Finite Group Databasebeta

← C2×C43×#1612 #24938136

Subgroups — C2×C43×#1612 #24938136

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#538C211yesmaximal, characteristic
2C2×C43×#483C211yesmaximal, characteristic, complemented
3C2×C43×#480C211yesmaximal, characteristic, complemented
4C2×C43×#397C211yesmaximal, characteristic, complemented
5C43×#1612C218yesmaximal, direct product factor
6C2×C43×#328C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic, complemented
8C2×C43×#323C211yesmaximal, characteristic, complemented
9C43×#538—22no—
10C43×#538—22no—
11C43×#538—22no—
12C43×#538C2214yes—
13C2×#126×C43—21no—
14C2×#124×C43—21no—
15C2×#123×C43—21no—
16C2×C22⋊Q8×C43C2211yescharacteristic
17C2×#121×C43—21no—
18C2×#121×C43C2211yescharacteristic
19C2×#120×C43—21no—
20C2×C4×D4×C43—21no—
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43—21no—
23C22×C22⋊C4×C43C2211yescharacteristic
24C43×#483—22no—
25C43×#483C2214yescomplemented
26C43×#480—22no—
27C43×#480C2214yescomplemented
28C2×#107×C43—21no—
29C2×#106×C43—21no—
30C2×#103×C43—21no—
31C2×#102×C43—21no—
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×C22⋊C8×C43C2211yescharacteristic
34C43×#397—22no—
35C43×#397C2214yescomplemented
36C2×#95×C43—21no—
37C2×#95×C43C2211yescharacteristic
38C43×#328C2214yescomplemented
39C43×#327C2214yescomplemented
40C43×#323C2214yescomplemented
41C25×C43D411yescharacteristic
42C22×Q8×C43D411yescharacteristic
43C22×D4×C43—21no—
44C22×D4×C43—21no—
45C22×D4×C43—21no—
46C22×D4×C43D411yescharacteristic
47C23×C4×C43—21no—
48C23×C4×C43—21no—
49C23×C4×C43—21no—
50C23×C4×C43D411yescharacteristic
51C23×C4×C43C2311yescharacteristic
52C22×C8×C43—21no—
53C22×C8×C43—21no—
54#126×C43—24no—
55#126×C43—24no—
56#124×C43—24no—
57#124×C43—24no—
58#123×C43—24no—
59#123×C43—24no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43D412yes—
63C22⋊Q8×C43C2312yes—
64#121×C43—24no—
65#121×C43—24no—
66#121×C43—21no—
67#121×C43—21no—
68#121×C43D412yes—
69#121×C43C2312yes—
70#120×C43—24no—
71#120×C43—24no—
72C4×D4×C43—24no—
73C4×D4×C43—24no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43D411yescharacteristic
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43C2312yes—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—24no—
94C2×C22⋊C4×C43—44no—
95C2×C22⋊C4×C43D412yes—
96C2×C22⋊C4×C43C2312yes—
97C2×C42×C43—21no—
98#107×C43—24no—
99#106×C43—24no—
100#103×C43—24no—
101#102×C43—24no—
102C22⋊C8×C43—21no—
103C22⋊C8×C43—21no—
104C22⋊C8×C43C2312yes—
105C22⋊C8×C43C2312yes—
106#95×C43—24no—
107#95×C43—21no—
108#95×C43C2312yes—
109C24×C43—21no—
110C24×C43—21no—
111C24×C43—22no—
112C24×C43—21no—
113C24×C43—22no—
114C24×C43—42no—
115C24×C43—42no—
116C24×C43C2×D411yescharacteristic
117C24×C43C2×D412yes—
118C2×Q8×C43—21no—
119C2×Q8×C43—42no—
120C2×Q8×C43C2×D412yes—
121C2×D4×C43—24no—
122C2×D4×C43—24no—
123C2×D4×C43—21no—
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C2×D4×C43—42no—
129C2×D4×C43—82no—
130C2×D4×C43—82no—
131C2×D4×C43C2×D412yes—
132C22×C4×C43—24no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—42no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—41no—
145C22×C4×C43—41no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—82no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43—42no—
160C2×C8×C43—42no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43C2×D412yes—
171C4⋊C4×C43C2×D412yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—48no—
