Finite Group Databasebeta

← C43×#29308 #24949325

Subgroups — C43×#29308 #24949325

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2628C211yesmaximal, characteristic
2C43×#2316C211yesmaximal, characteristic
3C43×#2085C211yesmaximal, characteristic, complemented
4C43×#2085C211yesmaximal, characteristic, complemented
5C43×#2058C211yesmaximal, characteristic, complemented
6C43×#2057C211yesmaximal, characteristic, complemented
7C43×#1944C211yesmaximal, characteristic, complemented
8C43×#1943C211yesmaximal, characteristic, complemented
9C43×#1942C211yesmaximal, characteristic, complemented
10C43×#1941C211yesmaximal, characteristic, complemented
11C43×#1854C211yesmaximal, characteristic
12C43×#1854C211yesmaximal, characteristic
13C43×#1853C211yesmaximal, characteristic
14C43×#1852C211yesmaximal, characteristic
15C43×#1750C211yesmaximal, characteristic
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#117×C43C2211yescharacteristic
18C2×#117×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C2×#97×C43C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C43×#400—21no—
33C43×#399—21no—
34C43×#395—21no—
35C43×#393—21no—
36C43×#389—21no—
37C43×#389—21no—
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#389C2211yescharacteristic
41C43×#389C2211yescharacteristic
42C43×#389C2211yescharacteristic
43C43×#389C2211yescharacteristic
44C43×#382C2211yescharacteristic
45C43×#380—21no—
46C43×#380—21no—
47C43×#380C2211yescharacteristic
48C43×#380C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C23×C4×C43—21no—
61C23×C4×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C4⋊Q8×C43—41no—
67C4⋊Q8×C43—41no—
68#117×C43—41no—
69#117×C43—41no—
70#117×C43—41no—
71#117×C43—41no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43—22no—
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×C43—21no—
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×C4⋊C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43D411yescharacteristic
96C2×C22⋊C4×C43D411yescharacteristic
97C2×C42×C43—21no—
98C2×C42×C43C2311yescharacteristic
99C2×C42×C43C2311yescharacteristic
100#107×C43—22no—
101#107×C43—22no—
102#107×C43—41no—
103#107×C43—41no—
104#106×C43—22no—
105#106×C43—22no—
106#106×C43—41no—
107#106×C43—41no—
108C22⋊C8×C43Q814yescomplemented
109C22⋊C8×C43Q814yescomplemented
110#97×C43—41no—
111C4×C8×C43—41no—
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—
122C24×C43C2×D411yescharacteristic
123C2×Q8×C43—42no—
124C2×Q8×C43—81no—
125C2×Q8×C43—81no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—24no—
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—81no—
140C22×C4×C43—81no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×Q812yes—
147C22×C4×C43C2×Q812yes—
148C22×C4×C43C2411yescharacteristic
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—
157C2×C8×C43C2×Q812yes—
158C2×C8×C43C2×Q812yes—
159C2×C8×C43C2×Q812yes—
160C2×C8×C43C2×Q812yes—
161C4⋊C4×C43—24no—
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—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—81no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43—81no—
184C4⋊C4×C43—81no—
185C4⋊C4×C43#4112yes—
186C4⋊C4×C43#4112yes—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—42no—
190C22⋊C4×C43—81no—
191C22⋊C4×C43—81no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—42no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43C4⋊Q812yes—
204C23×C43C22×D411yescharacteristic
205Q8×C43—84no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
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—84no—
249C2×C4×C43C4⋊Q812yes—
250C2×C4×C43C22×Q811yescharacteristic
251C2×C4×C43C22×Q811yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C8×C43—22no—
257C8×C43—22no—
258C8×C43—22no—
259C8×C43—22no—
260#29308C4311yesmaximal, characteristic, direct product factor, Sylow
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43#52511yescharacteristic
269C22×C43C2×C4⋊Q811yescharacteristic
270C22×C43#53411yescharacteristic
271C22×C43#57611yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C4×C43—22no—
276C4×C43—42no—
277C4×C43—42no—
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#55411yescharacteristic
289C4×C43#55411yescharacteristic
290C4×C43#55411yescharacteristic
291C4×C43#55411yescharacteristic
292#2628C2×C4311yescharacteristic
293#2316C2×C4311yescharacteristic
294#2085C2×C4311yescharacteristic, complemented
295#2085C2×C4311yescharacteristic, complemented
296#2058C2×C4311yescharacteristic, complemented
297#2057C2×C4311yescharacteristic, complemented
298#1944C2×C4311yescharacteristic, complemented
299#1943C2×C4311yescharacteristic, complemented
300#1942C2×C4311yescharacteristic, complemented
301#1941C2×C4311yescharacteristic, complemented
302#1854C2×C4311yescharacteristic
303#1854C2×C4311yescharacteristic
304#1853C2×C4311yescharacteristic
305#1852C2×C4311yescharacteristic
306#1750C2×C4311yescharacteristic
307C2×C43—42no—
308C2×C43#258311yescharacteristic
309C2×C43#311811yescharacteristic
310C2×C43#312111yescharacteristic
311C2×C43#316311yescharacteristic
312C2×C43#316411yescharacteristic
313C2×C43#319811yescharacteristic
314C2×C43#320111yescharacteristic
