Finite Group Databasebeta

← C43×#22122 #24942139

Subgroups — C43×#22122 #24942139

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#478C211yesmaximal, characteristic
2C43×#2330C211yesmaximal, characteristic, complemented
3C43×#2319C211yesmaximal, characteristic
4C43×#1989C211yesmaximal, characteristic, complemented
5C43×#1948C211yesmaximal, characteristic, complemented
6C43×#1943C211yesmaximal, characteristic, complemented
7C43×#1941C211yesmaximal, characteristic, complemented
8C43×#1936C211yesmaximal, characteristic
9C43×#1934C211yesmaximal, characteristic
10C43×#1926C211yesmaximal, characteristic
11C43×#1926C211yesmaximal, characteristic
12C43×#1920C211yesmaximal, characteristic, complemented
13C43×#1918C211yesmaximal, characteristic, complemented
14C43×#1802C211yesmaximal, characteristic
15C43×#1768C211yesmaximal, characteristic, complemented
16C2×#125×C43C2211yescharacteristic
17C2×C4×D4×C43C2211yescharacteristic
18C43×#478C418yescomplemented
19C2×#107×C43C2211yescharacteristic
20C2×#106×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×#390C2211yescharacteristic
32C43×#390C2211yescharacteristic
33C43×#389—21no—
34C43×#389—21no—
35C43×#389C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#388—21no—
40C43×#388—21no—
41C43×#387—21no—
42C43×#387—21no—
43C43×#384C2211yescharacteristic
44C43×#381—21no—
45C43×#380—21no—
46C4×C4⋊C4×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C43×#376C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D4×C43C2311yescharacteristic
61C23×C4×C43—21no—
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66#125×C43—22no—
67#125×C43C2×C414yes—
68C4×D4×C43—22no—
69C4×D4×C43C2×C414yes—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
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×C42×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43C2311yescharacteristic
94C2×C42×C43C2311yescharacteristic
95C2×C42×C43C2311yescharacteristic
96#107×C43C2×C414yes—
97#106×C43—41no—
98#106×C43—41no—
99#106×C43C2×C414yes—
100C4⋊C8×C43—22no—
101C4⋊C8×C43C2×C414yes—
102#102×C43—41no—
103#102×C43—41no—
104#102×C43C2×C414yes—
105#102×C43C2×C414yes—
106#97×C43—41no—
107C4×C8×C43—41no—
108#95×C43—21no—
109#95×C43—21no—
110#95×C43—21no—
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43D411yescharacteristic
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C24×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43C22×C412yes—
126C22×C4×C43—24no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—81no—
135C22×C4×C43—81no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43C22×C412yes—
154C2×C8×C43C22×C412yes—
155C4⋊C4×C43—24no—
156C4⋊C4×C43—24no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—81no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43C22×C412yes—
175C4⋊C4×C43C22×C412yes—
176C4⋊C4×C43C22×C412yes—
177C22⋊C4×C43—24no—
178C22⋊C4×C43—81no—
179C22⋊C4×C43—81no—
180C22⋊C4×C43—81no—
181C22⋊C4×C43—81no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—81no—
187C42×C43—81no—
188C42×C43—81no—
189C42×C43C22×C412yes—
190C42×C43#4112yes—
191C23×C43—22no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43C22×D411yescharacteristic
199D4×C43—22no—
200D4×C43—22no—
201D4×C43—41no—
202D4×C43—41no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—84no—
241C2×C4×C43C4×D412yes—
242C2×C4×C43C4×D412yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C8×C43—22no—
250C8×C43—22no—
251C8×C43—41no—
252C8×C43—41no—
253#22122C4311yesmaximal, characteristic, direct product factor, Sylow
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43C2×C4×D411yescharacteristic
262C22×C43#53611yescharacteristic
263C22×C43#53711yescharacteristic
264C22×C43#57611yescharacteristic
265C22×C43#57711yescharacteristic
266C22×C43#57711yescharacteristic
267C22×C43#57711yescharacteristic
268C4×C43—22no—
269C4×C43—22no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#51911yescharacteristic
282C4×C43#52011yescharacteristic
283C4×C43#54111yescharacteristic
284C4×C43#54211yescharacteristic
285C2×#478C2×C4311yescharacteristic
286#2330C2×C4311yescharacteristic, complemented
287#2319C2×C4311yescharacteristic
288#1989C2×C4311yescharacteristic, complemented
289#1948C2×C4311yescharacteristic, complemented
290#1943C2×C4311yescharacteristic, complemented
291#1941C2×C4311yescharacteristic, complemented
292#1936C2×C4311yescharacteristic
293#1934C2×C4311yescharacteristic
294#1926C2×C4311yescharacteristic
295#1926C2×C4311yescharacteristic
296#1920C2×C4311yescharacteristic, complemented
297#1918C2×C4311yescharacteristic, complemented
298#1802C2×C4311yescharacteristic
299#1768C2×C4311yescharacteristic, complemented
300C2×C43—82no—
301C2×C43#232311yescharacteristic
302C2×C43#294611yescharacteristic
303C2×C43#295211yescharacteristic
304C2×C43#324111yescharacteristic
305C2×C43#324411yescharacteristic
306C2×C43#325711yescharacteristic
307C2×C43#326011yescharacteristic
308C2×#125C22×C4311yescharacteristic
309C2×C4×D4C22×C4311yescharacteristic
