Finite Group Databasebeta

← C43×#26375 #24946392

Subgroups — C43×#26375 #24946392

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#479C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C43C211yesmaximal, characteristic
3C43×#2454C211yesmaximal, characteristic
4C43×#2351C211yesmaximal, characteristic, complemented
5C43×#2092C211yesmaximal, characteristic
6C43×#2085C211yesmaximal, characteristic, complemented
7C43×#2065C211yesmaximal, characteristic
8C43×#2059C211yesmaximal, characteristic, complemented
9C43×#1941C211yesmaximal, characteristic, complemented
10C43×#1916C211yesmaximal, characteristic, complemented
11C43×#1880C211yesmaximal, characteristic
12C43×#1880C211yesmaximal, characteristic
13C43×#1865C211yesmaximal, characteristic, complemented
14C43×#1863C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic
16C22×SD16×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×C4×Q8×C43C2211yescharacteristic
19C2×C4×Q8×C43C2211yescharacteristic
20C2×C4×Q8×C43C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C43×#479—24no—
23C4×SD16×C43—24no—
24C2×#107×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C2×#106×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×C4×C8×C43C2211yescharacteristic
37C43×#399—21no—
38C43×#396—21no—
39C43×#390C2211yescharacteristic
40C43×#390C2211yescharacteristic
41C43×#389—21no—
42C43×#389—21no—
43C43×#389C2211yescharacteristic
44C43×#389C2211yescharacteristic
45C43×#389C2211yescharacteristic
46C43×#389C2211yescharacteristic
47C43×#385—21no—
48C43×#382—21no—
49C43×#382C2211yescharacteristic
50C43×#380—21no—
51C4×C4⋊C4×C43—21no—
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C22×D4×C43C2311yescharacteristic
63C23×C4×C43—21no—
64C2×SD16×C43—22no—
65C2×SD16×C43—22no—
66C2×SD16×C43Q814yes—
67C22×C8×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71#125×C43—22no—
72#125×C43—41no—
73C4×Q8×C43—22no—
74C4×Q8×C43—22no—
75C4×Q8×C43—22no—
76C4×Q8×C43—22no—
77C4×Q8×C43—41no—
78C4×Q8×C43—41no—
79C4×D4×C43—22no—
80C4×D4×C43—41no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C4⋊C4×C43D411yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C42×C43—21no—
104C2×C42×C43—21no—
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109#107×C43—22no—
110#107×C43—41no—
111#106×C43—22no—
112#106×C43—22no—
113#106×C43—22no—
114C4⋊C8×C43—22no—
115#103×C43—22no—
116#103×C43—22no—
117#103×C43D414yes—
118#102×C43—22no—
119#102×C43—22no—
120#102×C43—41no—
121C4×C8×C43—22no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43D411yescharacteristic
129#95×C43D411yescharacteristic
130C24×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43C2×D412yes—
135C2×Q8×C43C2×Q812yes—
136C2×Q8×C43#4112yes—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43C2×Q812yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—81no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160SD16×C43—28no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D412yes—
172C2×C8×C43C2×Q812yes—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—42no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—81no—
193C4⋊C4×C43—81no—
194C4⋊C4×C43C2×D412yes—
195C4⋊C4×C43#4112yes—
196C22⋊C4×C43—42no—
197C22⋊C4×C43—42no—
198C22⋊C4×C43—81no—
199C22⋊C4×C43—81no—
200C22⋊C4×C43—81no—
201C42×C43—24no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—42no—
209C42×C43—42no—
210C23×C43—22no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43C22⋊Q814yes—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—84no—
265C2×C4×C43#13512yes—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×Q811yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43H(5,𝔽2)11yescharacteristic
