Finite Group Databasebeta

← C43×#9938 #24929955

Subgroups — C43×#9938 #24929955

Order 11008.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3006C211yesmaximal, characteristic, complemented
2C43×#2539C211yesmaximal, characteristic, complemented
3C43×#2404C211yesmaximal, characteristic, complemented
4C43×#1789C211yesmaximal, characteristic, complemented
5C43×#1510C211yesmaximal, characteristic, complemented
6C43×#1462C211yesmaximal, characteristic, complemented
7C43×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C43C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C43—21no—
10C2×#123×C43—21no—
11C2×#121×C43C2211yescharacteristic
12C2×#120×C43—21no—
13C2×#120×C43—21no—
14C22×C22⋊C4×C43C2211yescharacteristic
15C43×#449—22no—
16C43×#448—21no—
17C43×#447—21no—
18C2×#104×C43—22no—
19C43×#417—21no—
20C43×#407C2211yescharacteristic
21C43×#407C2211yescharacteristic
22C43×#399—21no—
23C43×#393—21no—
24C43×#392—21no—
25C43×#392—21no—
26C43×#390—22no—
27C43×#386—21no—
28C43×#386—22no—
29C43×#381C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C43×#327—22no—
32C43×#323—22no—
33C25×C43D411yescharacteristic
34C2×#41×C43—21no—
35C2×#41×C43—21no—
36C2×#41×C43—21no—
37C2×#41×C43—21no—
38C2×#41×C43—44no—
39C22×Q8×C43D411yescharacteristic, complemented
40C22×D4×C43—21no—
41C22×D4×C43—21no—
42C22×D4×C43—22no—
43C22×D4×C43—22no—
44C22×D4×C43D411yescharacteristic, complemented
45C22×D4×C43D411yescharacteristic, complemented
46C23×C4×C43—21no—
47C23×C4×C43D411yescharacteristic
48C23×C4×C43C2311yescharacteristic
49AGL(1,ℤ/8)×C43—44no—
50C2×SD16×C43—22no—
51C2×D8×C43—22no—
52C2×M16×C43—21no—
53C2×M16×C43—21no—
54#123×C43—44no—
55#121×C43—21no—
56#121×C43—21no—
57#121×C43—21no—
58#121×C43—21no—
59#120×C43—44no—
60#120×C43—44no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43D411yescharacteristic, complemented
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—22no—
65C2×C22⋊C4×C43—22no—
66C2×C22⋊C4×C43—22no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—22no—
76C2×C42×C43D412yescomplemented
77#104×C43—44no—
78#103×C43—22no—
79#102×C43—22no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43D412yescomplemented
84#95×C43—22no—
85#95×C43—21no—
86#95×C43—21no—
87#95×C43D412yescomplemented
88C24×C43—21no—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—21no—
92C24×C43—21no—
93C24×C43—42no—
94C24×C43—42no—
95C24×C43—42no—
96C24×C43C2×D411yescharacteristic
97#41×C43—24no—
98#41×C43—24no—
99#41×C43—42no—
100#41×C43—42no—
101#41×C43—42no—
102#41×C43—42no—
103#41×C43—42no—
104#41×C43—42no—
105C2×Q8×C43—21no—
106C2×Q8×C43—21no—
107C2×Q8×C43—42no—
108C2×D4×C43—24no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—42no—
114C2×D4×C43—42no—
115C2×D4×C43—42no—
116C2×D4×C43—44no—
117C2×D4×C43—42no—
118C2×D4×C43—44no—
119C2×D4×C43—44no—
120C2×D4×C43—44no—
121C2×D4×C43—41no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C2×D4×C43—41no—
125C2×D4×C43—42no—
126C2×D4×C43—82no—
127C2×D4×C43—82no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147SD16×C43—44no—
148D8×C43—44no—
149M16×C43—42no—
150M16×C43—42no—
151C2×C8×C43—22no—
152C2×C8×C43—41no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—44no—
156C22⋊C4×C43—24no—
157C22⋊C4×C43—42no—
158C22⋊C4×C43—44no—
159C22⋊C4×C43—44no—
160C22⋊C4×C43—44no—
161C22⋊C4×C43—41no—
162C22⋊C4×C43—41no—
163C22⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—82no—
168C42×C43—42no—
169C23×C43—22no—
170C23×C43—22no—
171C23×C43—22no—
172C23×C43—22no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—41no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—41no—
179C23×C43—42no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—42no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—41no—
192C23×C43—42no—
193C23×C43—81no—
194C23×C43—81no—
195C23×C43—88no—
196C23×C43#12011yescharacteristic
197C23×C43#12011yescharacteristic
198C23×C43#12111yescharacteristic
199Q8×C43—22no—
200Q8×C43—22no—
201Q8×C43—41no—
202Q8×C43—41no—
203D4×C43—22no—
204D4×C43—22no—
205D4×C43—41no—
206D4×C43—41no—
207D4×C43—42no—
208D4×C43—44no—
209D4×C43—44no—
210D4×C43—81no—
211D4×C43—88no—
212D4×C43—82no—
213D4×C43—88no—
214D4×C43—82no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—44no—
224C2×C4×C43—44no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—41no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—81no—