310#478C4×C4318yescomplemented
311C2×#107C22×C4311yescharacteristic
312C2×#106C22×C4311yescharacteristic
313C2×#106C22×C4311yescharacteristic
314C2×#106C22×C4311yescharacteristic
315C2×C4⋊C8C22×C4311yescharacteristic
316C2×C4⋊C8C22×C4311yescharacteristic
317C2×#102C22×C4311yescharacteristic
318C2×#102C22×C4311yescharacteristic
319C2×#102C22×C4311yescharacteristic
320C2×#102C22×C4311yescharacteristic
321C2×#97C22×C4311yescharacteristic
322C2×C4×C8C22×C4311yescharacteristic
323#390C22×C4311yescharacteristic
324#390C22×C4311yescharacteristic
325#389—21no—
326#389—21no—
327#389C22×C4311yescharacteristic
328#389C22×C4311yescharacteristic
329#389C22×C4311yescharacteristic
330#389C22×C4311yescharacteristic
331#388—21no—
332#388—21no—
333#387—21no—
334#387—21no—
335#384C22×C4311yescharacteristic
336#381—21no—
337#380—21no—
338C4×C4⋊C4C22×C4311yescharacteristic
339C4×C4⋊C4C22×C4311yescharacteristic
340C4×C4⋊C4C22×C4311yescharacteristic
341#376C22×C4311yescharacteristic
342#340C22×C4311yescharacteristic
343#340C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#340C22×C4311yescharacteristic
347#340C22×C4311yescharacteristic
348#340C22×C4311yescharacteristic
349#340C22×C4311yescharacteristic
350#336C22×C4311yescharacteristic
351#336C22×C4311yescharacteristic
352C43#2212211yescharacteristic, direct product factor, Sylow
353C22×D4C23×C4311yescharacteristic
354C23×C4—21no—
355C22×C8C23×C4311yescharacteristic
356C22×C8C23×C4311yescharacteristic
357C22×C8C23×C4311yescharacteristic
358C22×C8C23×C4311yescharacteristic
359#125—22no—
360#125C2×C4×C4314yes—
361C4×D4—22no—
362C4×D4C2×C4×C4314yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C23×C4311yescharacteristic
372C2×C4⋊C4C23×C4311yescharacteristic
373C2×C4⋊C4C23×C4311yescharacteristic
374C2×C4⋊C4C23×C4311yescharacteristic
375C2×C4⋊C4C23×C4311yescharacteristic
376C2×C4⋊C4C23×C4311yescharacteristic
377C2×C4⋊C4C23×C4311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C23×C4311yescharacteristic
387C2×C42C23×C4311yescharacteristic
388C2×C42C23×C4311yescharacteristic
389#107C2×C4×C4314yes—
390#106—41no—
391#106—41no—
392#106C2×C4×C4314yes—
393C4⋊C8—22no—
394C4⋊C8C2×C4×C4314yes—
395#102—41no—
396#102—41no—
397#102C2×C4×C4314yes—
398#102C2×C4×C4314yes—
399#97—41no—
400C4×C8—41no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95D4×C4311yescharacteristic
409#95D4×C4311yescharacteristic
410#95D4×C4311yescharacteristic
411#95D4×C4311yescharacteristic
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C22×C4×C4312yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4C2×D4×C4311yescharacteristic
430C22×C4C2×D4×C4311yescharacteristic
431C22×C4C2×D4×C4311yescharacteristic
432C22×C4C2×D4×C4311yescharacteristic
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×D4×C4311yescharacteristic
435C22×C4C24×C4311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8C22×C4×C4312yes—
447C2×C8C22×C4×C4312yes—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4C22×C4×C4312yes—
468C4⋊C4C22×C4×C4312yes—
469C4⋊C4C22×C4×C4312yes—
470C22⋊C4—24no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—81no—
481C42—81no—
482C42C22×C4×C4312yes—
483C42#41×C4312yes—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×D4×C4311yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4C4×D4×C4312yes—
535C2×C4C4×D4×C4312yes—
536C2×C4C23×C4×C4311yescharacteristic
537C2×C4C2×#41×C4311yescharacteristic
538C2×C4H(5,𝔽2)×C4311yescharacteristic
539C2×C42−1+4×C4311yescharacteristic
540C2×C42−1+4×C4311yescharacteristic
541C2×C42−1+4×C4311yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×C4×D4×C4311yescharacteristic
554C22C43×#53611yescharacteristic
555C22C43×#53711yescharacteristic
556C22C43×#57611yescharacteristic
557C22C43×#57711yescharacteristic
558C22C43×#57711yescharacteristic
559C22C43×#57711yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4C43×#51911yescharacteristic
574C4C43×#52011yescharacteristic
575C4C43×#54111yescharacteristic
576C4C43×#54211yescharacteristic
577C2—82no—
578C2C43×#232311yescharacteristic
579C2C43×#294611yescharacteristic
580C2C43×#295211yescharacteristic
581C2C43×#324111yescharacteristic
582C2C43×#324411yescharacteristic
583C2C43×#325711yescharacteristic
584C2C43×#326011yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2330C2semidirect
4. C43×#1989C2semidirect
5. C43×#1948C2semidirect
6. C43×#1943C2semidirect
7. C43×#1941C2semidirect
12. C43×#1920C2semidirect
13. C43×#1918C2semidirect
15. C43×#1768C2semidirect
18. C43×#478C4semidirect
253. #22122C43direct (N × H)
286. #2330C2×C43semidirect
288. #1989C2×C43semidirect
289. #1948C2×C43semidirect
290. #1943C2×C43semidirect
291. #1941C2×C43semidirect
296. #1920C2×C43semidirect
297. #1918C2×C43semidirect
299. #1768C2×C43semidirect
310. #478C4×C43semidirect
352. C43#22122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4782
C43×#23302
C43×#23192
C43×#19892
C43×#19482
C43×#19432
C43×#19412
C43×#19362
C43×#19342
C43×#19262
C43×#19202
C43×#19182
C43×#18022
C43×#17682
#2212243