271C2×C4×C432−1+411yescharacteristic
272C8×C43—22no—
273C8×C43—22no—
274C8×C43—41no—
275C8×C43—41no—
276#26375C4311yesmaximal, characteristic, direct product factor, Sylow
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43#52511yescharacteristic
285C22×C43D4211yescharacteristic
286C22×C43D4×Q811yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43#57511yescharacteristic
289C22×C43#57711yescharacteristic
290C22×C43#57711yescharacteristic
291C4×C43—24no—
292C4×C43—22no—
293C4×C43—41no—
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—42no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43C2×C22⋊Q811yescharacteristic
305C4×C43#53911yescharacteristic
306C4×C43#54711yescharacteristic
307C4×C43#55411yescharacteristic
308C2×#479C2×C4311yescharacteristic, complemented
309C2×C4×SD16C2×C4311yescharacteristic
310#2454C2×C4311yescharacteristic
311#2351C2×C4311yescharacteristic, complemented
312#2092C2×C4311yescharacteristic
313#2085C2×C4311yescharacteristic, complemented
314#2065C2×C4311yescharacteristic
315#2059C2×C4311yescharacteristic, complemented
316#1941C2×C4311yescharacteristic, complemented
317#1916C2×C4311yescharacteristic, complemented
318#1880C2×C4311yescharacteristic
319#1880C2×C4311yescharacteristic
320#1865C2×C4311yescharacteristic, complemented
321#1863C2×C4311yescharacteristic, complemented
322#1862C2×C4311yescharacteristic
323C2×C43—82no—
324C2×C43#244911yescharacteristic
325C2×C43#310211yescharacteristic
326C2×C43#312611yescharacteristic
327C2×C43#327111yescharacteristic
328C2×C43#328211yescharacteristic
329C2×C43#338111yescharacteristic
330C2×C43#338811yescharacteristic
331C22×SD16C22×C4311yescharacteristic
332C2×#125C22×C4311yescharacteristic
333C2×C4×Q8C22×C4311yescharacteristic
334C2×C4×Q8C22×C4311yescharacteristic
335C2×C4×Q8C22×C4311yescharacteristic
336C2×C4×D4C22×C4311yescharacteristic
337#479—24no—
338C4×SD16—24no—
339C2×#107C22×C4311yescharacteristic
340C2×#107C22×C4311yescharacteristic
341C2×#106C22×C4311yescharacteristic
342C2×#106C22×C4311yescharacteristic
343C2×#106C22×C4311yescharacteristic
344C2×C4⋊C8C22×C4311yescharacteristic
345C2×#103C22×C4311yescharacteristic
346C2×#103C22×C4311yescharacteristic
347C2×#103C22×C4311yescharacteristic
348C2×#102C22×C4311yescharacteristic
349C2×#102C22×C4311yescharacteristic
350C2×#102C22×C4311yescharacteristic
351C2×C4×C8C22×C4311yescharacteristic
352#399—21no—
353#396—21no—
354#390C22×C4311yescharacteristic
355#390C22×C4311yescharacteristic
356#389—21no—
357#389—21no—
358#389C22×C4311yescharacteristic
359#389C22×C4311yescharacteristic
360#389C22×C4311yescharacteristic
361#389C22×C4311yescharacteristic
362#385—21no—
363#382—21no—
364#382C22×C4311yescharacteristic
365#380—21no—
366C4×C4⋊C4—21no—
367C4×C4⋊C4C22×C4311yescharacteristic
368#340C22×C4311yescharacteristic
369#340C22×C4311yescharacteristic
370#340C22×C4311yescharacteristic
371#340C22×C4311yescharacteristic
372#336C22×C4311yescharacteristic
373#336C22×C4311yescharacteristic
374#336C22×C4311yescharacteristic
375#336C22×C4311yescharacteristic
376C43#2637511yescharacteristic, direct product factor, Sylow
377C22×Q8C23×C4311yescharacteristic
378C22×D4C23×C4311yescharacteristic
379C23×C4—21no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16Q8×C4314yes—
383C22×C8C23×C4311yescharacteristic
384C22×C8C23×C4311yescharacteristic
385C22×C8C23×C4311yescharacteristic
386C22×C8C23×C4311yescharacteristic
387#125—22no—
388#125—41no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—41no—
394C4×Q8—41no—
395C4×D4—22no—
