Finite Group Databasebeta

← C43×#32845 #24952862

Subgroups — C43×#32845 #24952862

Order 11008.

590 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
1C43×#2660C211yesmaximal, characteristic, complemented
2C43×#2644C211yesmaximal, characteristic
3C43×#2101C211yesmaximal, characteristic, complemented
4C43×#2100C211yesmaximal, characteristic, complemented
5C43×#2093C211yesmaximal, characteristic
6C43×#2092C211yesmaximal, characteristic
7C43×#2085C211yesmaximal, characteristic, complemented
8C43×#2083C211yesmaximal, characteristic, complemented
9C43×#2073C211yesmaximal, characteristic
10C43×#2071C211yesmaximal, characteristic
11C43×#2059C211yesmaximal, characteristic, complemented
12C43×#2057C211yesmaximal, characteristic, complemented
13C43×#2025C211yesmaximal, characteristic
14C43×#2023C211yesmaximal, characteristic
15C43×#1840C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×#107×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×#102×C43C2211yescharacteristic
23C2×#102×C43C2211yescharacteristic
24C2×#102×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C43×#398—21no—
27C43×#398—21no—
28C43×#397—21no—
29C43×#397—21no—
30C43×#397—21no—
31C43×#396—21no—
32C43×#395—21no—
33C43×#395—21no—
34C43×#390C2211yescharacteristic
35C43×#390C2211yescharacteristic
36C43×#390C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#384C2211yescharacteristic
41C43×#384C2211yescharacteristic
42C43×#382C2211yescharacteristic
43C43×#382C2211yescharacteristic
44C43×#376C2211yescharacteristic
45C43×#340C2211yescharacteristic
46C43×#340C2211yescharacteristic
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#336C2211yescharacteristic
54C43×#336C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C22×D4×C43C2311yescharacteristic
61C22×C8×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C4⋊Q8×C43—41no—
66C4⋊Q8×C43—41no—
67#125×C43—41no—
68#125×C43—41no—
69C2×C4⋊C4×C43—21no—
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×C43—21no—
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×C4⋊C4×C43C2311yescharacteristic
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C2×C42×C43C2311yescharacteristic
94C2×C42×C43C2311yescharacteristic
95#107×C43—41no—
96#107×C43—41no—
97#107×C43—41no—
98#106×C43—41no—
99#102×C43—41no—
100#102×C43—41no—
101#102×C43—41no—
102#102×C43—41no—
103#95×C43—21no—
104#95×C43—21no—
105#95×C43—21no—
106#95×C43—21no—
107#95×C43—21no—
108#95×C43—21no—
109#95×C43—21no—
110#95×C43D411yescharacteristic
111#95×C43D411yescharacteristic
112#95×C43D411yescharacteristic
113#95×C43D411yescharacteristic
114C24×C43—21no—
115C2×Q8×C43—42no—
116C2×Q8×C43—81no—
117C2×Q8×C43—81no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
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—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×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—42no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—81no—
168C4⋊C4×C43—81no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43—81no—
174C22⋊C4×C43—81no—
175C22⋊C4×C43—81no—
176C22⋊C4×C43—81no—
177C22⋊C4×C43—81no—
178C22⋊C4×C43—81no—
179C22⋊C4×C43—81no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43C22×D411yescharacteristic
194Q8×C43—84no—
195D4×C43—41no—
196D4×C43—41no—
197D4×C43—41no—
198D4×C43—41no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
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—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
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×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248#32845C4311yesmaximal, characteristic, direct product factor, Sylow
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43#53511yescharacteristic
257C22×C43#53611yescharacteristic
258C22×C43#53611yescharacteristic
259C22×C43#57611yescharacteristic
260C22×C43#57611yescharacteristic
261C22×C43#57711yescharacteristic
262C22×C43#57811yescharacteristic
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43#56311yescharacteristic
277C4×C43#56311yescharacteristic
278C4×C43#56311yescharacteristic
279C4×C43#56311yescharacteristic
280#2660C2×C4311yescharacteristic, complemented
281#2644C2×C4311yescharacteristic
282#2101C2×C4311yescharacteristic, complemented
283#2100C2×C4311yescharacteristic, complemented
284#2093C2×C4311yescharacteristic
285#2092C2×C4311yescharacteristic
286#2085C2×C4311yescharacteristic, complemented
287#2083C2×C4311yescharacteristic, complemented
288#2073C2×C4311yescharacteristic
289#2071C2×C4311yescharacteristic
290#2059C2×C4311yescharacteristic, complemented
291#2057C2×C4311yescharacteristic, complemented
292#2025C2×C4311yescharacteristic
293#2023C2×C4311yescharacteristic
294#1840C2×C4311yescharacteristic, complemented
295C2×C43—161no—
296C2×C43#282111yescharacteristic
297C2×C43#322011yescharacteristic
298C2×C43#322511yescharacteristic
