Finite Group Databasebeta

← C43×#29613 #24949630

Subgroups — C43×#29613 #24949630

Order 11008.

1256 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#536C211yesmaximal, characteristic
2C43×#3095C211yesmaximal, characteristic, complemented
3C43×#3007C211yesmaximal, characteristic
4C43×#2434C211yesmaximal, characteristic, complemented
5C43×#2038C214yesmaximal, complemented
6C43×#2005C214yesmaximal, complemented
7C43×#1826C211yesmaximal, characteristic, complemented
8C43×#1789C211yesmaximal, characteristic
9C43×#1784C211yesmaximal, characteristic, complemented
10C22×#41×C43C2211yescharacteristic
11C23×Q8×C43C2211yescharacteristic
12C2×#137×C43C2212yes—
13C43×#536—22no—
14C43×#536—22no—
15C43×#536—22no—
16C43×#536C2214yes—
17C2×C4⋊Q8×C43—21no—
18C2×C4⋊Q8×C43C2212yescomplemented
19C2×#124×C43—21no—
20C2×#123×C43—22no—
21C2×C22⋊Q8×C43—21no—
22C2×C22⋊Q8×C43—21no—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×#117×C43C2211yescharacteristic
25C43×#485—22no—
26C43×#484—21no—
27C43×#483—21no—
28C43×#452—22no—
29C43×#451—21no—
30C43×#450—21no—
31C43×#428C2212yescomplemented
32C2×#104×C43C2214yes—
33C43×#419C2212yescomplemented
34C43×#417C2212yes—
35C2×#101×C43C2214yescomplemented
36C43×#407C2211yescharacteristic
37C43×#407C2211yescharacteristic
38C43×#395—22no—
39C43×#391C2212yescomplemented
40C43×#385—22no—
41C4×C22⋊C4×C43C2211yescharacteristic
42C43×#339C2214yescomplemented
43C2×#41×C43—21no—
44C2×#41×C43—21no—
45C2×#41×C43—44no—
46C2×#41×C43D412yes—
47C2×#41×C43C2312yes—
48C22×Q8×C43—21no—
49C22×Q8×C43—21no—
50C22×Q8×C43—21no—
51C22×Q8×C43—21no—
52C22×Q8×C43—44no—
53C22×Q8×C43D411yescharacteristic
54C22×Q8×C43D412yes—
55C22×Q8×C43C2311yescharacteristic
56C22×Q8×C43C2312yes—
57C22×D4×C43—21no—
58C22×D4×C43D411yescharacteristic
59C23×C4×C43—21no—
60C23×C4×C43D412yes—
61C23×C4×C43C2311yescharacteristic
62#137×C43—44no—
63C2×Q16×C43—22no—
64C2×SD16×C43—22no—
65C2×M16×C43C2312yes—
66C2×M16×C43C2312yes—
67C4⋊Q8×C43—24no—
68C4⋊Q8×C43—24no—
69C4⋊Q8×C43—44no—
70#124×C43—24no—
71#124×C43—24no—
72#123×C43—28no—
73#123×C43—28no—
74C22⋊Q8×C43—24no—
75C22⋊Q8×C43—24no—
76C22⋊Q8×C43—24no—
77C22⋊Q8×C43—24no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82#117×C43—21no—
83#117×C43—21no—
84#117×C43D412yes—
85#117×C43C2312yes—
86C2×C4⋊C4×C43—22no—
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—24no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C4⋊C4×C43D411yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43C2312yes—
100#107×C43—22no—
101#106×C43—22no—
102#104×C43—44no—
103#103×C43—22no—
104#103×C43—22no—
105#103×C43—22no—
106#102×C43—22no—
107#101×C43—44no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43—21no—
110C22⋊C8×C43—21no—
111C22⋊C8×C43—21no—
112#95×C43—21no—
113#95×C43—24no—
114C24×C43—21no—
115C24×C43C2×D411yescharacteristic
116#41×C43—24no—
117#41×C43—24no—
118#41×C43—42no—
119#41×C43—42no—
120#41×C43—44no—
121#41×C43—44no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—21no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—24no—
128C2×Q8×C43—24no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—24no—
132C2×Q8×C43—44no—
133C2×Q8×C43—42no—
134C2×Q8×C43—44no—
135C2×Q8×C43—44no—
136C2×Q8×C43—44no—
137C2×Q8×C43—44no—
138C2×Q8×C43C2×D412yes—
139C2×D4×C43—21no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—44no—
143C2×D4×C43—42no—
144C2×D4×C43C2×D412yes—
145C22×C4×C43—24no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—44no—
157C22×C4×C43—44no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D414yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165Q16×C43—44no—
166SD16×C43—44no—
167M16×C43—24no—
