Finite Group Databasebeta

← C2×#19135795 #25124066

Subgroups — C2×#19135795 #25124066

Order 11008.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063258C211yesmaximal, characteristic, complemented
2C22×#13063249C211yesmaximal, characteristic, complemented
3C22×#13063249C211yesmaximal, characteristic, complemented
4C22×C22⋊(C43⋊C8)C211yesmaximal, characteristic
5C2×#14582759C211yesmaximal, characteristic
6#19135795C218yesmaximal, direct product factor
7C2×#14582661C211yesmaximal, characteristic, complemented
8C22×C22⋊Q8×C43C211yesmaximal, characteristic
9C23×C43⋊C8C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C22⋊Dic43—21no—
14C2×#13063258—24no—
15C2×#13063258C2214yescomplemented
16C2×#13063249—24no—
17C2×#13063249—24no—
18C2×#13063249C2214yescomplemented
19C2×#13063249C2214yescomplemented
20C2×C22⋊(C43⋊C8)—24no—
21C2×C22⋊(C43⋊C8)C2214yes—
22#14582759—22no—
23#14582759C2214yes—
24C2×C43⋊#95—21no—
25#14582661C2214yescomplemented
26C23×Q8×C43C2211yescharacteristic
27C24×C4×C43C2211yescharacteristic
28C2×C22⋊Q8×C43—24no—
29C2×C22⋊Q8×C43—22no—
30C2×C22⋊Q8×C43—24no—
31C2×C22⋊Q8×C43C2214yes—
32C22×C4⋊C4×C43—21no—
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43—21no—
35C23×Dic43—21no—
36C23×Dic43—21no—
37C22×C43⋊C8—22no—
38C22×C43⋊C8—22no—
39C22×C43⋊C8—22no—
40C22×C43⋊C8—22no—
41C22×C43⋊C8—22no—
42C22×C43⋊C8D414yes—
43C22×C43⋊C8C2312yes—
44C22×C43⋊C8C2312yes—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43C2312yes—
52C2×C4⋊Dic43C2312yes—
53C2×C22⋊Dic43—24no—
54C2×C22⋊Dic43—44no—
55#13063258—28no—
56#13063249—28no—
57#13063249—28no—
58C22⋊(C43⋊C8)—28no—
59C43⋊#95—24no—
60C25×C43D411yescharacteristic
61C22×Q8×C43—22no—
62C22×Q8×C43—21no—
63C22×Q8×C43—22no—
64C22×Q8×C43—22no—
65C22×Q8×C43—22no—
66C22×Q8×C43—22no—
67C22×Q8×C43D414yes—
68C22×Q8×C43C2312yes—
69C23×C4×C43—21no—
70C23×C4×C43—21no—
71C23×C4×C43—22no—
72C23×C4×C43—22no—
73C23×C4×C43—22no—
74C23×C4×C43—22no—
75C23×C4×C43—22no—
76C23×C4×C43—22no—
77C23×C4×C43D411yescharacteristic
78C23×C4×C43D412yes—
79C23×C4×C43C2312yes—
80C23×C4×C43C2311yescharacteristic
81C22⋊Q8×C43—216no—
82C22⋊Q8×C43—28no—
83C22⋊Q8×C43—28no—
84C2×C4⋊C4×C43—28no—
85C2×C4⋊C4×C43—24no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43D414yes—
89C2×C4⋊C4×C43C2312yes—
90C2×C22⋊C4×C43—28no—
91C2×C22⋊C4×C43—24no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—22no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43Q1614yes—
99C24×C43C2×D412yes—
100C24×C43C2×D411yescharacteristic
101C2×Q8×C43—24no—
102C2×Q8×C43—22no—
103C2×Q8×C43—28no—
104C2×Q8×C43—28no—
105C2×Q8×C43—22no—
106C2×Q8×C43—22no—
107C2×Q8×C43—22no—
108C2×Q8×C43—22no—
109C2×Q8×C43—44no—
110C2×Q8×C43—42no—
111C2×Q8×C43—42no—
112C2×Q8×C43—44no—
113C2×Q8×C43C2×D414yes—
114C22×C4×C43—24no—
115C22×C4×C43—24no—
116C22×C4×C43—24no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—24no—
124C22×C4×C43—24no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—44no—
131C22×C4×C43—44no—
132C22×C4×C43—44no—
133C22×C4×C43—44no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43#4112yes—
144C22×C4×C43#4112yes—
145C22×C4×C43#4112yes—
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C4⋊C4×C43—216no—
156C4⋊C4×C43—24no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43C2×D414yes—
159C22⋊C4×C43—216no—
160C22⋊Dic43—48no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43—42no—
166C4⋊Dic43—42no—
167C2×C43⋊C8—28no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—44no—
174C2×C43⋊C8C2×D414yes—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43—28no—
182C23×C43—28no—
183C23×C43—28no—
184C23×C43—44no—
185C23×C43—44no—
186C23×C43—44no—
187C23×C43—44no—
188C23×C43#12012yes—
189C23×C43#12112yes—
190C23×C43#12312yes—
191C23×C43C2×Q1614yes—
192C23×C43C2×Q1612yes—
