Finite Group Databasebeta

← C43×#29194 #24949211

Subgroups — C43×#29194 #24949211

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2864C211yesmaximal, characteristic, complemented
2C4×#124×C43C211yesmaximal, characteristic
3C43×#2068C211yesmaximal, characteristic, complemented
4C43×#2067C211yesmaximal, characteristic
5C43×#2066C211yesmaximal, characteristic, complemented
6C43×#2065C211yesmaximal, characteristic
7C43×#1958C211yesmaximal, characteristic
8C43×#1958C211yesmaximal, characteristic
9C43×#1865C211yesmaximal, characteristic, complemented
10C43×#1864C211yesmaximal, characteristic
11C43×#1863C211yesmaximal, characteristic, complemented
12C43×#1862C211yesmaximal, characteristic
13C43×#1846C211yesmaximal, characteristic, complemented
14C43×#1835C211yesmaximal, characteristic, complemented
15C4×C4⋊C8×C43C211yesmaximal, characteristic, complemented
16C2×#124×C43C2211yescharacteristic
17C2×C4×Q8×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×C4×C8×C43C2211yescharacteristic
34C2×C4×C8×C43C2211yescharacteristic
35C43×#391C2211yescharacteristic
36C43×#390C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#389C2211yescharacteristic
41C43×#388—21no—
42C43×#388—21no—
43C43×#387—21no—
44C43×#387—21no—
45C43×#387—21no—
46C43×#387—21no—
47C43×#382C2211yescharacteristic
48C43×#382C2211yescharacteristic
49C43×#382C2211yescharacteristic
50C4×C22⋊C4×C43—21no—
51C4×C22⋊C4×C43—21no—
52C43×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43C2311yescharacteristic
60C22×D4×C43C2311yescharacteristic
61C23×C4×C43—21no—
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66#124×C43—22no—
67#124×C43Q814yes—
68C4×Q8×C43—41no—
69C4×Q8×C43—41no—
70C4×D4×C43—41no—
71C4×D4×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×C43C2311yescharacteristic
78C2×C4⋊C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C42×C43—21no—
89C2×C42×C43D411yescharacteristic
90C2×C42×C43D411yescharacteristic
91C2×C42×C43D411yescharacteristic
92C2×C42×C43D411yescharacteristic
93C2×C42×C43C2311yescharacteristic
94C2×C42×C43C2311yescharacteristic
95C2×C42×C43C2311yescharacteristic
96#107×C43—41no—
97#107×C43—41no—
98#106×C43—41no—
99#106×C43—41no—
100C4⋊C8×C43—22no—
101C4⋊C8×C43—22no—
102#103×C43—22no—
103#103×C43—22no—
104#103×C43—41no—
105#103×C43—41no—
106#102×C43—22no—
107#102×C43—22no—
108#102×C43—41no—
109#102×C43—41no—
110C4×C8×C43—22no—
111C4×C8×C43—22no—
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—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×Q812yes—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43C2×Q812yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
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—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43#4112yes—
165C2×C8×C43#4112yes—
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—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—42no—
188C42×C43—22no—
189C42×C43—22no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—41no—
195C42×C43—41no—
196C42×C43—42no—
197C42×C43C2×Q812yes—
198C42×C43#4112yes—
199C23×C43—22no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43C22×D411yescharacteristic
207Q8×C43—22no—
208Q8×C43—22no—
209Q8×C43—41no—
210Q8×C43—41no—
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—41no—
214D4×C43—41no—
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—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
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×C43C22⋊Q812yes—
252C2×C4×C43C22⋊Q812yes—
253C2×C4×C43#13512yes—
