Finite Group Databasebeta

← C2×#19134826 #25097457

Subgroups — C2×#19134826 #25097457

Order 11008.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583382C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3C22×#13063252C211yesmaximal, characteristic
4C2×#14582764C211yesmaximal, characteristic, complemented
5#19134826C218yesmaximal, direct product factor
6C2×#14582667C211yesmaximal, characteristic, complemented
7C2×#14582660C211yesmaximal, characteristic, complemented
8C2×C43×#417C211yesmaximal, characteristic
9C22×#10621877C2211yescharacteristic
10#14583382—22no—
11#14583382—22no—
12#14583382—22no—
13#14583382C2214yes—
14C2×Q8×Dic43—21no—
15C2×D4×Dic43—22no—
16C2×D4×Dic43—21no—
17C2×#13063284—21no—
18C2×#13063284C2211yescharacteristic
19C22×C4⋊Dic43—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582939—22no—
23#14582939C2214yescomplemented
24C2×#13063258—21no—
25C2×#13063256—21no—
26C2×#13063252C418yescomplemented
27C2×#13063252C2214yes—
28#14582764—22no—
29#14582764C2214yescomplemented
30C2×C43⋊#95—22no—
31#14582667C2214yescomplemented
32#14582660C2214yescomplemented
33C22×#41×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#417—22no—
37C43×#417C2214yes—
38C2×#103×C43—21no—
39C2×#102×C43—21no—
40C23×Dic43—21no—
41C23×Dic43—22no—
42C23×Dic43D412yes—
43C2×#10621877—21no—
44C2×#10621877—22no—
45C2×#10621877C2×C414yescomplemented
46C2×#10621877C2312yes—
47C22×C43⋊C8—21no—
48Q8×Dic43—24no—
49Q8×Dic43—24no—
50D4×Dic43—28no—
51D4×Dic43—24no—
52D4×Dic43—24no—
53D4×Dic43—28no—
54#13063284—24no—
55#13063284—21no—
56#13063284—21no—
57#13063284—24no—
58#13063284D412yes—
59#13063284C2312yes—
60C2×C4⋊Dic43—22no—
61C2×C4⋊Dic43—24no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—24no—
67C2×C4⋊Dic43D412yes—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2312yes—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—21no—
73C2×C4×Dic43—22no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43—22no—
77C2×C4×Dic43C2×C414yescomplemented
78C2×C4×Dic43C2312yes—
79#13063258—24no—
80#13063256—24no—
81#13063252C2×C4116yescomplemented
82C43⋊#95—28no—
83C2×#41×C43—21no—
84C2×#41×C43—21no—
85C2×#41×C43—22no—
86C2×#41×C43—22no—
87C2×#41×C43C2×C414yes—
88C2×#41×C43D412yes—
89C2×#41×C43Q814yes—
90C2×#41×C43C2312yes—
91C22×Q8×C43D411yescharacteristic
92C22×D4×C43—21no—
93C22×D4×C43D411yescharacteristic
94C23×C4×C43—21no—
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C2×M16×C43—21no—
98C2×M16×C43—22no—
99C2×M16×C43—22no—
100C2×M16×C43C2312yes—
101C22×C8×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2312yes—
108#103×C43—24no—
109#102×C43—24no—
110C24×C43—21no—
111C24×C43C2×D411yescharacteristic
112#41×C43—24no—
113#41×C43—24no—
114#41×C43—24no—
115#41×C43—24no—
116#41×C43—24no—
117#41×C43—22no—
118#41×C43—22no—
119#41×C43C4⋊C418yes—
120#41×C43C22×C414yes—
121#41×C43C2×Q814yes—
122C2×Q8×C43—21no—
123C2×Q8×C43—22no—
124C2×Q8×C43C4⋊C414yes—
125C2×Q8×C43C2×D412yes—
126C2×D4×C43—21no—
127C2×D4×C43—22no—
128C2×D4×C43—24no—
129C2×D4×C43—22no—
130C2×D4×C43—24no—
131C2×D4×C43—22no—
132C2×D4×C43C4⋊C414yes—
133C2×D4×C43C2×D412yes—
134C22×C4×C43—24no—
135C22×C4×C43—22no—
136C22×C4×C43—24no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—22no—
140C22×C4×C43—44no—
141C22×C4×C43—41no—
142C22×C4×C43—41no—
143C22×C4×C43C22×C412yes—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×Q812yes—
150C22×C4×C43#4112yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—28no—
154C22×Dic43—24no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—44no—
163C22×Dic43—84no—
164C22×Dic43C2×D414yes—
165M16×C43—22no—
166M16×C43—22no—
167M16×C43—42no—
168C2×C8×C43—22no—
169C2×C8×C43—42no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C22⋊Dic43—28no—
175C22⋊Dic43—22no—
176C22⋊Dic43—22no—
177C4⋊Dic43—28no—
178C4⋊Dic43—22no—
179C4⋊Dic43—21no—
180C4⋊Dic43—22no—
181C4⋊Dic43—21no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43C2×D412yes—
185C4⋊Dic43C2×D412yes—
186C4×Dic43—28no—
187C4×Dic43—24no—
188C4×Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43C22×C414yescomplemented
192#10621877—24no—
193#10621877—22no—
194#10621877C22×C414yescomplemented