193C23×C43#13512yes—
194C23×C43AGL(1,ℤ/8)12yes—
195C23×C43#13712yes—
196C23×C43C22×D411yescharacteristic
197Q8×C43—24no—
198Q8×C43—24no—
199Q8×C43—42no—
200Q8×C43—42no—
201Q8×C43—48no—
202C2×C4×C43—24no—
203C2×C4×C43—24no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—44no—
212C2×C4×C43—48no—
213C2×C4×C43—48no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—48no—
219C2×C4×C43#12012yes—
220C2×C4×C43#12114yes—
221C2×C4×C43#12114yes—
222C2×C4×C43#12112yes—
223C2×C4×C43#12314yes—
224C2×C4×C43#12312yes—
225C2×C4×C43#12414yes—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—84no—
239C2×Dic43—84no—
240C43⋊C8—24no—
241C43⋊C8—42no—
242C2×#2036—431nomaximal, Sylow
243C22×C43—24no—
244C22×C43—24no—
245C22×C43—24no—
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—416no—
251C22×C43#39414yes—
252C22×C43#44914yes—
253C22×C43#45114yes—
254C22×C43#46714yes—
255C22×C43#46814yes—
256C22×C43#48414yes—
257C22×C43#48514yes—
258C22×C43C2×#12011yescharacteristic
259C22×C43C2×#12111yescharacteristic
260C22×C43C2×#12311yescharacteristic
261C22×C43C22×Q1611yescharacteristic
262C22×C43C2×#13511yescharacteristic
263C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C43C2×#13711yescharacteristic
265C4×C43—42no—
266C4×C43—44no—
267C4×C43—44no—
268C4×C43#39414yes—
269C4×C43C2×#12111yescharacteristic
270C4×C43C2×#12111yescharacteristic
271C4×C43C2×#12311yescharacteristic
272C4×C43C2×#12411yescharacteristic
273Dic43—82no—
274Dic43—82no—
275C22×C22⋊Q8D4311yescharacteristic
276C22×#107—431no—
277C22×#103—431no—
278C22×#103—431no—
279C22×C22⋊C8—431no—
280C2×#380—431no—
281#2036—438no—
282C2×#340—431no—
283C2×C43—44no—
284C2×C43#203618yescomplemented
285C2×C43C2×#39411yescharacteristic
286C2×C43C2×#45111yescharacteristic
287C2×C43C2×#44911yescharacteristic
288C2×C43C2×#46711yescharacteristic
289C2×C43C2×#46811yescharacteristic
290C2×C43C2×#48511yescharacteristic
291C2×C43C2×#48411yescharacteristic
292C23×Q8C2×D4311yescharacteristic
293C24×C4C2×D4311yescharacteristic
294C23×C8—431no—
295C23×C8—431no—
296C2×C22⋊Q8—24no—
297C2×C22⋊Q8—22no—
298C2×C22⋊Q8—24no—
299C2×C22⋊Q8C2×D4314yes—
300C22×C4⋊C4—21no—
301C22×C4⋊C4—431no—
302C22×C4⋊C4—431no—
303C22×C4⋊C4C2×D4311yescharacteristic
304C22×C22⋊C4—21no—
305C22×C22⋊C4—861no—
306C2×#107—434no—
307C2×#107—864no—
308C2×#103—434no—
309C2×#103—434no—
310C2×#103—864no—
311C2×#103—864no—
312C2×C22⋊C8—434no—
313C2×C22⋊C8—864no—
314#380—434no—
315#380—862no—
316C2×#95—861no—
317#340—434no—
318C43C2×#203611yescharacteristic, complemented, Sylow
319C25C22⋊D4311yescharacteristic
320C22×Q8—22no—
321C22×Q8—21no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8C22⋊D4314yes—
327C22×Q8C22×D4312yes—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—861no—
337C23×C4—861no—
338C23×C4C22⋊D4312yes—
339C23×C4C22⋊D4311yescharacteristic
340C23×C4C22×D4312yes—
341C23×C4C22×D4311yescharacteristic
342C22×C8—434no—
343C22×C8—432no—
344C22×C8—432no—
345C22×C8—862no—
346C22×C8—862no—
347C22×C8—862no—
348C22×C8—862no—
349C22×C8—862no—
350C22⋊Q8—216no—
351C22⋊Q8—28no—
352C22⋊Q8—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—432no—
358C2×C4⋊C4—432no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4—862no—
362C2×C4⋊C4—862no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4C22⋊D4314yes—
366C2×C4⋊C4C22×D4312yes—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—864no—
370C2×C22⋊C4—1724no—
371#107—868no—
372#103—868no—
373#103—868no—
374C22⋊C8—868no—
375#95—864no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24#1062188514yes—
383C24C2×C22⋊D4312yes—
384C24C2×C22⋊D4311yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—28no—
388C2×Q8—28no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—44no—
394C2×Q8—42no—
395C2×Q8—42no—
396C2×Q8—44no—