254C2×C4×C43#13512yes—
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C8×C43—22no—
262C8×C43—22no—
263C8×C43—41no—
264C8×C43—41no—
265#29194C4311yesmaximal, characteristic, direct product factor, Sylow
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43C2×C22⋊Q811yescharacteristic
274C22×C43#53211yescharacteristic
275C22×C43#53511yescharacteristic
276C22×C43C2×#13511yescharacteristic
277C22×C43C2×#13511yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57511yescharacteristic
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—42no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#55311yescharacteristic
294C4×C43#55311yescharacteristic
295C4×C43#55411yescharacteristic
296C4×C43#55411yescharacteristic
297#2864C2×C4311yescharacteristic, complemented
298C4×#124C2×C4311yescharacteristic
299#2068C2×C4311yescharacteristic, complemented
300#2067C2×C4311yescharacteristic
301#2066C2×C4311yescharacteristic, complemented
302#2065C2×C4311yescharacteristic
303#1958C2×C4311yescharacteristic
304#1958C2×C4311yescharacteristic
305#1865C2×C4311yescharacteristic, complemented
306#1864C2×C4311yescharacteristic
307#1863C2×C4311yescharacteristic, complemented
308#1862C2×C4311yescharacteristic
309#1846C2×C4311yescharacteristic, complemented
310#1835C2×C4311yescharacteristic, complemented
311C4×C4⋊C8C2×C4311yescharacteristic, complemented
312C2×C43—82no—
313C2×C43#256611yescharacteristic
314C2×C43#307611yescharacteristic
315C2×C43#307611yescharacteristic
316C2×C43#316811yescharacteristic
317C2×C43#318311yescharacteristic
318C2×C43#321111yescharacteristic
319C2×C43#321211yescharacteristic
320C2×#124C22×C4311yescharacteristic
321C2×C4×Q8C22×C4311yescharacteristic
322C2×C4×D4C22×C4311yescharacteristic
323C2×#107C22×C4311yescharacteristic
324C2×#107C22×C4311yescharacteristic
325C2×#106C22×C4311yescharacteristic
326C2×#106C22×C4311yescharacteristic
327C2×C4⋊C8C22×C4311yescharacteristic
328C2×C4⋊C8C22×C4311yescharacteristic
329C2×#103C22×C4311yescharacteristic
330C2×#103C22×C4311yescharacteristic
331C2×#103C22×C4311yescharacteristic
332C2×#103C22×C4311yescharacteristic
333C2×#102C22×C4311yescharacteristic
334C2×#102C22×C4311yescharacteristic
335C2×#102C22×C4311yescharacteristic
336C2×#102C22×C4311yescharacteristic
337C2×C4×C8C22×C4311yescharacteristic
338C2×C4×C8C22×C4311yescharacteristic
339#391C22×C4311yescharacteristic
340#390C22×C4311yescharacteristic
341#389C22×C4311yescharacteristic
342#389C22×C4311yescharacteristic
343#389C22×C4311yescharacteristic
344#389C22×C4311yescharacteristic
345#388—21no—
346#388—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#382C22×C4311yescharacteristic
352#382C22×C4311yescharacteristic
353#382C22×C4311yescharacteristic
354C4×C22⋊C4—21no—
355C4×C22⋊C4—21no—
356C43C22×C4311yescharacteristic
357#340C22×C4311yescharacteristic
358#340C22×C4311yescharacteristic
359#340C22×C4311yescharacteristic
360#340C22×C4311yescharacteristic
361#336C22×C4311yescharacteristic
362#336C22×C4311yescharacteristic
363C43#2919411yescharacteristic, direct product factor, Sylow
364C22×Q8C23×C4311yescharacteristic
365C22×D4C23×C4311yescharacteristic
366C23×C4—21no—
367C22×C8C23×C4311yescharacteristic
368C22×C8C23×C4311yescharacteristic
369C22×C8C23×C4311yescharacteristic
370C22×C8C23×C4311yescharacteristic
371#124—22no—
372#124Q8×C4314yes—
373C4×Q8—41no—
374C4×Q8—41no—
375C4×D4—41no—
376C4×D4—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4C23×C4311yescharacteristic
383C2×C4⋊C4C23×C4311yescharacteristic
384C2×C4⋊C4C23×C4311yescharacteristic
