Finite Group Databasebeta

← C43×#29991 #24950008

Subgroups — C43×#29991 #24950008

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2660C211yesmaximal, characteristic, complemented
2C43×#2319C211yesmaximal, characteristic
3C43×#2101C211yesmaximal, characteristic, complemented
4C43×#2100C211yesmaximal, characteristic, complemented
5C43×#2093C211yesmaximal, characteristic
6C43×#2092C211yesmaximal, characteristic
7C43×#2059C211yesmaximal, characteristic, complemented
8C43×#2057C211yesmaximal, characteristic, complemented
9C43×#2025C211yesmaximal, characteristic
10C43×#2023C211yesmaximal, characteristic
11C43×#1949C211yesmaximal, characteristic, complemented
12C43×#1947C211yesmaximal, characteristic, complemented
13C43×#1832C211yesmaximal, characteristic, complemented
14C43×#1804C211yesmaximal, characteristic
15C43×#1802C211yesmaximal, characteristic
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C43×#398—21no—
30C43×#398—21no—
31C43×#395—21no—
32C43×#395—21no—
33C43×#390C2211yescharacteristic
34C43×#390C2211yescharacteristic
35C43×#389C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#388—21no—
38C43×#388—21no—
39C43×#384C2211yescharacteristic
40C43×#384C2211yescharacteristic
41C43×#382C2211yescharacteristic
42C43×#382C2211yescharacteristic
43C43×#381—21no—
44C43×#380—21no—
45C4×C4⋊C4×C43C2211yescharacteristic
46C43×#376C2211yescharacteristic
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C22×D4×C43C2311yescharacteristic
61C23×C4×C43—21no—
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C4⋊Q8×C43—41no—
67C4⋊Q8×C43—41no—
68#125×C43—41no—
69#125×C43—41no—
70C4×D4×C43—22no—
71C4×D4×C43Q814yescomplemented
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×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43C2311yescharacteristic
95C2×C42×C43C2311yescharacteristic
96C2×C42×C43C2311yescharacteristic
97#107×C43—41no—
98#107×C43—41no—
99#107×C43—41no—
100#106×C43—41no—
101C4⋊C8×C43—22no—
102C4⋊C8×C43—22no—
103#102×C43—41no—
104#102×C43—41no—
105#102×C43—41no—
106#102×C43—41no—
107#95×C43—21no—
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×C43D411yescharacteristic
115#95×C43D411yescharacteristic
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118C24×C43—21no—
119C2×Q8×C43—42no—
120C2×Q8×C43—81no—
121C2×Q8×C43—81no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43C2×Q812yes—
128C22×C4×C43—24no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—81no—
137C22×C4×C43—81no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
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×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
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—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43—81no—
175C4⋊C4×C43—81no—
176C4⋊C4×C43—81no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43C2×Q812yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—81no—
182C22⋊C4×C43—81no—
183C22⋊C4×C43—81no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—81no—
190C42×C43C2×Q812yes—
191C42×C43#4112yes—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200Q8×C43—84no—
201D4×C43—22no—
202D4×C43—22no—
203D4×C43—41no—
204D4×C43—41no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
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—41no—
241C2×C4×C43—41no—
242C2×C4×C43—84no—
243C2×C4×C43C22⋊Q812yes—
244C2×C4×C43C22⋊Q812yes—
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255#29991C4311yesmaximal, characteristic, direct product factor, Sylow
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43#53511yescharacteristic
265C22×C43#53611yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57611yescharacteristic
268C22×C43#57711yescharacteristic
269C22×C43#57811yescharacteristic
270C4×C43—22no—
271C4×C43—22no—
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—81no—
282C4×C43—81no—
283C4×C43#54211yescharacteristic
284C4×C43#54211yescharacteristic
285C4×C43#54411yescharacteristic
286C4×C43#54411yescharacteristic
287#2660C2×C4311yescharacteristic, complemented
288#2319C2×C4311yescharacteristic
289#2101C2×C4311yescharacteristic, complemented
290#2100C2×C4311yescharacteristic, complemented
291#2093C2×C4311yescharacteristic
292#2092C2×C4311yescharacteristic
293#2059C2×C4311yescharacteristic, complemented
294#2057C2×C4311yescharacteristic, complemented
295#2025C2×C4311yescharacteristic
296#2023C2×C4311yescharacteristic
297#1949C2×C4311yescharacteristic, complemented
298#1947C2×C4311yescharacteristic, complemented
299#1832C2×C4311yescharacteristic, complemented
300#1804C2×C4311yescharacteristic
301#1802C2×C4311yescharacteristic
302C2×C43—82no—
303C2×C43#262811yescharacteristic
304C2×C43#308111yescharacteristic
305C2×C43#308311yescharacteristic
306C2×C43#322011yescharacteristic
307C2×C43#322511yescharacteristic
308C2×C43#324111yescharacteristic
309C2×C43#324311yescharacteristic
310C2×C4⋊Q8C22×C4311yescharacteristic
311C2×#125C22×C4311yescharacteristic
312C2×C4×D4C22×C4311yescharacteristic
313C2×#107C22×C4311yescharacteristic
314C2×#107C22×C4311yescharacteristic
315C2×#107C22×C4311yescharacteristic
