Finite Group Databasebeta

← C43×#14327 #24934344

Subgroups — C43×#14327 #24934344

Order 11008.

1346 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#395C211yesmaximal, characteristic
2C2×C43×#391C211yesmaximal, characteristic
3C2×C43×#387C211yesmaximal, characteristic
4C43×#1446C211yesmaximal, characteristic
5C43×#1444C211yesmaximal, characteristic
6C43×#1442C212yesmaximal
7C43×#1441C211yesmaximal, characteristic
8C43×#1441C212yesmaximal
9C43×C4⋊#95C212yesmaximal
10C43×#1434C212yesmaximal
11C4×#95×C43C211yesmaximal, characteristic
12C23×Q8×C43C2211yescharacteristic
13C22×C4⋊C4×C43C2211yescharacteristic
14C22×C4⋊C4×C43C2212yes—
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C4⋊C4×C43C2211yescharacteristic
17C22×C4⋊C4×C43C2212yes—
18C22×C42×C43C2211yescharacteristic
19C22×C42×C43C2212yes—
20C43×#395C418yescomplemented
21C43×#391—24no—
22C43×#387—24no—
23C2×#95×C43C2212yes—
24C2×#95×C43C2211yescharacteristic
25C2×#95×C43C2211yescharacteristic
26C2×#95×C43C2212yes—
27C2×#95×C43C2212yes—
28C2×#95×C43C2211yescharacteristic
29C2×#95×C43C2212yes—
30C2×#95×C43C2211yescharacteristic
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2212yes—
33C2×#95×C43C2212yes—
34C2×#95×C43C2212yes—
35C2×#95×C43C2212yes—
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C22×Q8×C43—22no—
39C22×Q8×C43—22no—
40C22×Q8×C43—42no—
41C22×Q8×C43—42no—
42C22×Q8×C43C2×C414yes—
43C23×C4×C43C2311yescharacteristic
44C23×C4×C43C2312yes—
45C23×C4×C43C2311yescharacteristic
46C23×C4×C43C2311yescharacteristic
47C23×C4×C43C2312yes—
48C23×C4×C43C2311yescharacteristic
49C23×C4×C43C2311yescharacteristic
50C23×C4×C43C2312yes—
51C23×C4×C43C2311yescharacteristic
52C23×C4×C43C2312yes—
53C23×C4×C43C2311yescharacteristic
54C2×C4⋊C4×C43—22no—
55C2×C4⋊C4×C43—22no—
56C2×C4⋊C4×C43—22no—
57C2×C4⋊C4×C43—22no—
58C2×C4⋊C4×C43—24no—
59C2×C4⋊C4×C43—42no—
60C2×C4⋊C4×C43—42no—
61C2×C4⋊C4×C43—42no—
62C2×C4⋊C4×C43—42no—
63C2×C4⋊C4×C43—42no—
64C2×C4⋊C4×C43—42no—
65C2×C4⋊C4×C43C2×C414yes—
66C2×C4⋊C4×C43C2×C418yes—
67C2×C42×C43—42no—
68C2×C42×C43—42no—
69C2×C42×C43—42no—
70C2×C42×C43D414yes—
71C2×C42×C43Q818yescomplemented
72#95×C43—22no—
73#95×C43—22no—
74#95×C43—22no—
75#95×C43—22no—
76#95×C43—24no—
77#95×C43—24no—
78#95×C43—22no—
79#95×C43—24no—
80#95×C43—24no—
81#95×C43—42no—
82#95×C43—42no—
83#95×C43—42no—
84#95×C43—42no—
85#95×C43C2×C418yes—
86#95×C43C2×C414yes—
87C24×C43C2411yescharacteristic
88C2×Q8×C43—28no—
89C2×Q8×C43—48no—
90C2×Q8×C43—44no—
91C2×Q8×C43—44no—
92C2×Q8×C43—48no—
93C22×C4×C43—21no—
94C22×C4×C43—22no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—22no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43C22×C412yes—
146C22×C4×C43C22×C414yes—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C22×C412yes—
149C22×C4×C43C22×C414yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×Q814yes—
154C22×C4×C43C2×Q814yes—
155C22×C4×C43C2×Q814yes—
156C22×C4×C43#4112yes—
157C22×C4×C43#4114yes—
158C4⋊C4×C43—28no—
159C4⋊C4×C43—48no—
160C4⋊C4×C43—44no—
161C4⋊C4×C43—48no—
162C4⋊C4×C43—44no—
163C42×C43—44no—
164C42×C43—48no—
165C23×C43C23×C411yescharacteristic
166C23×C43C22×D411yescharacteristic
167C23×C43C22×Q812yes—
168C23×C43C2×#4111yescharacteristic
169C23×C43C2×#4112yes—
170C23×C43H(5,𝔽2)12yes—
171C23×C43H(5,𝔽2)12yes—
172C23×C43H(5,𝔽2)11yescharacteristic
