Finite Group Databasebeta

← C43×#10972 #24930989

Subgroups — C43×#10972 #24930989

Order 11008.

1634 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#534C211yesmaximal, characteristic
2C22×#99×C43C211yesmaximal, characteristic, complemented
3C22×#99×C43C212yesmaximal, complemented
4C43×#2308C211yesmaximal, characteristic, complemented
5C2×C43×#342C212yesmaximal, complemented
6C23×D4×C43C2211yescharacteristic
7C23×D4×C43C2211yescharacteristic
8C43×#534—24no—
9C43×#534—24no—
10C2×#123×C43—21no—
11C2×#123×C43C412yescomplemented
12C2×#121×C43—22no—
13C2×#120×C43—21no—
14C2×#120×C43C412yescomplemented
15C22×C22⋊C4×C43C2212yes—
16C22×C22⋊C4×C43C2212yes—
17C22×C22⋊C4×C43C2211yescharacteristic
18C2×#99×C43—22no—
19C2×#99×C43—24no—
20C2×#99×C43—24no—
21C2×#99×C43—24no—
22C2×#99×C43—24no—
23C43×#386—24no—
24C43×#381—21no—
25C43×#379—21no—
26C43×#342—24no—
27C25×C43C2×C411yescharacteristic
28C25×C43D411yescharacteristic
29C25×C43C2311yescharacteristic
30C22×D4×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43—22no—
33C22×D4×C43—22no—
34C22×D4×C43—22no—
35C22×D4×C43—22no—
36C22×D4×C43—22no—
37C22×D4×C43—22no—
38C22×D4×C43—22no—
39C22×D4×C43—22no—
40C22×D4×C43—22no—
41C22×D4×C43—22no—
42C22×D4×C43—22no—
43C22×D4×C43—22no—
44C22×D4×C43C2×C412yes—
45C22×D4×C43D412yes—
46C22×D4×C43D414yes—
47C23×C4×C43—21no—
48C23×C4×C43—22no—
49C23×C4×C43—22no—
50C23×C4×C43C2×C411yescharacteristic
51C23×C4×C43D411yescharacteristic
52#123×C43—28no—
53#123×C43—24no—
54#123×C43—24no—
55#121×C43—216no—
56#120×C43—28no—
57#120×C43—24no—
58#120×C43—24no—
59C2×C4⋊C4×C43—22no—
60C2×C22⋊C4×C43—22no—
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—22no—
63C2×C22⋊C4×C43—22no—
64C2×C22⋊C4×C43—22no—
65C2×C22⋊C4×C43—22no—
66C2×C22⋊C4×C43—22no—
67C2×C22⋊C4×C43—22no—
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43—22no—
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—24no—
75C2×C22⋊C4×C43C2×C412yes—
76C2×C22⋊C4×C43D414yes—
77C2×C22⋊C4×C43D414yescomplemented
78C2×C22⋊C4×C43D414yescomplemented
79#99×C43—216no—
80#99×C43—28no—
81#95×C43—24no—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—22no—
86C24×C43—22no—
87C24×C43—22no—
88C24×C43—22no—
89C24×C43—21no—
90C24×C43—82no—
91C24×C43—82no—
92C24×C43—82no—
93C24×C43C22⋊C412yes—
94C24×C43C22⋊C412yescomplemented
95C24×C43C22×C411yescharacteristic
96C24×C43C2×D411yescharacteristic
97C24×C43C2×D411yescharacteristic
98C24×C43C2×D412yes—
99C24×C43C2×D412yes—
100C24×C43C2×D412yes—
101C24×C43C2×D412yes—
102C24×C43#4112yes—
103C24×C43#4112yes—
104C2×D4×C43—28no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—24no—
108C2×D4×C43—24no—
109C2×D4×C43—22no—
110C2×D4×C43—24no—
111C2×D4×C43—24no—
112C2×D4×C43—24no—
113C2×D4×C43—24no—
114C2×D4×C43—24no—
115C2×D4×C43—24no—
116C2×D4×C43—24no—
117C2×D4×C43—22no—
118C2×D4×C43—24no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C2×D4×C43—42no—
129C2×D4×C43—42no—
130C2×D4×C43—41no—
131C2×D4×C43—41no—
132C2×D4×C43—42no—
133C2×D4×C43—42no—
134C2×D4×C43—42no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43—84no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—24no—
146C22×C4×C43—24no—
147C22×C4×C43—22no—
148C22×C4×C43—24no—
149C22×C4×C43—21no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—82no—
155C22×C4×C43—84no—
156C22×C4×C43—84no—
157C22×C4×C43C22⋊C412yes—
158C22×C4×C43C22⋊C412yescomplemented
159C4⋊C4×C43—28no—
160C22⋊C4×C43—28no—
161C22⋊C4×C43—28no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—84no—
173C22⋊C4×C43C22⋊C414yescomplemented
