Finite Group Databasebeta

← C2×#19135843 #25124354

Subgroups — C2×#19135843 #25124354

Order 11008.

2046 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063240C212yesmaximal, complemented
2C2×#14582779C212yesmaximal, complemented
3C2×#14582771C211yesmaximal, characteristic, complemented
4#19135843C218yesmaximal, direct product factor
5C2×#14582666C211yesmaximal, characteristic, complemented
6C2×C43×#534C211yesmaximal, characteristic
7C24×Dic43C2211yescharacteristic
8C22×Dic43⋊C4—21no—
9C22×C22⋊Dic43—22no—
10C22×C22⋊Dic43C2212yes—
11C22×C22⋊Dic43C2211yescharacteristic
12C2×#13063240—28no—
13C2×#13063240C2218yescomplemented
14#14582779—24no—
15#14582779C2218yescomplemented
16#14582771—22no—
17#14582771C2214yescomplemented
18C2×C43⋊#95—21no—
19C2×C43⋊#95—22no—
20#14582666C2214yescomplemented
21C23×D4×C43C2212yes—
22C43×#534—24no—
23C43×#534—22no—
24C43×#534C2214yes—
25C2×#123×C43—22no—
26C2×#121×C43—21no—
27C2×#121×C43—21no—
28C2×#120×C43—22no—
29C22×C22⋊C4×C43C2211yescharacteristic
30C23×Dic43—22no—
31C23×Dic43—21no—
32C23×Dic43—21no—
33C23×Dic43—22no—
34C23×Dic43—21no—
35C23×Dic43—22no—
36C23×Dic43—44no—
37C23×Dic43C2312yes—
38C2×Dic43⋊C4—24no—
39C2×Dic43⋊C4—44no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—22no—
42C2×C22⋊Dic43—24no—
43C2×C22⋊Dic43—24no—
44C2×C22⋊Dic43—28no—
45C2×C22⋊Dic43—22no—
46C2×C22⋊Dic43—48no—
47C2×C22⋊Dic43D414yescomplemented
48C2×C22⋊Dic43C2314yes—
49C2×C22⋊Dic43C2312yes—
50#13063240—216no—
51C43⋊#95—24no—
52C43⋊#95—28no—
53C25×C43D412yes—
54C25×C43C2311yescharacteristic
55C22×D4×C43—22no—
56C22×D4×C43—22no—
57C22×D4×C43—22no—
58C22×D4×C43—22no—
59C22×D4×C43—24no—
60C22×D4×C43—24no—
61C22×D4×C43—24no—
62C22×D4×C43—24no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43D414yes—
66C22×D4×C43C2314yes—
67C23×C4×C43D412yes—
68C23×C4×C43D411yescharacteristic
69C23×C4×C43D411yescharacteristic
70#123×C43—28no—
71#123×C43—28no—
72#121×C43—24no—
73#121×C43—24no—
74#121×C43—24no—
75#121×C43—24no—
76#120×C43—28no—
77#120×C43—28no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43—22no—
82C2×C22⋊C4×C43—22no—
83C2×C22⋊C4×C43—22no—
84C2×C22⋊C4×C43D412yes—
85C2×C22⋊C4×C43C2312yes—
86C24×C43—22no—
87C24×C43—24no—
88C24×C43—22no—
89C24×C43—24no—
90C24×C43—42no—
91C24×C43—42no—
92C24×C43—44no—
93C24×C43—44no—
94C24×C43C2×D412yes—
95C24×C43C2×D411yescharacteristic
96C24×C43C2×D414yes—
97C24×C43C2×D412yes—
98C24×C43C2×D411yescharacteristic
99C24×C43C2×D412yes—
100C24×C43#4112yes—
101C24×C43#4114yes—
102C24×C43C2411yescharacteristic
103C2×D4×C43—24no—
104C2×D4×C43—24no—
105C2×D4×C43—24no—
106C2×D4×C43—24no—
107C2×D4×C43—28no—
108C2×D4×C43—28no—
109C2×D4×C43—24no—
110C2×D4×C43—24no—
111C2×D4×C43—24no—
112C2×D4×C43—24no—
113C2×D4×C43—24no—
114C2×D4×C43—24no—
115C2×D4×C43—44no—
116C2×D4×C43—44no—
117C2×D4×C43—44no—
118C2×D4×C43—44no—
119C2×D4×C43—44no—
120C2×D4×C43—44no—
121C2×D4×C43—44no—
122C2×D4×C43—44no—
123C2×D4×C43—82no—
124C2×D4×C43—82no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—24no—
132C22×C4×C43—24no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43C2×D414yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×Dic43—28no—
139C22×Dic43—24no—
140C22×Dic43—24no—
141C22×Dic43—24no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—24no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—42no—
148C22×Dic43—44no—
149C22×Dic43—44no—
150C22×Dic43—44no—
151C22×Dic43—44no—
152C22×Dic43—44no—
153C22×Dic43—48no—
154C22×Dic43—42no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43—44no—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—24no—
160C22⋊C4×C43—28no—
161C22⋊C4×C43—28no—
162C22⋊C4×C43—24no—
163C22⋊C4×C43—24no—
164C22⋊Dic43—24no—
165C22⋊Dic43—24no—
166C22⋊Dic43—22no—
167C22⋊Dic43—24no—
168C22⋊Dic43—416no—
169C22⋊Dic43—44no—
170C22⋊Dic43C2×D414yescomplemented
171Dic43⋊C4—48no—
172C23×C43—22no—
173C23×C43—24no—
174C23×C43—22no—
175C23×C43—24no—
176C23×C43—24no—
