Finite Group Databasebeta

← C43×#29918 #24949935

Subgroups — C43×#29918 #24949935

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2625C211yesmaximal, characteristic
2C43×#2317C211yesmaximal, characteristic
3C43×#2101C211yesmaximal, characteristic, complemented
4C43×#2099C211yesmaximal, characteristic, complemented
5C43×#2097C211yesmaximal, characteristic, complemented
6C43×#2095C211yesmaximal, characteristic, complemented
7C43×#2085C211yesmaximal, characteristic, complemented
8C43×#2083C211yesmaximal, characteristic, complemented
9C43×#2074C211yesmaximal, characteristic, complemented
10C43×#2072C211yesmaximal, characteristic, complemented
11C43×#1873C211yesmaximal, characteristic
12C43×#1872C211yesmaximal, characteristic
13C43×#1854C211yesmaximal, characteristic
14C43×#1852C211yesmaximal, characteristic
15C43×#1818C211yesmaximal, characteristic
16C2×C22⋊Q8×C43C2211yescharacteristic
17C2×#117×C43C2211yescharacteristic
18C2×#117×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×#103×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#400—21no—
31C43×#398—21no—
32C43×#397—21no—
33C43×#397—21no—
34C43×#391C2211yescharacteristic
35C43×#391C2211yescharacteristic
36C43×#389—21no—
37C43×#389—21no—
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#385—21no—
41C43×#385—21no—
42C43×#384C2211yescharacteristic
43C43×#384C2211yescharacteristic
44C43×#382C2211yescharacteristic
45C43×#382C2211yescharacteristic
46C43×#380C2211yescharacteristic
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×C43C2311yescharacteristic
60C23×C4×C43—21no—
61C23×C4×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22⋊Q8×C43—22no—
67C22⋊Q8×C43—22no—
68#117×C43—22no—
69#117×C43—22no—
70#117×C43—41no—
71#117×C43—41no—
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—41no—
81C2×C4⋊C4×C43—41no—
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43D411yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43D411yescharacteristic
95C2×C22⋊C4×C43D411yescharacteristic
96C2×C42×C43—21no—
97C2×C42×C43C2311yescharacteristic
98C2×C42×C43C2311yescharacteristic
99#107×C43—41no—
100#107×C43—41no—
101#107×C43—41no—
102#106×C43—41no—
103#103×C43—41no—
104#103×C43—41no—
105#103×C43—41no—
106#103×C43—41no—
107C22⋊C8×C43—22no—
108C22⋊C8×C43—22no—
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×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120C24×C43C2×D411yescharacteristic
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
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—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—42no—
140C22×C4×C43—81no—
141C22×C4×C43—81no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43#4112yes—
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
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—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
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—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43—81no—
184C4⋊C4×C43—81no—
185C4⋊C4×C43—81no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—42no—
189C22⋊C4×C43—42no—
190C22⋊C4×C43—81no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—42no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43#12312yes—
203C23×C43C22×D411yescharacteristic
204Q8×C43—41no—
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
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—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
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—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—84no—
251C2×C4×C43#12312yes—
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262#29918C4311yesmaximal, characteristic, direct product factor, Sylow
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43C2×#12311yescharacteristic
271C22×C43#53511yescharacteristic
272C22×C43#53611yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57811yescharacteristic
276C22×C43#57811yescharacteristic
277C4×C43—22no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43#53911yescharacteristic
291C4×C43#53911yescharacteristic
292C4×C43#53911yescharacteristic
293C4×C43#53911yescharacteristic
294#2625C2×C4311yescharacteristic
295#2317C2×C4311yescharacteristic
296#2101C2×C4311yescharacteristic, complemented
297#2099C2×C4311yescharacteristic, complemented
298#2097C2×C4311yescharacteristic, complemented
299#2095C2×C4311yescharacteristic, complemented
300#2085C2×C4311yescharacteristic, complemented
301#2083C2×C4311yescharacteristic, complemented
302#2074C2×C4311yescharacteristic, complemented
303#2072C2×C4311yescharacteristic, complemented
304#1873C2×C4311yescharacteristic
305#1872C2×C4311yescharacteristic
306#1854C2×C4311yescharacteristic
307#1852C2×C4311yescharacteristic
308#1818C2×C4311yescharacteristic
309C2×C43—42no—
310C2×C43#262311yescharacteristic
311C2×C43#309711yescharacteristic
312C2×C43#309811yescharacteristic
313C2×C43#322311yescharacteristic