184C42×C43—24no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—48no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—81no—
202C23×C43—81no—
203C23×C43—84no—
204C23×C43#12011yescharacteristic
205C23×C43#12011yescharacteristic
206C23×C43#13512yes—
207C23×C43AGL(1,ℤ/8)12yes—
208C23×C43C22×D411yescharacteristic
209Q8×C43—42no—
210Q8×C43—81no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—44no—
215D4×C43—81no—
216D4×C43—84no—
217D4×C43—84no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—81no—
240C2×C4×C43—84no—
241C2×C4×C43—84no—
242C2×C4×C43—82no—
243C2×C4×C43—82no—
244C2×C4×C43#12011yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C8×C43—42no—
249C8×C43—42no—
250C2×#1612C4311yesmaximal, characteristic, direct product factor, Sylow
251C22×C43—24no—
252C22×C43—24no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—44no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—82no—
265C22×C43—84no—
266C22×C43—84no—
267C22×C43—84no—
268C22×C43#44912yes—
269C22×C43#44912yes—
270C22×C43#45512yes—
271C22×C43#45812yes—
272C22×C43C2×#12011yescharacteristic
273C22×C43C2×#13511yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43—82no—
284C4×C43—82no—
285C2×#538C2×C4311yescharacteristic
286C2×#483C2×C4311yescharacteristic, complemented
287C2×#480C2×C4311yescharacteristic, complemented
288C2×#397C2×C4311yescharacteristic, complemented
289#1612C2×C4318yesdirect product factor
290C2×#328C2×C4311yescharacteristic, complemented
291C2×#327C2×C4311yescharacteristic, complemented
292C2×#323C2×C4311yescharacteristic, complemented
293C2×C43—21no—
294C2×C43—21no—
295C2×C43—22no—
296C2×C43—82no—
297C2×C43—82no—
298C2×C43#161214yesdirect product factor
299C2×C43C2×#44911yescharacteristic
300C2×C43C2×#45511yescharacteristic
301C2×C43C2×#45811yescharacteristic
302#538—22no—
303#538—22no—
304#538—22no—
305#538C22×C4314yes—
306C2×#126—21no—
307C2×#124—21no—
308C2×#123—21no—
309C2×C22⋊Q8C22×C4311yescharacteristic
310C2×#121—21no—
311C2×#121C22×C4311yescharacteristic
312C2×#120—21no—
313C2×C4×D4—21no—
314C22×C4⋊C4C22×C4311yescharacteristic
315C22×C22⋊C4—21no—
316C22×C22⋊C4C22×C4311yescharacteristic
317#483—22no—
318#483C22×C4314yescomplemented
319#480—22no—
320#480C22×C4314yescomplemented
321C2×#107—21no—
322C2×#106—21no—
323C2×#103—21no—
324C2×#102—21no—
325C2×C22⋊C8C22×C4311yescharacteristic
326C2×C22⋊C8C22×C4311yescharacteristic
327#397—22no—
328#397C22×C4314yescomplemented
329C2×#95—21no—
330C2×#95C22×C4311yescharacteristic
331#328C22×C4314yescomplemented
332#327C22×C4314yescomplemented
333#323C22×C4314yescomplemented
334C43C2×#161211yescharacteristic, direct product factor, Sylow
335C25D4×C4311yescharacteristic
336C22×Q8D4×C4311yescharacteristic
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4D4×C4311yescharacteristic
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4D4×C4311yescharacteristic
345C23×C4C23×C4311yescharacteristic
346C22×C8—21no—
347C22×C8—21no—
348#126—24no—
349#126—24no—
350#124—24no—
351#124—24no—
352#123—24no—
353#123—24no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8D4×C4312yes—
357C22⋊Q8C23×C4312yes—
358#121—24no—
359#121—24no—
360#121—21no—
361#121—21no—
362#121D4×C4312yes—
363#121C23×C4312yes—
364#120—24no—
365#120—24no—
366C4×D4—24no—
367C4×D4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C4311yescharacteristic
376C2×C4⋊C4D4×C4311yescharacteristic