195C2×C43⋊C8—24no—
196C2×C43⋊C8—22no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—24no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43C4×D412yes—
204C23×C43#12011yescharacteristic
205C23×C43#12011yescharacteristic
206C23×C43C22⋊Q812yes—
207C23×C43C22×D411yescharacteristic
208Q8×C43—22no—
209Q8×C43—24no—
210Q8×C43C2×C4⋊C414yes—
211D4×C43—24no—
212D4×C43—24no—
213D4×C43—28no—
214D4×C43—22no—
215D4×C43—24no—
216D4×C43C2×C4⋊C414yes—
217C2×C4×C43—22no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—28no—
222C2×C4×C43—44no—
223C2×C4×C43—42no—
224C2×C4×C43—82no—
225C2×C4×C43—82no—
226C2×C4×C43C2×C4⋊C412yes—
227C2×C4×C43C2×C4⋊C412yes—
228C2×C4×C43C4×D412yes—
229C2×C4×C43C4×D412yes—
230C2×C4×C43C4×D412yes—
231C2×C4×C43#12011yescharacteristic
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43C22⋊Q812yes—
234C2×C4×C43C22⋊Q812yes—
235C2×C4×C43C22⋊Q812yes—
236C2×C4×C43#12312yes—
237C2×C4×C43#12312yes—
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×Dic43—24no—
245C2×Dic43—22no—
246C2×Dic43—24no—
247C2×Dic43—22no—
248C2×Dic43—48no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—44no—
253C2×Dic43—42no—
254C2×Dic43—44no—
255C2×Dic43—82no—
256C2×Dic43—88no—
257C8×C43—42no—
258C43⋊C8—24no—
259C2×#1860—431nomaximal, Sylow
260C22×C43—24no—
261C22×C43—24no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—24no—
267C22×C43—48no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43#38512yes—
271C22×C43#38512yes—
272C22×C43#45412yes—
273C22×C43#45512yes—
274C22×C43C2×C4×D411yescharacteristic
275C22×C43C2×#12011yescharacteristic
276C22×C43C2×C22⋊Q811yescharacteristic
277C4×C43—24no—
278C4×C43—82no—
279C4×C43#38512yes—
280C4×C43#38512yes—
281C4×C43C22×C4⋊C411yescharacteristic
282C4×C43C2×C4×D411yescharacteristic
283C4×C43C2×C22⋊Q811yescharacteristic
284C4×C43C2×#12311yescharacteristic
285Dic43—44no—
286Dic43—44no—
287Dic43—42no—
288Dic43—42no—
289C2×#520—431no—
290C2×#428—431no—
291C22×#104—431no—
292C2×#417D4311yescharacteristic
293C2×#382—431no—
294#1860—438no—
295C2×#343—431no—
296C2×#339—431no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—22no—
300C2×C43—44no—
301C2×C43#186014yescomplemented
302C2×C43C2×#38511yescharacteristic
303C2×C43C2×#45511yescharacteristic
304C2×C43C2×#45411yescharacteristic
305C22×#41C2×D4311yescharacteristic
306C22×M16—431no—
307C22×M16C2×D4311yescharacteristic
308#520—434no—
309#520—862no—
310#520—862no—
311#520—862no—
312C2×C4×Q8—861no—
313C2×C4×D4—862no—
314C2×C4×D4—861no—
315C2×#117—431no—
316C2×#117—861no—
317C22×C4⋊C4—431no—
318C22×C4⋊C4—861no—
319C22×C4⋊C4C2×D4311yescharacteristic
320C22×C42—431no—
321#428—434no—
322#428—862no—
323C2×#107—861no—
324C2×#106—861no—
325C2×#104—434no—
326C2×#104—438no—
327#417—22no—
328#417C2×D4314yes—
329C2×#103—21no—
330C2×#102—21no—
331#382—434no—
332#382—862no—
333C2×#95—862no—
334#343—434no—
335#339—434no—
336C43C2×#186011yescharacteristic, complemented, Sylow
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41Dic8614yes—
342C2×#41C4×D4314yes—
343C2×#41C22⋊D4312yes—
344C2×#41C22×D4312yes—
345C22×Q8C22⋊D4311yescharacteristic
346C22×D4—21no—
347C22×D4C22⋊D4311yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—432no—
351C23×C4—862no—
352C23×C4—861no—
353C23×C4C22×D4311yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—434no—
358C2×M16—432no—
359C2×M16—861no—
360C2×M16—862no—
361C2×M16C22×D4312yes—
362C22×C8—21no—
363C22×C8—861no—
364C4×Q8—864no—
365C4×Q8—864no—
366C4×D4—868no—
367C4×D4—868no—
368C4×D4—864no—
369C4×D4—864no—
370#117—432no—
371#117—432no—
372#117—864no—
373#117—864no—
374#117—861no—
375#117—861no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—432no—
384C2×C4⋊C4—432no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—864no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4C22×D4312yes—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—861no—
395C2×C42—434no—
396C2×C42—432no—
397C2×C42—862no—
398C2×C42—861no—
399C2×C42—862no—
400C2×C42—861no—
401#107—864no—
402#106—864no—
403#104—4316no—
404#103—24no—
405#102—24no—
406#95—868no—
407C24—21no—
408C24D4×D4311yescharacteristic
409#41—24no—
410#41—24no—
411#41—24no—