177C23×C43—24no—
178C23×C43—24no—
179C23×C43—42no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—44no—
183C23×C43—42no—
184C23×C43—41no—
185C23×C43—44no—
186C23×C43—48no—
187C23×C43—41no—
188C23×C43—44no—
189C23×C43—44no—
190C23×C43—416no—
191C23×C43—44no—
192C23×C43—44no—
193C23×C43—44no—
194C23×C43—44no—
195C23×C43—82no—
196C23×C43—82no—
197C23×C43—88no—
198C23×C43#12012yes—
199C23×C43#12011yescharacteristic
200C23×C43#12011yescharacteristic
201C23×C43#12112yes—
202C23×C43#12112yes—
203C23×C43#12114yes—
204C23×C43#12114yes—
205C23×C43#12314yes—
206C23×C43#12314yes—
207C23×C43#12412yes—
208C23×C43#12412yes—
209C23×C43C22×D411yescharacteristic
210C23×C43C22×D412yes—
211C23×C43C22×D411yescharacteristic
212C23×C43C2×#4111yescharacteristic
213C23×C43C2×#4112yes—
214D4×C43—44no—
215D4×C43—44no—
216D4×C43—44no—
217D4×C43—44no—
218D4×C43—48no—
219D4×C43—48no—
220D4×C43—84no—
221D4×C43—84no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—44no—
228C2×C4×C43—44no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—81no—
234C2×C4×C43—81no—
235C2×Dic43—24no—
236C2×Dic43—28no—
237C2×Dic43—24no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—48no—
241C2×Dic43—44no—
242C2×Dic43—48no—
243C2×Dic43—44no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—44no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249C2×Dic43—44no—
250C2×Dic43—88no—
251C2×#2044—431nomaximal, Sylow
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—28no—
261C22×C43—28no—
262C22×C43—24no—
263C22×C43—24no—
264C22×C43—42no—
265C22×C43—44no—
266C22×C43—44no—
267C22×C43—42no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—42no—
271C22×C43—48no—
272C22×C43—44no—
273C22×C43—44no—
274C22×C43—44no—
275C22×C43—84no—
276C22×C43—88no—
277C22×C43—88no—
278C22×C43#39414yes—
279C22×C43#39412yes—
280C22×C43#39412yes—
281C22×C43B(4,𝔽2)12yes—
282C22×C43#45812yes—
283C22×C43C2×#12011yescharacteristic
284C22×C43C2×#12111yescharacteristic
285C22×C43C2×#12112yes—
286C22×C43C2×#12312yes—
287C22×C43C2×#12411yescharacteristic
288C4×C43—44no—
289C4×C43—42no—
290C4×C43—42no—
291Dic43—44no—
292Dic43—44no—
293Dic43—84no—
294C2×#534D4311yescharacteristic
295C22×#99—432no—
296C2×#386—432no—
297C2×#385—431no—
298#2044—438no—
299C2×#342—431no—
300C2×C43—21no—
301C2×C43—22no—
302C2×C43—22no—
303C2×C43—24no—
304C2×C43—21no—
305C2×C43—22no—
306C2×C43—84no—
307C2×C43#204414yescomplemented
308C2×C43C2×#39411yescharacteristic
309C2×C43C2×B(4,𝔽2)11yescharacteristic
310C2×C43C2×#45811yescharacteristic
311C23×D4C2×D4312yes—
312C24×C4—431no—
313#534—24no—
314#534—22no—
315#534C2×D4314yes—
316C2×#123—22no—
317C2×#121—21no—
318C2×#121—21no—
319C2×#120—22no—
320C22×C4⋊C4—861no—
321C22×C22⋊C4—431no—
322C22×C22⋊C4—432no—
323C22×C22⋊C4—862no—
324C22×C22⋊C4C2×D4311yescharacteristic
325C2×#99—438no—
326C2×#99—868no—
327#386—438no—
328#386—864no—
329#385—434no—
330#385—862no—
331C2×#95—861no—
332C2×#95—862no—
333#342—434no—
334C43C2×#204411yescharacteristic, complemented, Sylow
335C25C22⋊D4312yes—
336C25C22×D4311yescharacteristic
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4C22⋊D4314yes—
348C22×D4C22×D4314yes—
349C23×C4—432no—
350C23×C4—861no—
351C23×C4—862no—
352C23×C4—861no—
353C23×C4—862no—
354C23×C4—861no—
355C23×C4—862no—
356C23×C4—1724no—
357C23×C4C22⋊D4312yes—
358C23×C4C22⋊D4311yescharacteristic
359C23×C4C22⋊D4311yescharacteristic
360#123—28no—
361#123—28no—
362#121—24no—
363#121—24no—
364#121—24no—
365#121—24no—
366#120—28no—
367#120—28no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—1724no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—434no—
377C2×C22⋊C4—432no—
378C2×C22⋊C4—434no—
379C2×C22⋊C4—862no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—864no—
382C2×C22⋊C4—864no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—868no—
385C2×C22⋊C4—1728no—
386C2×C22⋊C4C22⋊D4312yes—
387C2×C22⋊C4C22×D4312yes—
388#99—8616no—
389#95—864no—