314C2×C43#322411yescharacteristic
315C2×C43#324211yescharacteristic
316C2×C43#324311yescharacteristic
317C2×C22⋊Q8C22×C4311yescharacteristic
318C2×#117C22×C4311yescharacteristic
319C2×#117C22×C4311yescharacteristic
320C22×C4⋊C4C22×C4311yescharacteristic
321C2×#107C22×C4311yescharacteristic
322C2×#107C22×C4311yescharacteristic
323C2×#107C22×C4311yescharacteristic
324C2×#106C22×C4311yescharacteristic
325C2×#103C22×C4311yescharacteristic
326C2×#103C22×C4311yescharacteristic
327C2×#103C22×C4311yescharacteristic
328C2×#103C22×C4311yescharacteristic
329C2×C22⋊C8C22×C4311yescharacteristic
330C2×C22⋊C8C22×C4311yescharacteristic
331#400—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#391C22×C4311yescharacteristic
336#391C22×C4311yescharacteristic
337#389—21no—
338#389—21no—
339#389C22×C4311yescharacteristic
340#389C22×C4311yescharacteristic
341#385—21no—
342#385—21no—
343#384C22×C4311yescharacteristic
344#384C22×C4311yescharacteristic
345#382C22×C4311yescharacteristic
346#382C22×C4311yescharacteristic
347#380C22×C4311yescharacteristic
348#340C22×C4311yescharacteristic
349#340C22×C4311yescharacteristic
350#340C22×C4311yescharacteristic
351#340C22×C4311yescharacteristic
352#340C22×C4311yescharacteristic
353#340C22×C4311yescharacteristic
354#340C22×C4311yescharacteristic
355#340C22×C4311yescharacteristic
356#336C22×C4311yescharacteristic
357#336C22×C4311yescharacteristic
358#336C22×C4311yescharacteristic
359#336C22×C4311yescharacteristic
360C43#2991811yescharacteristic, direct product factor, Sylow
361C22×Q8C23×C4311yescharacteristic
362C23×C4—21no—
363C23×C4C23×C4311yescharacteristic
364C22×C8C23×C4311yescharacteristic
365C22×C8C23×C4311yescharacteristic
366C22×C8C23×C4311yescharacteristic
367C22×C8C23×C4311yescharacteristic
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370#117—22no—
371#117—22no—
372#117—41no—
373#117—41no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4D4×C4311yescharacteristic
385C2×C4⋊C4D4×C4311yescharacteristic
386C2×C4⋊C4C23×C4311yescharacteristic
387C2×C4⋊C4C23×C4311yescharacteristic
388C2×C4⋊C4C23×C4311yescharacteristic
389C2×C4⋊C4C23×C4311yescharacteristic
390C2×C4⋊C4C23×C4311yescharacteristic
391C2×C4⋊C4C23×C4311yescharacteristic
392C2×C4⋊C4C23×C4311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D4×C4311yescharacteristic
397C2×C22⋊C4D4×C4311yescharacteristic
398C2×C42—21no—
399C2×C42C23×C4311yescharacteristic
400C2×C42C23×C4311yescharacteristic
401#107—41no—
402#107—41no—
403#107—41no—
404#106—41no—
405#103—41no—
406#103—41no—
407#103—41no—
408#103—41no—
409C22⋊C8—22no—
410C22⋊C8—22no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422C24C2×D4×C4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×D4×C4311yescharacteristic
447C22×C4C2×D4×C4311yescharacteristic
448C22×C4C2×D4×C4311yescharacteristic
449C22×C4#41×C4312yes—
450C22×C4#41×C4312yes—
451C22×C4C24×C4311yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—81no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#123×C4312yes—
505C23C22×D4×C4311yescharacteristic
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
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—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—84no—
553C2×C4#123×C4312yes—
554C2×C4C2×#41×C4311yescharacteristic
555C2×C4C2×#41×C4311yescharacteristic
556C2×C4H(5,𝔽2)×C4311yescharacteristic
557C2×C4H(5,𝔽2)×C4311yescharacteristic
558C2×C42−1+4×C4311yescharacteristic
559C2×C42−1+4×C4311yescharacteristic
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22C2×#123×C4311yescharacteristic
572C22C43×#53511yescharacteristic
573C22C43×#53611yescharacteristic
574C22C43×#57611yescharacteristic
575C22C43×#57711yescharacteristic
576C22C43×#57811yescharacteristic
577C22C43×#57811yescharacteristic
578C4—22no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C43×#53911yescharacteristic
592C4C43×#53911yescharacteristic
593C4C43×#53911yescharacteristic
594C4C43×#53911yescharacteristic
595C2—42no—
596C2C43×#262311yescharacteristic
597C2C43×#309711yescharacteristic
598C2C43×#309811yescharacteristic
599C2C43×#322311yescharacteristic
600C2C43×#322411yescharacteristic
601C2C43×#324211yescharacteristic
602C2C43×#324311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2101C2semidirect
4. C43×#2099C2semidirect
5. C43×#2097C2semidirect
6. C43×#2095C2semidirect
7. C43×#2085C2semidirect
8. C43×#2083C2semidirect
9. C43×#2074C2semidirect
10. C43×#2072C2semidirect
262. #29918C43direct (N × H)
296. #2101C2×C43semidirect
297. #2099C2×C43semidirect
298. #2097C2×C43semidirect
299. #2095C2×C43semidirect
300. #2085C2×C43semidirect
301. #2083C2×C43semidirect
302. #2074C2×C43semidirect
303. #2072C2×C43semidirect
360. C43#29918direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26252
C43×#23172
C43×#21012
C43×#20992
C43×#20972
C43×#20952
C43×#20852
C43×#20832
C43×#20742
C43×#20722
C43×#18732
C43×#18722
C43×#18542
C43×#18522
C43×#18182
#2991843