173C23×C432−1+411yescharacteristic
174C23×C432−1+411yescharacteristic
175C23×C432−1+411yescharacteristic
176Q8×C43—416no—
177C2×C4×C43—24no—
178C2×C4×C43—24no—
179C2×C4×C43—24no—
180C2×C4×C43—22no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—24no—
185C2×C4×C43—24no—
186C2×C4×C43—24no—
187C2×C4×C43—24no—
188C2×C4×C43—24no—
189C2×C4×C43—24no—
190C2×C4×C43—24no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—24no—
194C2×C4×C43—24no—
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—24no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—41no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
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×C43C4×D414yes—
240C2×C4×C43C4×Q818yes—
241C2×C4×C43C4⋊Q814yes—
242#14327C4311yesmaximal, characteristic, direct product factor, Sylow
243C22×C43C2×C4×D411yescharacteristic
244C22×C43C2×C4×Q812yes—
245C22×C43#51812yes—
246C22×C43#51911yescharacteristic
247C22×C43#52011yescharacteristic
248C22×C43C2×C4⋊Q811yescharacteristic
249C22×C43#53211yescharacteristic
250C22×C43#53312yes—
251C22×C43#53411yescharacteristic
252C22×C43#53511yescharacteristic
253C22×C43#53611yescharacteristic
254C22×C43#53711yescharacteristic
255C22×C43#53812yes—
256C22×C43#53812yes—
257C22×C43#53912yes—
258C22×C43#54111yescharacteristic
259C22×C43#54211yescharacteristic
260C22×C43#54212yes—
261C22×C43#54212yes—
262C22×C43#54312yes—
263C22×C43#54412yes—
264C22×C43#54412yes—
265C22×C43#54412yes—
266C4×C43—24no—
267C4×C43—28no—
268C4×C43—24no—
269C4×C43—42no—
270C4×C43—44no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—44no—
274C4×C43—82no—
275C4×C43—81no—
276C4×C43—81no—
277C2×#395C2×C4311yescharacteristic
278C2×#391C2×C4311yescharacteristic
279C2×#387C2×C4311yescharacteristic
280#1446C2×C4311yescharacteristic
281#1444C2×C4311yescharacteristic
282#1442C2×C4312yes—
283#1441C2×C4311yescharacteristic
284#1441C2×C4312yes—
285C4⋊#95C2×C4312yes—
286#1434C2×C4312yes—
287C4×#95C2×C4311yescharacteristic
288C2×C43C4×C4⋊Q811yescharacteristic
289C2×C43#232111yescharacteristic
290C2×C43#232311yescharacteristic
291C2×C43#232912yes—
292C2×C43#233112yes—
293C2×C43#265911yescharacteristic
294C2×C43#266011yescharacteristic
295C2×C43#266211yescharacteristic
296C2×C43#266311yescharacteristic
297C2×C43#266512yes—
298C2×C43#266612yes—
299C23×Q8C22×C4311yescharacteristic
300C22×C4⋊C4C22×C4311yescharacteristic
301C22×C4⋊C4C22×C4312yes—
302C22×C4⋊C4C22×C4311yescharacteristic
303C22×C4⋊C4C22×C4311yescharacteristic
304C22×C4⋊C4C22×C4312yes—
305C22×C42C22×C4311yescharacteristic
306C22×C42C22×C4312yes—
307#395C4×C4318yescomplemented
308#391—24no—
309#387—24no—
310C2×#95C22×C4312yes—
311C2×#95C22×C4311yescharacteristic
312C2×#95C22×C4311yescharacteristic
313C2×#95C22×C4312yes—
314C2×#95C22×C4312yes—
315C2×#95C22×C4311yescharacteristic
316C2×#95C22×C4312yes—
317C2×#95C22×C4311yescharacteristic
318C2×#95C22×C4311yescharacteristic
319C2×#95C22×C4312yes—
320C2×#95C22×C4312yes—
321C2×#95C22×C4312yes—
322C2×#95C22×C4312yes—
323C2×#95C22×C4311yescharacteristic
324C2×#95C22×C4312yes—
325C43#1432711yescharacteristic, direct product factor, Sylow
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—42no—
329C22×Q8—42no—
330C22×Q8C2×C4×C4314yes—
331C23×C4C23×C4311yescharacteristic
332C23×C4C23×C4312yes—
