Finite Group Databasebeta

← C43×#13222 #24933239

Subgroups — C43×#13222 #24933239

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2534C211yesmaximal, characteristic
2C2×C43×#352C212yesmaximal, complemented
3C2×C43×AΣL(1,𝔽16)C212yesmaximal
4C43×#1800C211yesmaximal, characteristic, complemented
5C4×#99×C43C211yesmaximal, characteristic, complemented
6C2×#123×C43C2211yescharacteristic
7C2×#120×C43C2211yescharacteristic
8C2×C4×D4×C43C2211yescharacteristic
9C22×C22⋊C4×C43C411yescharacteristic, complemented
10C43×#423—21no—
11C2×#100×C43C2212yes—
12C2×#99×C43C2212yes—
13C43×#396—21no—
14C43×#394—21no—
15C43×#388—21no—
16C43×#386—21no—
17C43×#381C411yescharacteristic, complemented
18C43×#380C411yescharacteristic, complemented
19C43×#379C411yescharacteristic, complemented
20C4×C22⋊C4×C43—21no—
21C43×#352—24no—
22C43×AΣL(1,𝔽16)—24no—
23C43×#343—21no—
24C43×#342—21no—
25C25×C43C2×C411yescharacteristic
26C22×D4×C43—21no—
27C22×D4×C43C2311yescharacteristic
28C23×C4×C43C2×C411yescharacteristic
29C23×C4×C43C2×C411yescharacteristic
30C23×C4×C43D411yescharacteristic
31C2×M16×C43—22no—
32#123×C43—22no—
33#123×C43—22no—
34#120×C43—22no—
35#120×C43—22no—
36C4×D4×C43—41no—
37C4×D4×C43—41no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—41no—
49C2×C22⋊C4×C43—41no—
50C2×C22⋊C4×C43C2×C411yescharacteristic
51C2×C22⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C42×C43—41no—
55C2×C42×C43D411yescharacteristic
56C4⋊C8×C43—41no—
57C4⋊C8×C43—41no—
58#100×C43—22no—
59#100×C43—22no—
60#99×C43—22no—
61#99×C43D414yes—
62#95×C43—21no—
63#95×C43—21no—
64#95×C43—21no—
65#95×C43—41no—
66C24×C43—21no—
67C24×C43—22no—
68C24×C43—41no—
69C24×C43—42no—
70C24×C43—41no—
71C24×C43—81no—
72C24×C43C22×C411yescharacteristic
73C24×C43C2×D411yescharacteristic
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—42no—
77C2×D4×C43—42no—
78C2×D4×C43—81no—
79C2×D4×C43C2×D412yes—
80C2×D4×C43#4112yes—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—22no—
89C22×C4×C43—42no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—81no—
93C22×C4×C43—81no—
94C22×C4×C43C22⋊C411yescharacteristic
95C22×C4×C43C22⋊C411yescharacteristic
96C22×C4×C43C22⋊C411yescharacteristic
97C22×C4×C43C22⋊C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99M16×C43—42no—
100M16×C43—42no—
101C2×C8×C43—42no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—81no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—24no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—42no—
112C22⋊C4×C43—42no—
113C22⋊C4×C43—42no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—42no—
119C22⋊C4×C43—81no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—82no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—22no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—42no—
136C23×C43—42no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43—82no—
141C23×C43—84no—
142C23×C43—84no—
143C23×C43—82no—
144C23×C43C2×C22⋊C411yescharacteristic
145C23×C43C4×D412yes—
146C23×C43#12112yes—
147D4×C43—42no—
148D4×C43—42no—
149D4×C43—84no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—44no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—81no—
171C2×C4×C43—81no—
172C2×C4×C43—81no—
173C2×C4×C43—82no—
174C2×C4×C43—82no—
175C2×C4×C43—82no—
176C2×C4×C43#9911yescharacteristic
177C2×C4×C43#9911yescharacteristic
178C2×C4×C43#12411yescharacteristic
179C2×C4×C43#12711yescharacteristic
180C8×C43—82no—
181#13222C4311yesmaximal, characteristic, direct product factor, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—42no—
190C22×C43—42no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—42no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43—84no—
200C22×C43—84no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43#39011yescharacteristic
204C22×C43C2×#9911yescharacteristic
205C22×C43#41011yescharacteristic
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—41no—
213C4×C43—81no—
214C4×C43—81no—
215C4×C43—84no—
216C4×C43—81no—
217#2534C2×C4311yescharacteristic
218C2×#352C2×C4312yescomplemented
219C2×AΣL(1,𝔽16)C2×C4312yes—
220#1800C2×C4311yescharacteristic, complemented
221C4×#99C2×C4311yescharacteristic, complemented