385C2×C4⋊C4C23×C4311yescharacteristic
386C2×C4⋊C4C23×C4311yescharacteristic
387C2×C4⋊C4C23×C4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42D4×C4311yescharacteristic
395C2×C42D4×C4311yescharacteristic
396C2×C42D4×C4311yescharacteristic
397C2×C42D4×C4311yescharacteristic
398C2×C42C23×C4311yescharacteristic
399C2×C42C23×C4311yescharacteristic
400C2×C42C23×C4311yescharacteristic
401#107—41no—
402#107—41no—
403#106—41no—
404#106—41no—
405C4⋊C8—22no—
406C4⋊C8—22no—
407#103—22no—
408#103—22no—
409#103—41no—
410#103—41no—
411#102—22no—
412#102—22no—
413#102—41no—
414#102—41no—
415C4×C8—22no—
416C4×C8—22no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429C24—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×Q8×C4312yes—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×Q8×C4312yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4C2×D4×C4311yescharacteristic
453C22×C4C2×D4×C4311yescharacteristic
454C22×C4C2×D4×C4311yescharacteristic
455C22×C4C2×D4×C4311yescharacteristic
456C22×C4C2×D4×C4311yescharacteristic
457C22×C4C2×D4×C4311yescharacteristic
458C22×C4C24×C4311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8#41×C4312yes—
470C2×C8#41×C4312yes—
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—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42—41no—
501C42—42no—
502C42C2×Q8×C4312yes—
503C42#41×C4312yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×D4×C4311yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
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—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
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—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4C22⋊Q8×C4312yes—
557C2×C4C22⋊Q8×C4312yes—
558C2×C4#135×C4312yes—
559C2×C4#135×C4312yes—
560C2×C4C22×Q8×C4311yescharacteristic
561C2×C4C2×#41×C4311yescharacteristic
562C2×C4C2×#41×C4311yescharacteristic
563C2×C4C2×#41×C4311yescharacteristic
564C2×C4H(5,𝔽2)×C4311yescharacteristic
565C2×C4H(5,𝔽2)×C4311yescharacteristic
566C8—22no—
567C8—22no—
568C8—41no—
569C8—41no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C22⋊Q8×C4311yescharacteristic
578C22C43×#53211yescharacteristic
579C22C43×#53511yescharacteristic
580C22C2×#135×C4311yescharacteristic
581C22C2×#135×C4311yescharacteristic
582C22C43×#57511yescharacteristic
583C22C43×#57511yescharacteristic
584C4—22no—
585C4—22no—
586C4—22no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C43×#55311yescharacteristic
598C4C43×#55311yescharacteristic
599C4C43×#55411yescharacteristic
600C4C43×#55411yescharacteristic
601C2—82no—
602C2C43×#256611yescharacteristic
603C2C43×#307611yescharacteristic
604C2C43×#307611yescharacteristic
605C2C43×#316811yescharacteristic
606C2C43×#318311yescharacteristic
607C2C43×#321111yescharacteristic
608C2C43×#321211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2864C2semidirect
3. C43×#2068C2semidirect
5. C43×#2066C2semidirect
9. C43×#1865C2semidirect
11. C43×#1863C2semidirect
13. C43×#1846C2semidirect
14. C43×#1835C2semidirect
15. C4×C4⋊C8×C43C2semidirect
265. #29194C43direct (N × H)
297. #2864C2×C43semidirect
299. #2068C2×C43semidirect
301. #2066C2×C43semidirect
305. #1865C2×C43semidirect
307. #1863C2×C43semidirect
309. #1846C2×C43semidirect
310. #1835C2×C43semidirect
311. C4×C4⋊C8C2×C43semidirect
363. C43#29194direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28642
C4×#124×C432
C43×#20682
C43×#20672
C43×#20662
C43×#20652
C43×#19582
C43×#18652
C43×#18642
C43×#18632
C43×#18622
C43×#18462
C43×#18352
C4×C4⋊C8×C432
#2919443