168M16×C43—24no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C4⋊C4×C43—28no—
172C4⋊C4×C43—28no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—48no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43C2×D412yes—
181C4⋊C4×C43C2×D412yes—
182C22⋊C4×C43—24no—
183C22⋊C4×C43—28no—
184C22⋊C4×C43—28no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C42×C43—22no—
190C42×C43—22no—
191C42×C43—24no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—41no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43#12011yescharacteristic
200C23×C43#12011yescharacteristic
201C23×C43C22×D411yescharacteristic
202Q8×C43—22no—
203Q8×C43—22no—
204Q8×C43—44no—
205Q8×C43—44no—
206Q8×C43—42no—
207Q8×C43—44no—
208Q8×C43—44no—
209Q8×C43—42no—
210Q8×C43—42no—
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—42no—
214D4×C43—44no—
215D4×C43—44no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—24no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—44no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—44no—
233C2×C4×C43—44no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—44no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43#12011yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)14yes—
246C8×C43—42no—
247C8×C43—42no—
248#29613C4311yesmaximal, characteristic, direct product factor, Sylow
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—44no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—84no—
261C22×C43#45612yes—
262C22×C43C2×#12011yescharacteristic
263C22×C43#53412yes—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—44no—
267C4×C43—44no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43#53412yes—
274C4×C43#53512yes—
275C2×#536C2×C4311yescharacteristic
276#3095C2×C4311yescharacteristic, complemented
277#3007C2×C4311yescharacteristic
278#2434C2×C4311yescharacteristic, complemented
279#2038C2×C4314yescomplemented
280#2005C2×C4314yescomplemented
281#1826C2×C4311yescharacteristic, complemented
282#1789C2×C4311yescharacteristic
283#1784C2×C4311yescharacteristic, complemented
284C2×C43—22no—
285C2×C43—22no—
286C2×C43—41no—
287C2×C43—82no—
288C2×C43#261311yescharacteristic
289C2×C43C2×#45611yescharacteristic
290C2×C43#302011yescharacteristic
291C22×#41C22×C4311yescharacteristic
292C23×Q8C22×C4311yescharacteristic
293C2×#137C22×C4312yes—
294#536—22no—
295#536—22no—
296#536—22no—
297#536C22×C4314yes—
298C2×C4⋊Q8—21no—
299C2×C4⋊Q8C22×C4312yescomplemented
300C2×#124—21no—
301C2×#123—22no—
302C2×C22⋊Q8—21no—
303C2×C22⋊Q8—21no—
304C2×C22⋊Q8C22×C4311yescharacteristic
305C2×#117C22×C4311yescharacteristic
306#485—22no—
307#484—21no—
308#483—21no—
309#452—22no—
310#451—21no—
311#450—21no—
312#428C22×C4312yescomplemented
313C2×#104C22×C4314yes—
314#419C22×C4312yescomplemented
315#417C22×C4312yes—
316C2×#101C22×C4314yescomplemented
317#407C22×C4311yescharacteristic
318#407C22×C4311yescharacteristic
319#395—22no—
320#391C22×C4312yescomplemented
321#385—22no—
322C4×C22⋊C4C22×C4311yescharacteristic
323#339C22×C4314yescomplemented
324C43#2961311yescharacteristic, direct product factor, Sylow
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—44no—
328C2×#41D4×C4312yes—
329C2×#41C23×C4312yes—
330C22×Q8—21no—
331C22×Q8—21no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8—44no—
335C22×Q8D4×C4311yescharacteristic
336C22×Q8D4×C4312yes—
337C22×Q8C23×C4311yescharacteristic
338C22×Q8C23×C4312yes—
339C22×D4—21no—
340C22×D4D4×C4311yescharacteristic
341C23×C4—21no—
342C23×C4D4×C4312yes—
343C23×C4C23×C4311yescharacteristic
344#137—44no—
345C2×Q16—22no—
346C2×SD16—22no—
347C2×M16C23×C4312yes—
348C2×M16C23×C4312yes—
349C4⋊Q8—24no—
350C4⋊Q8—24no—
351C4⋊Q8—44no—
352#124—24no—