397C2×Q8C2×C22⋊D4314yes—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—1722no—
425C22×C4—1722no—
426C22×C4—1722no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4—1722no—
430C22×C4D4×D4312yes—
431C22×C4#1062190012yes—
432C22×C4#1062190012yes—
433C22×C4#1062190012yes—
434C22×C4C2×C22⋊D4312yes—
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4312yes—
437C22×C4C2×C22⋊D4312yes—
438C22×C4C23×D4311yescharacteristic
439C2×C8—434no—
440C2×C8—868no—
441C2×C8—862no—
442C2×C8—862no—
443C2×C8—862no—
444C2×C8—862no—
445C2×C8—862no—
446C2×C8—1724no—
447C4⋊C4—216no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—862no—
451C4⋊C4—862no—
452C4⋊C4—862no—
453C4⋊C4—862no—
454C4⋊C4—1722no—
455C4⋊C4—1722no—
456C4⋊C4C2×C22⋊D4314yes—
457C22⋊C4—216no—
458C22⋊C4—1728no—
459C23—28no—
460C23—22no—
461C23—22no—
462C23—28no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—28no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23#1306329412yes—
473C23#1306329712yes—
474C23#1306330612yes—
475C23C2×#1062188514yes—
476C23C2×#1062188512yes—
477C23#1306334512yes—
478C23#1306335012yes—
479C23#1306335612yes—
480C23C22×C22⋊D4311yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—48no—
484Q8—42no—
485Q8—42no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—48no—
492C2×C4—44no—
493C2×C4—48no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—48no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—3444no—
504C2×C4—3444no—
505C2×C4—1722no—
506C2×C4—1722no—
507C2×C4—1722no—
508C2×C4—1722no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4#1306329412yes—
512C2×C4#1306329614yes—
513C2×C4#1306329712yes—
514C2×C4#1306329714yes—
515C2×C4#1306330612yes—
516C2×C4#1306330614yes—
517C2×C4#1306331214yes—
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C22×C22⋊D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4C2×#1062190011yescharacteristic
522C2×C4C2×#1062190011yescharacteristic
523C2×C4C2×#1062190011yescharacteristic
524C8—864no—
525C8—1722no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—42no—
531C22—416no—
532C22—42no—
533C22—42no—
534C22#1458281314yes—
535C22#1458304414yes—
536C22#1458305514yes—
537C22#1458313814yes—
538C22#1458314714yes—
539C22#1458323214yes—
540C22#1458323714yes—
541C22C2×#1306329411yescharacteristic
542C22C2×#1306329711yescharacteristic
543C22C2×#1306330611yescharacteristic
544C22C22×#1062188511yescharacteristic
545C22C2×#1306334511yescharacteristic
546C22C2×#1306335011yescharacteristic
547C22C2×#1306335611yescharacteristic
548C4—42no—
549C4—44no—
550C4—44no—
551C4—3442no—
552C4—3442no—
553C4#1458281314yes—
554C4C2×#1306329611yescharacteristic
555C4C2×#1306329711yescharacteristic
556C4C2×#1306330611yescharacteristic
557C4C2×#1306331211yescharacteristic
558C2—44no—
559C2#1913579518yesdirect product factor
560C2C2×#1458281311yescharacteristic
561C2C2×#1458305511yescharacteristic
562C2C2×#1458304411yescharacteristic
563C2C2×#1458313811yescharacteristic
564C2C2×#1458314711yescharacteristic
565C2C2×#1458323711yescharacteristic
566C2C2×#1458323211yescharacteristic
subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×C22⋊Q8×C43C2
socleC24×C43C2×D4
prime radicalC25×C43D4
hypercenterC22×C22⋊Q8D43
hypocenterC43C2×#2036
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13063258C2semidirect
2. C22×#13063249C2semidirect
3. C22×#13063249C2semidirect
6. #19135795C2direct (N × H)
7. C2×#14582661C2semidirect
15. C2×#13063258C22semidirect
18. C2×#13063249C22semidirect
19. C2×#13063249C22semidirect
25. #14582661C22semidirect
284. C2×C43#2036semidirect
318. C43C2×#2036semidirect
559. C2#19135795direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632582
C22×#130632492
C22×C22⋊(C43⋊C8)2
C2×#145827592
#191357952
C2×#145826612
C22×C22⋊Q8×C432
C2×#203643