315C2×C4⋊Q8C22×C4311yescharacteristic
316C2×#117C22×C4311yescharacteristic
317C2×#117C22×C4311yescharacteristic
318C22×C4⋊C4C22×C4311yescharacteristic
319C2×#107C22×C4311yescharacteristic
320C2×#107C22×C4311yescharacteristic
321C2×#107C22×C4311yescharacteristic
322C2×#107C22×C4311yescharacteristic
323C2×#106C22×C4311yescharacteristic
324C2×#106C22×C4311yescharacteristic
325C2×#106C22×C4311yescharacteristic
326C2×#106C22×C4311yescharacteristic
327C2×C22⋊C8C22×C4311yescharacteristic
328C2×C22⋊C8C22×C4311yescharacteristic
329C2×#97C22×C4311yescharacteristic
330C2×C4×C8C22×C4311yescharacteristic
331#400—21no—
332#399—21no—
333#395—21no—
334#393—21no—
335#389—21no—
336#389—21no—
337#389C22×C4311yescharacteristic
338#389C22×C4311yescharacteristic
339#389C22×C4311yescharacteristic
340#389C22×C4311yescharacteristic
341#389C22×C4311yescharacteristic
342#389C22×C4311yescharacteristic
343#382C22×C4311yescharacteristic
344#380—21no—
345#380—21no—
346#380C22×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
358C43#2930811yescharacteristic, direct product factor, Sylow
359C22×Q8—21no—
360C23×C4—21no—
361C23×C4C23×C4311yescharacteristic
362C22×C8C23×C4311yescharacteristic
363C22×C8C23×C4311yescharacteristic
364C22×C8C23×C4311yescharacteristic
365C22×C8C23×C4311yescharacteristic
366C4⋊Q8—41no—
367C4⋊Q8—41no—
368#117—41no—
369#117—41no—
370#117—41no—
371#117—41no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
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⋊C4D4×C4311yescharacteristic
383C2×C4⋊C4D4×C4311yescharacteristic
384C2×C4⋊C4C23×C4311yescharacteristic
385C2×C4⋊C4C23×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×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4D4×C4311yescharacteristic
396C2×C22⋊C4D4×C4311yescharacteristic
397C2×C42—21no—
398C2×C42C23×C4311yescharacteristic
399C2×C42C23×C4311yescharacteristic
400#107—22no—
401#107—22no—
402#107—41no—
403#107—41no—
404#106—22no—
405#106—22no—
406#106—41no—
407#106—41no—
408C22⋊C8Q8×C4314yescomplemented
409C22⋊C8Q8×C4314yescomplemented
410#97—41no—
411C4×C8—41no—
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—42no—
424C2×Q8—81no—
425C2×Q8—81no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—81no—
440C22×C4—81no—
441C22×C4C2×D4×C4311yescharacteristic
442C22×C4C2×D4×C4311yescharacteristic
443C22×C4C2×D4×C4311yescharacteristic
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×Q8×C4312yes—
447C22×C4C2×Q8×C4312yes—
448C22×C4C24×C4311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8C2×Q8×C4312yes—
458C2×C8C2×Q8×C4312yes—
459C2×C8C2×Q8×C4312yes—
460C2×C8C2×Q8×C4312yes—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
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—41no—
477C4⋊C4—41no—
478C4⋊C4—42no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4#41×C4312yes—
486C4⋊C4#41×C4312yes—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—42no—
490C22⋊C4—81no—
491C22⋊C4—81no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23C4⋊Q8×C4312yes—
504C23C22×D4×C4311yescharacteristic
505Q8—84no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
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—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—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—84no—
549C2×C4C4⋊Q8×C4312yes—
550C2×C4C22×Q8×C4311yescharacteristic
551C2×C4C22×Q8×C4311yescharacteristic
552C2×C4C2×#41×C4311yescharacteristic
553C2×C4C2×#41×C4311yescharacteristic
554C2×C4H(5,𝔽2)×C4311yescharacteristic
555C2×C4H(5,𝔽2)×C4311yescharacteristic
556C8—22no—
557C8—22no—
558C8—22no—
559C8—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C43×#52511yescharacteristic
568C22C2×C4⋊Q8×C4311yescharacteristic
569C22C43×#53411yescharacteristic
570C22C43×#57611yescharacteristic
571C22C43×#57711yescharacteristic
572C22C43×#57711yescharacteristic
573C22C43×#57811yescharacteristic
574C4—22no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C43×#55411yescharacteristic
588C4C43×#55411yescharacteristic
589C4C43×#55411yescharacteristic
590C4C43×#55411yescharacteristic
591C2—42no—
592C2C43×#258311yescharacteristic
593C2C43×#311811yescharacteristic
594C2C43×#312111yescharacteristic
595C2C43×#316311yescharacteristic
596C2C43×#316411yescharacteristic
597C2C43×#319811yescharacteristic
598C2C43×#320111yescharacteristic
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×#2085C2semidirect
4. C43×#2085C2semidirect
5. C43×#2058C2semidirect
6. C43×#2057C2semidirect
7. C43×#1944C2semidirect
8. C43×#1943C2semidirect
9. C43×#1942C2semidirect
10. C43×#1941C2semidirect
108. C22⋊C8×C43Q8semidirect
109. C22⋊C8×C43Q8semidirect
260. #29308C43direct (N × H)
294. #2085C2×C43semidirect
295. #2085C2×C43semidirect
296. #2058C2×C43semidirect
297. #2057C2×C43semidirect
298. #1944C2×C43semidirect
299. #1943C2×C43semidirect
300. #1942C2×C43semidirect
301. #1941C2×C43semidirect
358. C43#29308direct (N × H)
408. C22⋊C8Q8×C43semidirect
409. C22⋊C8Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#26282
C43×#23162
C43×#20852
C43×#20582
C43×#20572
C43×#19442
C43×#19432
C43×#19422
C43×#19412
C43×#18542
C43×#18532
C43×#18522
C43×#17502
#2930843