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—42no—
225C2×C43—42no—
226C2×C43—82no—
227C2×C43#196411yescharacteristic
228C2×C43#212011yescharacteristic
229C2×C43#212111yescharacteristic
230C2×#123C22×C4311yescharacteristic
231C2×#120C22×C4311yescharacteristic
232C2×C4×D4C22×C4311yescharacteristic
233C22×C22⋊C4C4×C4311yescharacteristic, complemented
234#423—21no—
235C2×#100C22×C4312yes—
236C2×#99C22×C4312yes—
237#396—21no—
238#394—21no—
239#388—21no—
240#386—21no—
241#381C4×C4311yescharacteristic, complemented
242#380C4×C4311yescharacteristic, complemented
243#379C4×C4311yescharacteristic, complemented
244C4×C22⋊C4—21no—
245#352—24no—
246AΣL(1,𝔽16)—24no—
247#343—21no—
248#342—21no—
249C43#1322211yescharacteristic, direct product factor, Sylow
250C25C2×C4×C4311yescharacteristic
251C22×D4—21no—
252C22×D4C23×C4311yescharacteristic
253C23×C4C2×C4×C4311yescharacteristic
254C23×C4C2×C4×C4311yescharacteristic
255C23×C4D4×C4311yescharacteristic
256C2×M16—22no—
257#123—22no—
258#123—22no—
259#120—22no—
260#120—22no—
261C4×D4—41no—
262C4×D4—41no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C4311yescharacteristic
266C2×C22⋊C4—22no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—41no—
275C2×C22⋊C4C2×C4×C4311yescharacteristic
276C2×C22⋊C4C2×C4×C4311yescharacteristic
277C2×C22⋊C4C2×C4×C4311yescharacteristic
278C2×C22⋊C4D4×C4311yescharacteristic
279C2×C42—41no—
280C2×C42D4×C4311yescharacteristic
281C4⋊C8—41no—
282C4⋊C8—41no—
283#100—22no—
284#100—22no—
285#99—22no—
286#99D4×C4314yes—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—41no—
291C24—21no—
292C24—22no—
293C24—41no—
294C24—42no—
295C24—41no—
296C24—81no—
297C24C22×C4×C4311yescharacteristic
298C24C2×D4×C4311yescharacteristic
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—81no—
304C2×D4C2×D4×C4312yes—
305C2×D4#41×C4312yes—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—81no—
318C22×C4—81no—
319C22×C4C22⋊C4×C4311yescharacteristic
320C22×C4C22⋊C4×C4311yescharacteristic
321C22×C4C22⋊C4×C4311yescharacteristic
322C22×C4C22⋊C4×C4311yescharacteristic
323C22×C4C2×D4×C4311yescharacteristic
324M16—42no—
325M16—42no—
326C2×C8—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—81no—
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—24no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—81no—
345C42—21no—
346C42—21no—
347C42—82no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—22no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—82no—
366C23—84no—
367C23—84no—
368C23—82no—
369C23C2×C22⋊C4×C4311yescharacteristic
370C23C4×D4×C4312yes—
371C23#121×C4312yes—
372D4—42no—
373D4—42no—
374D4—84no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—44no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4#99×C4311yescharacteristic
402C2×C4#99×C4311yescharacteristic
403C2×C4#124×C4311yescharacteristic
404C2×C4#127×C4311yescharacteristic
405C8—82no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—42no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—84no—
424C22—84no—
425C22—81no—
426C22—81no—
427C22C43×#39011yescharacteristic
428C22C2×#99×C4311yescharacteristic
429C22C43×#41011yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—81no—
438C4—81no—
439C4—84no—
440C4—81no—
441C2—21no—
442C2—21no—
443C2—42no—
444C2—42no—
445C2—82no—
446C2C43×#196411yescharacteristic
447C2C43×#212011yescharacteristic
448C2C43×#212111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#99
commutatorC24C22×C4×C43
Frattini, cosocleC22×D4C23×C43
prime radicalC2×#120×C43C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#352C2semidirect
4. C43×#1800C2semidirect
5. C4×#99×C43C2semidirect
9. C22×C22⋊C4×C43C4semidirect
17. C43×#381C4semidirect
18. C43×#380C4semidirect
19. C43×#379C4semidirect
181. #13222C43direct (N × H)
218. C2×#352C2×C43semidirect
220. #1800C2×C43semidirect
221. C4×#99C2×C43semidirect
233. C22×C22⋊C4C4×C43semidirect
241. #381C4×C43semidirect
242. #380C4×C43semidirect
243. #379C4×C43semidirect
249. C43#13222direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25342
C2×C43×#3522
C2×C43×AΣL(1,𝔽16)2
C43×#18002
C4×#99×C432
#1322243