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12711yescharacteristic
243C8×C43—42no—
244C8×C43—81no—
245#9938C4311yesmaximal, characteristic, direct product factor, Sylow
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—44no—
254C22×C43—44no—
255C22×C43—44no—
256C22×C43—44no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—82no—
260C22×C43—82no—
261C22×C43—82no—
262C22×C43—82no—
263C22×C43—82no—
264C22×C43—82no—
265C22×C43—82no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43#39211yescharacteristic
274C22×C43#45312yes—
275C22×C43B(4,𝔽2)12yes—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—44no—
281C4×C43—42no—
282C4×C43—82no—
283C4×C43—81no—
284C4×C43—81no—
285#3006C2×C4311yescharacteristic, complemented
286#2539C2×C4311yescharacteristic, complemented
287#2404C2×C4311yescharacteristic, complemented
288#1789C2×C4311yescharacteristic, complemented
289#1510C2×C4311yescharacteristic, complemented
290#1462C2×C4311yescharacteristic, complemented
291#1284C2×C4311yescharacteristic, complemented
292C2×C43—22no—
293C2×C43—22no—
294C2×C43—41no—
295C2×C43—82no—
296C2×C43—82no—
297C2×C43—161no—
298C2×C43#200211yescharacteristic
299C2×C43#201011yescharacteristic
300C2×C43#202111yescharacteristic
301C22×#41C22×C4311yescharacteristic
302C2×AGL(1,ℤ/8)—21no—
303C2×#123—21no—
304C2×#121C22×C4311yescharacteristic
305C2×#120—21no—
306C2×#120—21no—
307C22×C22⋊C4C22×C4311yescharacteristic
308#449—22no—
309#448—21no—
310#447—21no—
311C2×#104—22no—
312#417—21no—
313#407C22×C4311yescharacteristic
314#407C22×C4311yescharacteristic
315#399—21no—
316#393—21no—
317#392—21no—
318#392—21no—
319#390—22no—
320#386—21no—
321#386—22no—
322#381C22×C4311yescharacteristic
323C4×C22⋊C4C22×C4311yescharacteristic
324#327—22no—
325#323—22no—
326C43#993811yescharacteristic, direct product factor, Sylow
327C25D4×C4311yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C4311yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C4311yescharacteristic, complemented
339C22×D4D4×C4311yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C4311yescharacteristic
342C23×C4C23×C4311yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C4311yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C4312yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C4312yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C4312yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C4311yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C4311yescharacteristic
436C22×C4C2×D4×C4311yescharacteristic
437C22×C4C2×D4×C4311yescharacteristic
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C2×D4×C4311yescharacteristic
440C22×C4#41×C4311yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C4311yescharacteristic
491C23#120×C4311yescharacteristic
492C23#121×C4311yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4#120×C4311yescharacteristic
534C2×C4#121×C4311yescharacteristic
535C2×C4#121×C4311yescharacteristic
536C2×C4#127×C4311yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C43×#39211yescharacteristic
567C22C43×#45312yes—
568C22C43×B(4,𝔽2)12yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C43×#200211yescharacteristic
585C2C43×#201011yescharacteristic
586C2C43×#202111yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC23×C4C23×C43
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3006C2semidirect
2. C43×#2539C2semidirect
3. C43×#2404C2semidirect
4. C43×#1789C2semidirect
5. C43×#1510C2semidirect
6. C43×#1462C2semidirect
7. C43×#1284C2semidirect
39. C22×Q8×C43D4semidirect
44. C22×D4×C43D4semidirect
45. C22×D4×C43D4semidirect
62. C2×C4⋊C4×C43D4semidirect
76. C2×C42×C43D4semidirect
83. C22⋊C8×C43D4semidirect
87. #95×C43D4semidirect
245. #9938C43direct (N × H)
285. #3006C2×C43semidirect
286. #2539C2×C43semidirect
287. #2404C2×C43semidirect
288. #1789C2×C43semidirect
289. #1510C2×C43semidirect
290. #1462C2×C43semidirect
291. #1284C2×C43semidirect
326. C43#9938direct (N × H)
333. C22×Q8D4×C43semidirect
338. C22×D4D4×C43semidirect
339. C22×D4D4×C43semidirect
356. C2×C4⋊C4D4×C43semidirect
370. C2×C42D4×C43semidirect
377. C22⋊C8D4×C43semidirect
381. #95D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#30062
C43×#25392
C43×#24042
C43×#17892
C43×#15102
C43×#14622
C43×#12842
#993843