174C23×C43—22no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—24no—
179C23×C43—42no—
180C23×C43—44no—
181C23×C43—44no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—44no—
185C23×C43—44no—
186C23×C43—44no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—82no—
193C23×C43—84no—
194C23×C43—82no—
195C23×C43—82no—
196C23×C43—82no—
197C23×C43—82no—
198C23×C43—82no—
199C23×C43—82no—
200C23×C43—84no—
201C23×C43—84no—
202C23×C43—84no—
203C23×C43C2×C22⋊C411yescharacteristic
204C23×C43C2×C22⋊C411yescharacteristic
205C23×C43C2×C22⋊C411yescharacteristic
206C23×C43C4×D412yes—
207C23×C43C4×D412yes—
208C23×C43#12011yescharacteristic
209C23×C43#12012yes—
210C23×C43#12012yes—
211C23×C43#12011yescharacteristic
212C23×C43#12012yes—
213C23×C43#12112yes—
214C23×C43#12112yes—
215C23×C43#12112yes—
216C23×C43#12112yes—
217C23×C43#12112yes—
218C23×C43#12112yes—
219C23×C43#12311yescharacteristic
220C23×C43#12311yescharacteristic
221C23×C43#12312yes—
222C23×C43#12412yes—
223C23×C43#12712yes—
224D4×C43—44no—
225D4×C43—44no—
226D4×C43—44no—
227D4×C43—44no—
228D4×C43—44no—
229D4×C43—44no—
230D4×C43—44no—
231D4×C43—44no—
232D4×C43—88no—
233C2×C4×C43—24no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—44no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—48no—
246C2×C4×C43—44no—
247C2×C4×C43—44no—
248C2×C4×C43—84no—
249C2×C4×C43—84no—
250C2×C4×C43—84no—
251C2×C4×C43—84no—
252C2×C4×C43—84no—
253C2×C4×C43—84no—
254#10972C4311yesmaximal, characteristic, direct product factor, Sylow
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—24no—
258C22×C43—22no—
259C22×C43—24no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—41no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—41no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—44no—
277C22×C43—44no—
278C22×C43—44no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—82no—
282C22×C43—84no—
283C22×C43—84no—
284C22×C43—82no—
285C22×C43—84no—
286C22×C43—84no—
287C22×C43—82no—
288C22×C43#37911yescharacteristic
289C22×C43#38611yescharacteristic
290C22×C43#38612yes—
291C22×C43#38611yescharacteristic
292C22×C43#39012yes—
293C22×C43#39212yes—
294C22×C43#39212yes—
295C22×C43#39412yes—
296C22×C43#39412yes—
297C4×C43—44no—
298C4×C43—42no—
299C4×C43—42no—
300C4×C43—84no—
301C4×C43—84no—
302C2×#534C2×C4311yescharacteristic
303C22×#99C2×C4312yescomplemented
304C22×#99C2×C4311yescharacteristic, complemented
305#2308C2×C4311yescharacteristic, complemented
306C2×#342C2×C4312yescomplemented
307C2×C43—21no—
308C2×C43—22no—
309C2×C43—22no—
310C2×C43—21no—
311C2×C43—22no—
312C2×C43—22no—
313C2×C43—22no—
314C2×C43—22no—
315C2×C43—82no—
316C2×C43—82no—
317C2×C43#143811yescharacteristic
318C2×C43#191312yes—
319C23×D4C22×C4311yescharacteristic
320C23×D4C22×C4311yescharacteristic
321#534—24no—
322#534—24no—
323C2×#123—21no—
324C2×#123C4×C4312yescomplemented
325C2×#121—22no—
326C2×#120—21no—
327C2×#120C4×C4312yescomplemented
328C22×C22⋊C4C22×C4312yes—
329C22×C22⋊C4C22×C4312yes—
330C22×C22⋊C4C22×C4311yescharacteristic
331C2×#99—22no—
332C2×#99—24no—
333C2×#99—24no—
334C2×#99—24no—
335C2×#99—24no—
336#386—24no—
337#381—21no—
338#379—21no—
339#342—24no—
340C43#1097211yescharacteristic, direct product factor, Sylow
341C25C2×C4×C4311yescharacteristic
342C25D4×C4311yescharacteristic
343C25C23×C4311yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×C4×C4312yes—
359C22×D4D4×C4312yes—
360C22×D4D4×C4314yes—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4C2×C4×C4311yescharacteristic
365C23×C4D4×C4311yescharacteristic
366#123—28no—
367#123—24no—