316C2×#106C22×C4311yescharacteristic
317C2×C4⋊C8C22×C4311yescharacteristic
318C2×C4⋊C8C22×C4311yescharacteristic
319C2×#102C22×C4311yescharacteristic
320C2×#102C22×C4311yescharacteristic
321C2×#102C22×C4311yescharacteristic
322C2×#102C22×C4311yescharacteristic
323#398—21no—
324#398—21no—
325#395—21no—
326#395—21no—
327#390C22×C4311yescharacteristic
328#390C22×C4311yescharacteristic
329#389C22×C4311yescharacteristic
330#389C22×C4311yescharacteristic
331#388—21no—
332#388—21no—
333#384C22×C4311yescharacteristic
334#384C22×C4311yescharacteristic
335#382C22×C4311yescharacteristic
336#382C22×C4311yescharacteristic
337#381—21no—
338#380—21no—
339C4×C4⋊C4C22×C4311yescharacteristic
340#376C22×C4311yescharacteristic
341#340C22×C4311yescharacteristic
342#340C22×C4311yescharacteristic
343#340C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#340C22×C4311yescharacteristic
347#340C22×C4311yescharacteristic
348#340C22×C4311yescharacteristic
349#336C22×C4311yescharacteristic
350#336C22×C4311yescharacteristic
351#336C22×C4311yescharacteristic
352#336C22×C4311yescharacteristic
353C43#2999111yescharacteristic, direct product factor, Sylow
354C22×Q8—21no—
355C22×D4C23×C4311yescharacteristic
356C23×C4—21no—
357C22×C8C23×C4311yescharacteristic
358C22×C8C23×C4311yescharacteristic
359C22×C8C23×C4311yescharacteristic
360C22×C8C23×C4311yescharacteristic
361C4⋊Q8—41no—
362C4⋊Q8—41no—
363#125—41no—
364#125—41no—
365C4×D4—22no—
366C4×D4Q8×C4314yescomplemented
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C23×C4311yescharacteristic
377C2×C4⋊C4C23×C4311yescharacteristic
378C2×C4⋊C4C23×C4311yescharacteristic
379C2×C4⋊C4C23×C4311yescharacteristic
380C2×C4⋊C4C23×C4311yescharacteristic
381C2×C4⋊C4C23×C4311yescharacteristic
382C2×C4⋊C4C23×C4311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42C23×C4311yescharacteristic
390C2×C42C23×C4311yescharacteristic
391C2×C42C23×C4311yescharacteristic
392#107—41no—
393#107—41no—
394#107—41no—
395#106—41no—
396C4⋊C8—22no—
397C4⋊C8—22no—
398#102—41no—
399#102—41no—
400#102—41no—
401#102—41no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95D4×C4311yescharacteristic
410#95D4×C4311yescharacteristic
411#95D4×C4311yescharacteristic
412#95D4×C4311yescharacteristic
413C24—21no—
414C2×Q8—42no—
415C2×Q8—81no—
416C2×Q8—81no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×Q8×C4312yes—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×D4×C4311yescharacteristic
435C22×C4C2×D4×C4311yescharacteristic
436C22×C4C2×D4×C4311yescharacteristic
437C22×C4C2×D4×C4311yescharacteristic
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C24×C4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—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—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4C2×Q8×C4312yes—
475C22⋊C4—24no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—81no—
485C42C2×Q8×C4312yes—
486C42#41×C4312yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×D4×C4311yescharacteristic
495Q8—84no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
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—21no—
516C2×C4—21no—
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—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4C22⋊Q8×C4312yes—
539C2×C4C22⋊Q8×C4312yes—
540C2×C4C22×Q8×C4311yescharacteristic
541C2×C4C2×#41×C4311yescharacteristic
542C2×C4H(5,𝔽2)×C4311yescharacteristic
543C2×C4H(5,𝔽2)×C4311yescharacteristic
544C2×C42−1+4×C4311yescharacteristic
545C2×C42−1+4×C4311yescharacteristic
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C22⋊Q8×C4311yescharacteristic
558C22C43×#53511yescharacteristic
559C22C43×#53611yescharacteristic
560C22C43×#57611yescharacteristic
561C22C43×#57611yescharacteristic
562C22C43×#57711yescharacteristic
563C22C43×#57811yescharacteristic
564C4—22no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—42no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C43×#54211yescharacteristic
578C4C43×#54211yescharacteristic
579C4C43×#54411yescharacteristic
580C4C43×#54411yescharacteristic
581C2—82no—
582C2C43×#262811yescharacteristic
583C2C43×#308111yescharacteristic
584C2C43×#308311yescharacteristic
585C2C43×#322011yescharacteristic
586C2C43×#322511yescharacteristic
587C2C43×#324111yescharacteristic
588C2C43×#324311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2660C2semidirect
3. C43×#2101C2semidirect
4. C43×#2100C2semidirect
7. C43×#2059C2semidirect
8. C43×#2057C2semidirect
11. C43×#1949C2semidirect
12. C43×#1947C2semidirect
13. C43×#1832C2semidirect
71. C4×D4×C43Q8semidirect
255. #29991C43direct (N × H)
287. #2660C2×C43semidirect
289. #2101C2×C43semidirect
290. #2100C2×C43semidirect
293. #2059C2×C43semidirect
294. #2057C2×C43semidirect
297. #1949C2×C43semidirect
298. #1947C2×C43semidirect
299. #1832C2×C43semidirect
353. C43#29991direct (N × H)
366. C4×D4Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#26602
C43×#23192
C43×#21012
C43×#21002
C43×#20932
C43×#20922
C43×#20592
C43×#20572
C43×#20252
C43×#20232
C43×#19492
C43×#19472
C43×#18322
C43×#18042
C43×#18022
#2999143