396C4×D4—41no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4D4×C4311yescharacteristic
407C2×C4⋊C4D4×C4311yescharacteristic
408C2×C4⋊C4C23×C4311yescharacteristic
409C2×C4⋊C4C23×C4311yescharacteristic
410C2×C4⋊C4C23×C4311yescharacteristic
411C2×C4⋊C4C23×C4311yescharacteristic
412C2×C4⋊C4C23×C4311yescharacteristic
413C2×C4⋊C4C23×C4311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42C23×C4311yescharacteristic
423C2×C42C23×C4311yescharacteristic
424C2×C42C23×C4311yescharacteristic
425#107—22no—
426#107—41no—
427#106—22no—
428#106—22no—
429#106—22no—
430C4⋊C8—22no—
431#103—22no—
432#103—22no—
433#103D4×C4314yes—
434#102—22no—
435#102—22no—
436#102—41no—
437C4×C8—22no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95D4×C4311yescharacteristic
445#95D4×C4311yescharacteristic
446C24—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C4312yes—
451C2×Q8C2×Q8×C4312yes—
452C2×Q8#41×C4312yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×Q8×C4312yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4C2×D4×C4311yescharacteristic
470C22×C4C2×D4×C4311yescharacteristic
471C22×C4C2×D4×C4311yescharacteristic
472C22×C4C2×D4×C4311yescharacteristic
473C22×C4C2×D4×C4311yescharacteristic
474C22×C4C2×D4×C4311yescharacteristic
475C22×C4C24×C4311yescharacteristic
476SD16—28no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8C2×D4×C4312yes—
488C2×C8C2×Q8×C4312yes—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—81no—
509C4⋊C4—81no—
510C4⋊C4C2×D4×C4312yes—
511C4⋊C4#41×C4312yes—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C22⋊C4—81no—
517C42—24no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—42no—
525C42—42no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23C22×D4×C4311yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8C22⋊Q8×C4314yes—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4#135×C4312yes—
582C2×C4C22×D4×C4311yescharacteristic
583C2×C4C22×Q8×C4311yescharacteristic
584C2×C4C2×#41×C4311yescharacteristic
585C2×C4C2×#41×C4311yescharacteristic
586C2×C4H(5,𝔽2)×C4311yescharacteristic
587C2×C42−1+4×C4311yescharacteristic
588C8—22no—
589C8—22no—
590C8—41no—
591C8—41no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22C43×#52511yescharacteristic
600C22D42×C4311yescharacteristic
601C22D4×Q8×C4311yescharacteristic
602C22C2×#135×C4311yescharacteristic
603C22C43×#57511yescharacteristic
604C22C43×#57711yescharacteristic
605C22C43×#57711yescharacteristic
606C4—24no—
607C4—22no—
608C4—41no—
609C4—42no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4C2×C22⋊Q8×C4311yescharacteristic
620C4C43×#53911yescharacteristic
621C4C43×#54711yescharacteristic
622C4C43×#55411yescharacteristic
623C2—82no—
624C2C43×#244911yescharacteristic
625C2C43×#310211yescharacteristic
626C2C43×#312611yescharacteristic
627C2C43×#327111yescharacteristic
628C2C43×#328211yescharacteristic
629C2C43×#338111yescharacteristic
630C2C43×#338811yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#479C2semidirect
4. C43×#2351C2semidirect
6. C43×#2085C2semidirect
8. C43×#2059C2semidirect
9. C43×#1941C2semidirect
10. C43×#1916C2semidirect
13. C43×#1865C2semidirect
14. C43×#1863C2semidirect
276. #26375C43direct (N × H)
308. C2×#479C2×C43semidirect
311. #2351C2×C43semidirect
313. #2085C2×C43semidirect
315. #2059C2×C43semidirect
316. #1941C2×C43semidirect
317. #1916C2×C43semidirect
320. #1865C2×C43semidirect
321. #1863C2×C43semidirect
376. C43#26375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4792
C2×C4×SD16×C432
C43×#24542
C43×#23512
C43×#20922
C43×#20852
C43×#20652
C43×#20592
C43×#19412
C43×#19162
C43×#18802
C43×#18652
C43×#18632
C43×#18622
#2637543