377C2×C4⋊C4C23×C4312yes—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4D4×C4312yes—
390C2×C22⋊C4C23×C4312yes—
391C2×C42—21no—
392#107—24no—
393#106—24no—
394#103—24no—
395#102—24no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8C23×C4312yes—
399C22⋊C8C23×C4312yes—
400#95—24no—
401#95—21no—
402#95C23×C4312yes—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—42no—
409C24—42no—
410C24C2×D4×C4311yescharacteristic
411C24C2×D4×C4312yes—
412C2×Q8—21no—
413C2×Q8—42no—
414C2×Q8C2×D4×C4312yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4C2×D4×C4312yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—82no—
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×D4×C4312yes—
447C22×C4C2×D4×C4311yescharacteristic
448C22×C4C2×D4×C4311yescharacteristic
449C22×C4C2×D4×C4311yescharacteristic
450C22×C4C24×C4311yescharacteristic
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—42no—
454C2×C8—42no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C4312yes—
465C4⋊C4C2×D4×C4312yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—48no—
478C42—24no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—48no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23#120×C4311yescharacteristic
499C23#120×C4311yescharacteristic
500C23#135×C4312yes—
501C23AGL(1,ℤ/8)×C4312yes—
502C23C22×D4×C4311yescharacteristic
503Q8—42no—
504Q8—81no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—81no—
510D4—84no—
511D4—84no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—84no—
535C2×C4—84no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4#120×C4311yescharacteristic
539C2×C4#120×C4311yescharacteristic
540C2×C4C22×D4×C4311yescharacteristic
541C2×C4C22×D4×C4311yescharacteristic
542C8—42no—
543C8—42no—
544C22—24no—
545C22—24no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—82no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22C43×#44912yes—
562C22C43×#44912yes—
563C22C43×#45512yes—
564C22C43×#45812yes—
565C22C2×#120×C4311yescharacteristic
566C22C2×#135×C4311yescharacteristic
567C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—82no—
577C4—82no—
578C2—21no—
579C2—21no—
580C2—22no—
581C2—82no—
582C2—82no—
583C2C43×#161214yesdirect product factor
584C2C2×C43×#44911yescharacteristic
585C2C2×C43×#45511yescharacteristic
586C2C2×C43×#45811yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#538C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#483C2semidirect
3. C2×C43×#480C2semidirect
4. C2×C43×#397C2semidirect
5. C43×#1612C2direct (N × H)
6. C2×C43×#328C2semidirect
7. C2×C43×#327C2semidirect
8. C2×C43×#323C2semidirect
25. C43×#483C22semidirect
27. C43×#480C22semidirect
35. C43×#397C22semidirect
38. C43×#328C22semidirect
39. C43×#327C22semidirect
40. C43×#323C22semidirect
250. C2×#1612C43direct (N × H)
286. C2×#483C2×C43semidirect
287. C2×#480C2×C43semidirect
288. C2×#397C2×C43semidirect
289. #1612C2×C43direct (N × H)
290. C2×#328C2×C43semidirect
291. C2×#327C2×C43semidirect
292. C2×#323C2×C43semidirect
298. C2×C43#1612direct (N × H)
318. #483C22×C43semidirect
320. #480C22×C43semidirect
328. #397C22×C43semidirect
331. #328C22×C43semidirect
332. #327C22×C43semidirect
333. #323C22×C43semidirect
334. C43C2×#1612direct (N × H)
583. C2C43×#1612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5382
C2×C43×#4832
C2×C43×#4802
C2×C43×#3972
C43×#16122
C2×C43×#3282
C2×C43×#3272
C2×C43×#3232
C2×#161243