412#41—24no—
413#41—24no—
414#41—22no—
415#41—22no—
416#41Dic43⋊C418yes—
417#41C2×Dic8614yes—
418#41C2×C4×D4314yes—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8Dic43⋊C414yes—
422C2×Q8C2×C22⋊D4312yes—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4Dic43⋊C414yes—
430C2×D4C2×C22⋊D4312yes—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—44no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—434no—
441C22×C4—868no—
442C22×C4—862no—
443C22×C4—864no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—3444no—
449C22×C4—1724no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4C2×Dic8612yes—
453C22×C4C2×C4×D4312yes—
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4#1062190012yes—
458C22×C4#1062190012yes—
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462M16—22no—
463M16—22no—
464M16—42no—
465M16—434no—
466M16—864no—
467M16—862no—
468C2×C8—22no—
469C2×C8—42no—
470C2×C8—864no—
471C2×C8—862no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—432no—
477C4⋊C4—432no—
478C4⋊C4—868no—
479C4⋊C4—861no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—861no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C22⋊C4—868no—
486C22⋊C4—862no—
487C22⋊C4—862no—
488C42—434no—
489C42—868no—
490C42—864no—
491C42—862no—
492C42—862no—
493C42—862no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—24no—
498C23—42no—
499C23—42no—
500C23(C22⋊D43)⋊C412yes—
501C23#1306329311yescharacteristic
502C23#1306329311yescharacteristic
503C23#1306330212yes—
504C23C2×D4×D4311yescharacteristic
505Q8—22no—
506Q8—24no—
507Q8C2×Dic43⋊C414yes—
508D4—24no—
509D4—24no—
510D4—28no—
511D4—22no—
512D4—24no—
513D4C2×Dic43⋊C414yes—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—28no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—864no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—864no—
527C2×C4—3442no—
528C2×C4—3448no—
529C2×C4—1728no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1724no—
535C2×C4—1724no—
536C2×C4C2×Dic43⋊C412yes—
537C2×C4C2×Dic43⋊C412yes—
538C2×C4(C22⋊D43)⋊C412yes—
539C2×C4(C22⋊D43)⋊C412yes—
540C2×C4(C22⋊D43)⋊C412yes—
541C2×C4#1306329311yescharacteristic
542C2×C4#1306329311yescharacteristic
543C2×C4#1306330212yes—
544C2×C4#1306330212yes—
545C2×C4#1306330212yes—
546C2×C4#1306330612yes—
547C2×C4#1306330612yes—
548C2×C4C22×C4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C22×C22⋊D4311yescharacteristic
551C2×C4C22×Dic8611yescharacteristic
552C2×C4C2×#1062190011yescharacteristic
553C2×C4C2×#1062190011yescharacteristic
554C8—42no—
555C8—864no—
556C22—24no—
557C22—24no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—24no—
563C22—48no—
564C22—42no—
565C22—42no—
566C22#1458277112yes—
567C22#1458277112yes—
568C22#1458307012yes—
569C22#1458307512yes—
570C22C2×(C22⋊D43)⋊C411yescharacteristic
571C22C2×#1306329311yescharacteristic
572C22C2×#1306330211yescharacteristic
573C4—24no—
574C4—82no—
575C4—1724no—
576C4—1722no—
577C4—1724no—
578C4—1722no—
579C4#1458277112yes—
580C4#1458277112yes—
581C4C22×Dic43⋊C411yescharacteristic
582C4C2×(C22⋊D43)⋊C411yescharacteristic
583C4C2×#1306330211yescharacteristic
584C4C2×#1306330611yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—44no—
589C2#1913482614yesdirect product factor
590C2C2×#1458277111yescharacteristic
591C2C2×#1458307511yescharacteristic
592C2C2×#1458307011yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43#120
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43C2×#1860
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
4. C2×#14582764C2semidirect
5. #19134826C2direct (N × H)
6. C2×#14582667C2semidirect
7. C2×#14582660C2semidirect
23. #14582939C22semidirect
26. C2×#13063252C4semidirect
29. #14582764C22semidirect
31. #14582667C22semidirect
32. #14582660C22semidirect
45. C2×#10621877C2×C4semidirect
77. C2×C4×Dic43C2×C4semidirect
81. #13063252C2×C4semidirect
191. C4×Dic43C22×C4semidirect
194. #10621877C22×C4semidirect
301. C2×C43#1860semidirect
336. C43C2×#1860semidirect
589. C2#19134826direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833822
C2×#145829392
C22×#130632522
C2×#145827642
#191348262
C2×#145826672
C2×#145826602
C2×C43×#4172
C2×#186043