368#123—24no—
369#121—216no—
370#120—28no—
371#120—24no—
372#120—24no—
373C2×C4⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×C4×C4312yes—
390C2×C22⋊C4D4×C4314yes—
391C2×C22⋊C4D4×C4314yescomplemented
392C2×C22⋊C4D4×C4314yescomplemented
393#99—216no—
394#99—28no—
395#95—24no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—82no—
405C24—82no—
406C24—82no—
407C24C22⋊C4×C4312yes—
408C24C22⋊C4×C4312yescomplemented
409C24C22×C4×C4311yescharacteristic
410C24C2×D4×C4311yescharacteristic
411C24C2×D4×C4311yescharacteristic
412C24C2×D4×C4312yes—
413C24C2×D4×C4312yes—
414C24C2×D4×C4312yes—
415C24C2×D4×C4312yes—
416C24#41×C4312yes—
417C24#41×C4312yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—84no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—82no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4C22⋊C4×C4312yes—
472C22×C4C22⋊C4×C4312yescomplemented
473C4⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—84no—
487C22⋊C4C22⋊C4×C4314yescomplemented
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—42no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—82no—
507C23—84no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23—82no—
513C23—82no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23C2×C22⋊C4×C4311yescharacteristic
518C23C2×C22⋊C4×C4311yescharacteristic
519C23C2×C22⋊C4×C4311yescharacteristic
520C23C4×D4×C4312yes—
521C23C4×D4×C4312yes—
522C23#120×C4311yescharacteristic
523C23#120×C4312yes—
524C23#120×C4312yes—
525C23#120×C4311yescharacteristic
526C23#120×C4312yes—
527C23#121×C4312yes—
528C23#121×C4312yes—
529C23#121×C4312yes—
530C23#121×C4312yes—
531C23#121×C4312yes—
532C23#121×C4312yes—
533C23#123×C4311yescharacteristic
534C23#123×C4311yescharacteristic
535C23#123×C4312yes—
536C23#124×C4312yes—
537C23#127×C4312yes—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—88no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—84no—
563C2×C4—84no—
564C2×C4—84no—
565C2×C4—84no—
566C2×C4—84no—
567C2×C4—84no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—82no—
595C22—84no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22C43×#37911yescharacteristic
602C22C43×#38611yescharacteristic
603C22C43×#38612yes—
604C22C43×#38611yescharacteristic
605C22C43×#39012yes—
606C22C43×#39212yes—
607C22C43×#39212yes—
608C22C43×#39412yes—
609C22C43×#39412yes—
610C4—44no—
611C4—42no—
612C4—42no—
613C4—84no—
614C4—84no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—22no—
622C2—22no—
623C2—82no—
624C2—82no—
625C2C43×#143811yescharacteristic
626C2C43×#191312yes—
subgroupG/H
center, socleC22×C43#386
commutatorC24C22×C4×C43
Frattini, cosocleC25C23×C43
prime radicalC2×C43×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C25×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C43C2semidirect
3. C22×#99×C43C2semidirect
4. C43×#2308C2semidirect
5. C2×C43×#342C2semidirect
11. C2×#123×C43C4semidirect
14. C2×#120×C43C4semidirect
77. C2×C22⋊C4×C43D4semidirect
78. C2×C22⋊C4×C43D4semidirect
94. C24×C43C22⋊C4semidirect
158. C22×C4×C43C22⋊C4semidirect
173. C22⋊C4×C43C22⋊C4semidirect
254. #10972C43direct (N × H)
303. C22×#99C2×C43semidirect
304. C22×#99C2×C43semidirect
305. #2308C2×C43semidirect
306. C2×#342C2×C43semidirect
324. C2×#123C4×C43semidirect
327. C2×#120C4×C43semidirect
340. C43#10972direct (N × H)
391. C2×C22⋊C4D4×C43semidirect
392. C2×C22⋊C4D4×C43semidirect
408. C24C22⋊C4×C43semidirect
472. C22×C4C22⋊C4×C43semidirect
487. C22⋊C4C22⋊C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5342
C22×#99×C432
C43×#23082
C2×C43×#3422
#1097243