no—
326C22×Q8—432no—
327C22×Q8—862no—
328C22×Q8—861no—
329C22×Q8—862no—
330C22×Q8—862no—
331C22×Q8—862no—
332C22×Q8—862no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—431no—
336C23×C4—434no—
337C23×C4—434no—
338C23×C4—432no—
339C23×C4—432no—
340C23×C4—862no—
341C23×C4—862no—
342C23×C4—862no—
343C23×C4—862no—
344C23×C4—861no—
345C23×C4—861no—
346C23×C4C22×D4311yescharacteristic
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—434no—
350C22×C8—432no—
351C22×C8—868no—
352C22×C8—868no—
353C22×C8—8632no—
354C22×C8—862no—
355C22×C8—862no—
356C22×C8—868no—
357C22×C8D17214yes—
358C22×C8C22×D4312yes—
359C22⋊Q8—4316no—
360C22⋊Q8—8616no—
361C22⋊Q8—868no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—868no—
369C2×C4⋊C4—864no—
370C2×C4⋊C4—862no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4C4×D4314yes—
374C2×C4⋊C4C22×D4312yes—
375C2×C4⋊C4C22×D4312yes—
376C2×C22⋊C4—868no—
377C2×C22⋊C4—864no—
378C2×C22⋊C4—864no—
379C2×C22⋊C4—1724no—
380#103—868no—
381#103—868no—
382#95—864no—
383C24—434no—
384C24—434no—
385C24—434no—
386C24—432no—
387C24—862no—
388C24—862no—
389C24—862no—
390C24—862no—
391C24D4×D4311yescharacteristic
392C2×Q8—434no—
393C2×Q8—864no—
394C2×Q8—862no—
395C2×Q8—868no—
396C2×Q8—868no—
397C2×Q8—862no—
398C2×Q8—862no—
399C2×Q8—862no—
400C2×Q8—862no—
401C2×Q8—1724no—
402C2×Q8—1722no—
403C2×Q8—1722no—
404C2×Q8—1724no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—434no—
414C22×C4—432no—
415C22×C4—438no—
416C22×C4—434no—
417C22×C4—434no—
418C22×C4—862no—
419C22×C4—862no—
420C22×C4—868no—
421C22×C4—868no—
422C22×C4—868no—
423C22×C4—864no—
424C22×C4—864no—
425C22×C4—868no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—864no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—1722no—
434C22×C4—1722no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4—1722no—
438C22×C4C2×C4×D4312yes—
439C22×C4C2×D17212yes—
440C22×C4#1062189812yes—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4312yes—
443C22×C4D4×D4312yes—
444C22×C4#1062190212yes—
445C22×C4C23×D4311yescharacteristic
446C2×C8—28no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—434no—
450C2×C8—8632no—
451C2×C8—868no—
452C2×C8—862no—
453C2×C8—862no—
454C2×C8C2×D17214yes—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—42no—
460C4⋊C4—8616no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—1722no—
464C4⋊C4C2×C4×D4314yes—
465C22⋊C4—8616no—
466C22⋊C4—1728no—
467C23—434no—
468C23—4316no—
469C23—434no—
470C23—434no—
471C23—868no—
472C23—868no—
473C23—862no—
474C23—862no—
475C23—868no—
476C23—868no—
477C23—868no—
478C23—862no—
479C23—862no—
480C23—868no—
481C23C22⋊C4×D4312yes—
482C23#1306329812yes—
483C23#1306330012yes—
484C23SD16×D4312yes—
485C23Q16×D4312yes—
486C23#1306334412yes—
487C23#1306334612yes—
488C23C2×D4×D4311yescharacteristic
489Q8—864no—
490Q8—864no—
491Q8—1722no—
492Q8—1722no—
493Q8—1728no—
494C2×C4—24no—
495C2×C4—48no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—84no—
502C2×C4—434no—
503C2×C4—862no—
504C2×C4—862no—
505C2×C4—868no—
506C2×C4—864no—
507C2×C4—864no—
508C2×C4—864no—
509C2×C4—864no—
510C2×C4—8616no—
511C2×C4—864no—
512C2×C4—3444no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1728no—
519C2×C4C22⋊C4×D4312yes—
520C2×C4#1306328714yes—
521C2×C4C4×D17214yes—
522C2×C4#1306329514yes—
523C2×C4#1306329812yes—
524C2×C4#1306330012yes—
525C2×C4#1306331014yes—
526C2×C4C22×C4×D4311yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C22×D17211yescharacteristic
530C2×C4C2×#1062189811yescharacteristic
531C2×C4C2×#1062190211yescharacteristic
532C8—24no—
533C8—864no—
534C22—438no—
535C22—8632no—
536C22—864no—
537C22—864no—
538C22—864no—
539C22—864no—
540C22—864no—
541C22—864no—
542C22#1458277714yes—
543C22#103×D4314yes—
544C22#1458289214yes—
545C22#1458312714yes—
546C22#1458312914yes—
547C22#1458313914yes—
548C22#1458314114yes—
549C22C2×C22⋊C4×D4311yescharacteristic
550C22C2×#1306329811yescharacteristic
551C22C2×#1306330011yescharacteristic
552C22C2×SD16×D4311yescharacteristic
553C22C2×Q16×D4311yescharacteristic
554C22C2×#1306334411yescharacteristic
555C22C2×#1306334611yescharacteristic
556C4—44no—
557C4—82no—
558C4—864no—
559C4—3442no—
560C4—1724no—
561C4#1458277714yes—
562C4C2×#1306328711yescharacteristic
563C4C2×C4×D17211yescharacteristic
564C4C2×#1306329511yescharacteristic
565C4C2×#1306331011yescharacteristic
566C2—868no—
567C2#1913501718yesdirect product factor
568C2C2×#1458277711yescharacteristic
569C2C2×#103×D4311yescharacteristic
570C2C2×#1458289211yescharacteristic
571C2C2×#1458312711yescharacteristic
572C2C2×#1458312911yescharacteristic
573C2C2×#1458313911yescharacteristic
574C2C2×#1458314111yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC24×C43C2×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenterC2×#340D43
hypocenterC43C2×#1892
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. C22×#13063250C2semidirect
4. C22×#13063248C2semidirect
6. #19135017C2direct (N × H)
7. C2×#14582661C2semidirect
8. C2×C43×#340C2semidirect
18. C2×#13063305C4semidirect
25. C2×#13063250C22semidirect
27. C2×#13063248C22semidirect
31. #14582661C22semidirect
35. C43×#340C22semidirect
66. #13063305C2×C4semidirect
197. C22×D43#103semidirect
268. C2×D43C2×#103semidirect
286. C2×#340D43semidirect
287. C2×C43#1892semidirect
322. #340C2×D43semidirect
323. C43C2×#1892semidirect
567. C2#19135017direct (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×#130633052
C22×#130632502
C22×#130632482
C2×#145827562
#191350172
C2×#145826612
C2×C43×#3402
C2×#189243