333C23×C4C23×C4311yescharacteristic
334C23×C4C23×C4311yescharacteristic
335C23×C4C23×C4312yes—
336C23×C4C23×C4311yescharacteristic
337C23×C4C23×C4311yescharacteristic
338C23×C4C23×C4312yes—
339C23×C4C23×C4311yescharacteristic
340C23×C4C23×C4312yes—
341C23×C4C23×C4311yescharacteristic
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4C2×C4×C4314yes—
354C2×C4⋊C4C2×C4×C4318yes—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42D4×C4314yes—
359C2×C42Q8×C4318yescomplemented
360#95—22no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—24no—
365#95—24no—
366#95—22no—
367#95—24no—
368#95—24no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95C2×C4×C4318yes—
374#95C2×C4×C4314yes—
375C24C24×C4311yescharacteristic
376C2×Q8—28no—
377C2×Q8—48no—
378C2×Q8—44no—
379C2×Q8—44no—
380C2×Q8—48no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4C22×C4×C4312yes—
434C22×C4C22×C4×C4314yes—
435C22×C4C22×C4×C4312yes—
436C22×C4C22×C4×C4312yes—
437C22×C4C22×C4×C4314yes—
438C22×C4C2×D4×C4312yes—
439C22×C4C2×D4×C4312yes—
440C22×C4C2×D4×C4312yes—
441C22×C4C2×Q8×C4314yes—
442C22×C4C2×Q8×C4314yes—
443C22×C4C2×Q8×C4314yes—
444C22×C4#41×C4312yes—
445C22×C4#41×C4314yes—
446C4⋊C4—28no—
447C4⋊C4—48no—
448C4⋊C4—44no—
449C4⋊C4—48no—
450C4⋊C4—44no—
451C42—44no—
452C42—48no—
453C23C23×C4×C4311yescharacteristic
454C23C22×D4×C4311yescharacteristic
455C23C22×Q8×C4312yes—
456C23C2×#41×C4311yescharacteristic
457C23C2×#41×C4312yes—
458C23H(5,𝔽2)×C4312yes—
459C23H(5,𝔽2)×C4312yes—
460C23H(5,𝔽2)×C4311yescharacteristic
461C232−1+4×C4311yescharacteristic
462C232−1+4×C4311yescharacteristic
463C232−1+4×C4311yescharacteristic
464Q8—416no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4C4×D4×C4314yes—
528C2×C4C4×Q8×C4318yes—
529C2×C4C4⋊Q8×C4314yes—
530C22C2×C4×D4×C4311yescharacteristic
531C22C2×C4×Q8×C4312yes—
532C22C43×#51812yes—
533C22C43×#51911yescharacteristic
534C22C43×#52011yescharacteristic
535C22C2×C4⋊Q8×C4311yescharacteristic
536C22C43×#53211yescharacteristic
537C22C43×#53312yes—
538C22C43×#53411yescharacteristic
539C22C43×#53511yescharacteristic
540C22C43×#53611yescharacteristic
541C22C43×#53711yescharacteristic
542C22C43×#53812yes—
543C22C43×#53812yes—
544C22C43×#53912yes—
545C22C43×#54111yescharacteristic
546C22C43×#54211yescharacteristic
547C22C43×#54212yes—
548C22C43×#54212yes—
549C22C43×#54312yes—
550C22C43×#54412yes—
551C22C43×#54412yes—
552C22C43×#54412yes—
553C4—24no—
554C4—28no—
555C4—24no—
556C4—44no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—44no—
561C4—82no—
562C4—81no—
563C4—81no—
564C2C4×C4⋊Q8×C4311yescharacteristic
565C2C43×#232111yescharacteristic
566C2C43×#232311yescharacteristic
567C2C43×#232912yes—
568C2C43×#233112yes—
569C2C43×#265911yescharacteristic
570C2C43×#266011yescharacteristic
571C2C43×#266211yescharacteristic
572C2C43×#266311yescharacteristic
573C2C43×#266512yes—
574C2C43×#266612yes—
subgroupG/H
center, socle, prime radicalC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
20. C43×#395C4semidirect
71. C2×C42×C43Q8semidirect
242. #14327C43direct (N × H)
307. #395C4×C43semidirect
325. C43#14327direct (N × H)
359. C2×C42Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3952
C2×C43×#3912
C2×C43×#3872
C43×#14462
C43×#14442
C43×#14422
C43×#14412
C43×C4⋊#952
C43×#14342
C4×#95×C432
#1432743