390#95—868no—
391C24—22no—
392C24—24no—
393C24—22no—
394C24—24no—
395C24—42no—
396C24—42no—
397C24—44no—
398C24—44no—
399C24D4×D4312yes—
400C24#1062190012yes—
401C24#1062190014yes—
402C24C2×C22⋊D4311yescharacteristic
403C24C2×C22⋊D4312yes—
404C24C2×C22⋊D4314yes—
405C24C2×C22⋊D4311yescharacteristic
406C24C2×C22⋊D4312yes—
407C24C23×D4311yescharacteristic
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—82no—
429C2×D4—82no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—868no—
441C22×C4—864no—
442C22×C4—864no—
443C22×C4—862no—
444C22×C4—864no—
445C22×C4—862no—
446C22×C4—864no—
447C22×C4—1724no—
448C22×C4—1728no—
449C22×C4—1724no—
450C22×C4—1724no—
451C22×C4—1724no—
452C22×C4—1724no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4—1724no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4C2×C22⋊D4314yes—
461C22×C4C2×C22⋊D4312yes—
462C22×C4C2×C22⋊D4312yes—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—1728no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—434no—
471C22⋊C4—864no—
472C22⋊C4—862no—
473C22⋊C4—864no—
474C22⋊C4—864no—
475C22⋊C4—17216no—
476C22⋊C4—1724no—
477C23—22no—
478C23—24no—
479C23—22no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—44no—
488C23—48no—
489C23—44no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—44no—
494C23—44no—
495C23—416no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—82no—
501C23—82no—
502C23—88no—
503C23#1306329412yes—
504C23#1306329411yescharacteristic
505C23#1306329411yescharacteristic
506C23#1306329612yes—
507C23#1306329612yes—
508C23#1306329714yes—
509C23#1306329714yes—
510C23#1306330614yes—
511C23#1306330614yes—
512C23#1306331212yes—
513C23#1306331212yes—
514C23C2×D4×D4311yescharacteristic
515C23C22×C22⋊D4311yescharacteristic
516C23C22×C22⋊D4312yes—
517C23C2×#1062190011yescharacteristic
518C23C2×#1062190012yes—
519D4—48no—
520D4—48no—
521D4—44no—
522D4—44no—
523D4—44no—
524D4—44no—
525D4—84no—
526D4—84no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—868no—
541C2×C4—864no—
542C2×C4—864no—
543C2×C4—3448no—
544C2×C4—1724no—
545C2×C4—1724no—
546C2×C4—1724no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1724no—
550C2×C4—1724no—
551C2×C4—1728no—
552C2×C4—1722no—
553C2×C4—1728no—
554C2×C4—1724no—
555C2×C4—1722no—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—22no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—22no—
564C22—28no—
565C22—24no—
566C22—28no—
567C22—24no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—41no—
573C22—42no—
574C22—41no—
575C22—48no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—84no—
580C22—88no—
581C22—88no—
582C22#1458281314yes—
583C22#1458281312yes—
584C22#1458281312yes—
585C22#1458308612yes—
586C22#1458308912yes—
587C22C2×#1306329411yescharacteristic
588C22C2×#1306329611yescharacteristic
589C22C2×#1306329712yes—
590C22C2×#1306330612yes—
591C22C2×#1306331211yescharacteristic
592C4—44no—
593C4—42no—
594C4—42no—
595C4—3444no—
596C4—1724no—
597C4—1724no—
598C2—22no—
599C2—21no—
600C2—22no—
601C2—24no—
602C2—22no—
603C2—21no—
604C2—84no—
605C2#1913584314yesdirect product factor
606C2C2×#1458281311yescharacteristic
607C2C2×#1458308611yescharacteristic
608C2C2×#1458308911yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
Fitting, prime radicalC2×C43×#534C2
socleC23×C43#120
hypercenterC2×#534D43
hypocenterC43C2×#2044
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×#13063240C2semidirect
2. C2×#14582779C2semidirect
3. C2×#14582771C2semidirect
4. #19135843C2direct (N × H)
5. C2×#14582666C2semidirect
13. C2×#13063240C22semidirect
15. #14582779C22semidirect
17. #14582771C22semidirect
20. #14582666C22semidirect
47. C2×C22⋊Dic43D4semidirect
170. C22⋊Dic43C2×D4semidirect
307. C2×C43#2044semidirect
334. C43C2×#2044semidirect
605. C2#19135843direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632402
C2×#145827792
C2×#145827712
#191358432
C2×#145826662
C2×C43×#5342
C2×#204443