299C2×C43#324111yescharacteristic
300C2×C43#324111yescharacteristic
301C2×C43#324311yescharacteristic
302C2×C43#324311yescharacteristic
303C2×C4⋊Q8C22×C4311yescharacteristic
304C2×#125C22×C4311yescharacteristic
305C2×#107C22×C4311yescharacteristic
306C2×#107C22×C4311yescharacteristic
307C2×#107C22×C4311yescharacteristic
308C2×#106C22×C4311yescharacteristic
309C2×#102C22×C4311yescharacteristic
310C2×#102C22×C4311yescharacteristic
311C2×#102C22×C4311yescharacteristic
312C2×#102C22×C4311yescharacteristic
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#395—21no—
320#395—21no—
321#390C22×C4311yescharacteristic
322#390C22×C4311yescharacteristic
323#390C22×C4311yescharacteristic
324#389C22×C4311yescharacteristic
325#389C22×C4311yescharacteristic
326#389C22×C4311yescharacteristic
327#384C22×C4311yescharacteristic
328#384C22×C4311yescharacteristic
329#382C22×C4311yescharacteristic
330#382C22×C4311yescharacteristic
331#376C22×C4311yescharacteristic
332#340C22×C4311yescharacteristic
333#340C22×C4311yescharacteristic
334#340C22×C4311yescharacteristic
335#340C22×C4311yescharacteristic
336#340C22×C4311yescharacteristic
337#340C22×C4311yescharacteristic
338#340C22×C4311yescharacteristic
339#340C22×C4311yescharacteristic
340#336C22×C4311yescharacteristic
341#336C22×C4311yescharacteristic
342#336C22×C4311yescharacteristic
343#336C22×C4311yescharacteristic
344#336C22×C4311yescharacteristic
345#336C22×C4311yescharacteristic
346C43#3284511yescharacteristic, direct product factor, Sylow
347C22×Q8—21no—
348C22×D4C23×C4311yescharacteristic
349C22×C8C23×C4311yescharacteristic
350C22×C8C23×C4311yescharacteristic
351C22×C8C23×C4311yescharacteristic
352C22×C8C23×C4311yescharacteristic
353C4⋊Q8—41no—
354C4⋊Q8—41no—
355#125—41no—
356#125—41no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C23×C4311yescharacteristic
368C2×C4⋊C4C23×C4311yescharacteristic
369C2×C4⋊C4C23×C4311yescharacteristic
370C2×C4⋊C4C23×C4311yescharacteristic
371C2×C4⋊C4C23×C4311yescharacteristic
372C2×C4⋊C4C23×C4311yescharacteristic
373C2×C4⋊C4C23×C4311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42C23×C4311yescharacteristic
381C2×C42C23×C4311yescharacteristic
382C2×C42C23×C4311yescharacteristic
383#107—41no—
384#107—41no—
385#107—41no—
386#106—41no—
387#102—41no—
388#102—41no—
389#102—41no—
390#102—41no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95D4×C4311yescharacteristic
399#95D4×C4311yescharacteristic
400#95D4×C4311yescharacteristic
401#95D4×C4311yescharacteristic
402C24—21no—
403C2×Q8—42no—
404C2×Q8—81no—
405C2×Q8—81no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4C2×D4×C4311yescharacteristic
420C22×C4C2×D4×C4311yescharacteristic
421C22×C4C2×D4×C4311yescharacteristic
422C22×C4C2×D4×C4311yescharacteristic
423C22×C4C2×D4×C4311yescharacteristic
424C22×C4C2×D4×C4311yescharacteristic
425C22×C4C24×C4311yescharacteristic
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—42no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C22⋊C4—81no—
467C22⋊C4—81no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×D4×C4311yescharacteristic
482Q8—84no—
483D4—41no—
484D4—41no—
485D4—41no—
486D4—41no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
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×C4H(5,𝔽2)×C4311yescharacteristic
527C2×C4H(5,𝔽2)×C4311yescharacteristic
528C2×C42−1+4×C4311yescharacteristic
529C2×C42−1+4×C4311yescharacteristic
530C2×C42−1+4×C4311yescharacteristic
531C2×C42−1+4×C4311yescharacteristic
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C43×#53511yescharacteristic
544C22C43×#53611yescharacteristic
545C22C43×#53611yescharacteristic
546C22C43×#57611yescharacteristic
547C22C43×#57611yescharacteristic
548C22C43×#57711yescharacteristic
549C22C43×#57811yescharacteristic
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C43×#56311yescharacteristic
564C4C43×#56311yescharacteristic
565C4C43×#56311yescharacteristic
566C4C43×#56311yescharacteristic
567C2—161no—
568C2C43×#282111yescharacteristic
569C2C43×#322011yescharacteristic
570C2C43×#322511yescharacteristic
571C2C43×#324111yescharacteristic
572C2C43×#324111yescharacteristic
573C2C43×#324311yescharacteristic
574C2C43×#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×#2085C2semidirect
8. C43×#2083C2semidirect
11. C43×#2059C2semidirect
12. C43×#2057C2semidirect
15. C43×#1840C2semidirect
248. #32845C43direct (N × H)
280. #2660C2×C43semidirect
282. #2101C2×C43semidirect
283. #2100C2×C43semidirect
286. #2085C2×C43semidirect
287. #2083C2×C43semidirect
290. #2059C2×C43semidirect
291. #2057C2×C43semidirect
294. #1840C2×C43semidirect
346. C43#32845direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26602
C43×#26442
C43×#21012
C43×#21002
C43×#20932
C43×#20922
C43×#20852
C43×#20832
C43×#20732
C43×#20712
C43×#20592
C43×#20572
C43×#20252
C43×#20232
C43×#18402
#3284543