353#124—24no—
354#123—28no—
355#123—28no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364#117—21no—
365#117—21no—
366#117D4×C4312yes—
367#117C23×C4312yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4D4×C4311yescharacteristic
373C2×C4⋊C4D4×C4311yescharacteristic
374C2×C4⋊C4C23×C4311yescharacteristic
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42—21no—
381C2×C42C23×C4312yes—
382#107—22no—
383#106—22no—
384#104—44no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389#101—44no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394#95—21no—
395#95—24no—
396C24—21no—
397C24C2×D4×C4311yescharacteristic
398#41—24no—
399#41—24no—
400#41—42no—
401#41—42no—
402#41—44no—
403#41—44no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—24no—
410C2×Q8—24no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—24no—
414C2×Q8—44no—
415C2×Q8—42no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8C2×D4×C4312yes—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—44no—
426C2×D4C2×D4×C4312yes—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4C2×D4×C4314yes—
441C22×C4C2×D4×C4311yescharacteristic
442C22×C4C2×D4×C4311yescharacteristic
443C22×C4C2×D4×C4311yescharacteristic
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C24×C4311yescharacteristic
447Q16—44no—
448SD16—44no—
449M16—24no—
450M16—24no—
451C2×C8—22no—
452C2×C8—22no—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—48no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C4312yes—
463C4⋊C4C2×D4×C4312yes—
464C22⋊C4—28no—
465C22⋊C4—28no—
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—22no—
472C42—22no—
473C42—24no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23#120×C4311yescharacteristic
482C23#120×C4311yescharacteristic
483C23C22×D4×C4311yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—44no—
487Q8—44no—
488Q8—42no—
489Q8—44no—
490Q8—44no—
491Q8—42no—
492Q8—42no—
493D4—22no—
494D4—22no—
495D4—42no—
496D4—44no—
497D4—44no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4#120×C4311yescharacteristic
524C2×C4#120×C4311yescharacteristic
525C2×C4C22×D4×C4311yescharacteristic
526C2×C4C22×D4×C4311yescharacteristic
527C2×C4H(5,𝔽2)×C4314yes—
528C8—42no—
529C8—42no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—44no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—84no—
542C22C43×#45612yes—
543C22C2×#120×C4311yescharacteristic
544C22C43×#53412yes—
545C4—21no—
546C4—21no—
547C4—44no—
548C4—44no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—81no—
553C4—81no—
554C4C43×#53412yes—
555C4C43×#53512yes—
556C2—22no—
557C2—22no—
558C2—41no—
559C2—82no—
560C2C43×#261311yescharacteristic
561C2C2×C43×#45611yescharacteristic
562C2C43×#302011yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×#41×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3095C2semidirect
4. C43×#2434C2semidirect
5. C43×#2038C2semidirect
6. C43×#2005C2semidirect
7. C43×#1826C2semidirect
9. C43×#1784C2semidirect
18. C2×C4⋊Q8×C43C22semidirect
31. C43×#428C22semidirect
33. C43×#419C22semidirect
35. C2×#101×C43C22semidirect
39. C43×#391C22semidirect
42. C43×#339C22semidirect
248. #29613C43direct (N × H)
276. #3095C2×C43semidirect
278. #2434C2×C43semidirect
279. #2038C2×C43semidirect
280. #2005C2×C43semidirect
281. #1826C2×C43semidirect
283. #1784C2×C43semidirect
299. C2×C4⋊Q8C22×C43semidirect
312. #428C22×C43semidirect
314. #419C22×C43semidirect
316. C2×#101C22×C43semidirect
320. #391C22×C43semidirect
323. #339C22×C43semidirect
324. C43#29613direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5362
C43×#30952
C43×#30072
C43×#24342
C43×#20382
C43×#20052
C43×#18262
C43×#17892
C43×#17842
#2961343