Finite Group Databasebeta

← C43×#9097 #24929114

Subgroups — C43×#9097 #24929114

Order 11008.

520 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2965C211yesmaximal, characteristic, complemented
2C4×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic
3C43×#1477C211yesmaximal, characteristic, complemented
4C2×C43×D4⋊C8C211yesmaximal, characteristic, complemented
5C43×#1460C211yesmaximal, characteristic, complemented
6C43×#1283C211yesmaximal, characteristic, complemented
7C43×#1278C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C43C411yescharacteristic
9C4×#41×C43C2211yescharacteristic
10C2×C4×D4×C43C2211yescharacteristic
11C43×#446—21no—
12C43×#442—21no—
13C43×#440—21no—
14C4×SD16×C43—21no—
15C4×D8×C43—21no—
16C43×#436—21no—
17C43×#435—22no—
18C43×#431—21no—
19C43×#431C2211yescharacteristic
20C43×#431C2211yescharacteristic
21C43×#428C411yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C43×#418C411yescharacteristic
24C43×#417C411yescharacteristic
25C4×M16×C43—21no—
26C4×M16×C43C2211yescharacteristic
27C2×C4×C8×C43C2211yescharacteristic
28C43×Q8⋊C8—21no—
29C43×D4⋊C8—21no—
30C43×D4⋊C8—21no—
31C43×D4⋊C8—21no—
32C43×#323—22no—
33C2×#41×C43C2×C411yescharacteristic
34C22×D4×C43C2×C411yescharacteristic
35C23×C4×C43—21no—
36AGL(1,ℤ/8)×C43—22no—
37AGL(1,ℤ/8)×C43—22no—
38C2×SD16×C43—21no—
39C2×D8×C43—21no—
40C2×M16×C43—22no—
41C2×M16×C43C2×C411yescharacteristic
42C2×M16×C43C2×C411yescharacteristic
43C22×C8×C43—21no—
44C22×C8×C43—21no—
45C4×Q8×C43D411yescharacteristic
46C4×Q8×C43D411yescharacteristic
47C4×D4×C43—21no—
48C4×D4×C43—21no—
49C4×D4×C43—21no—
50C4×D4×C43—21no—
51C4×D4×C43—21no—
52C4×D4×C43—21no—
53C4×D4×C43D411yescharacteristic
54C4×D4×C43D411yescharacteristic
55#117×C43—21no—
56#117×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C42×C43—21no—
60C2×C42×C43C2311yescharacteristic
61#107×C43—21no—
62#106×C43—21no—
63C4⋊C8×C43—22no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68#103×C43—21no—
69#102×C43—21no—
70#102×C43—21no—
71#102×C43—21no—
72C22⋊C8×C43—22no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43D412yes—
75#97×C43—22no—
76#97×C43—21no—
77C4×C8×C43—21no—
78C4×C8×C43—21no—
79C4×C8×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43D411yescharacteristic
82C4×C8×C43D411yescharacteristic
83C24×C43—21no—
84#41×C43—21no—
85#41×C43—21no—
86#41×C43—21no—
87#41×C43—21no—
88C2×Q8×C43C22⋊C411yescharacteristic
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43C22⋊C411yescharacteristic
96C2×D4×C43M1612yescomplemented
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—81no—
104C22×C4×C43—81no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43#4111yescharacteristic
108SD16×C43—24no—
109D8×C43—24no—
110M16×C43—21no—
111M16×C43—21no—
112M16×C43—21no—
113M16×C43—44no—
114M16×C43M1612yescomplemented
115C2×C8×C43—21no—
116C2×C8×C43—21no—
117C2×C8×C43—21no—
118C2×C8×C43—21no—
119C2×C8×C43—22no—
120C2×C8×C43—42no—
121C2×C8×C43—41no—
122C2×C8×C43—41no—
123C2×C8×C43—81no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43C22⋊C411yescharacteristic
129C4⋊C4×C43C22⋊C411yescharacteristic
130C22⋊C4×C43—21no—
131C22⋊C4×C43—21no—
132C22⋊C4×C43—21no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C42×C43—21no—
136C42×C43—21no—
137C42×C43—21no—
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43#4111yescharacteristic
142C23×C43—21no—
143C23×C43—22no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—81no—
147C23×C43—81no—
148C23×C43C4×D411yescharacteristic
149Q8×C43—21no—
150Q8×C43—21no—
151D4×C43—21no—
152D4×C43—22no—
153D4×C43—21no—
154D4×C43—22no—
155D4×C43—41no—
156D4×C43—41no—
157D4×C43—41no—
158D4×C43—41no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—41no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—82no—
172C2×C4×C43—81no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43C2×C22⋊C411yescharacteristic
176C2×C4×C43C4×D411yescharacteristic
177C2×C4×C43#12011yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12311yescharacteristic
181C2×C4×C43C2×M1611yescharacteristic
182C2×C4×C43C2×M1611yescharacteristic
183C2×C4×C43#13111yescharacteristic
184C2×C4×C43#13111yescharacteristic
185C8×C43—22no—
186C8×C43—22no—
187C8×C43—41no—
188C8×C43—42no—
189C8×C43—41no—
190C8×C43—81no—
191C8×C43—81no—
192#9097C4311yesmaximal, characteristic, direct product factor, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—42no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—82no—
200C22×C43—82no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43#38611yescharacteristic
204C22×C43#43511yescharacteristic
205C22×C43#43611yescharacteristic
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—81no—
213C4×C43#40711yescharacteristic
214C4×C43#40811yescharacteristic
215C4×C43#43511yescharacteristic
216C4×C43#43611yescharacteristic
217C4×C43#47111yescharacteristic
218C4×C43#47211yescharacteristic
219#2965C2×C4311yescharacteristic, complemented
220C4×AGL(1,ℤ/8)C2×C4311yescharacteristic
221#1477C2×C4311yescharacteristic, complemented
222C2×D4⋊C8C2×C4311yescharacteristic, complemented
223#1460C2×C4311yescharacteristic, complemented
224#1283C2×C4311yescharacteristic, complemented
225#1278C2×C4311yescharacteristic, complemented
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—81no—
229C2×C43—82no—
230C2×C43#187011yescharacteristic
231C2×C43#190611yescharacteristic
232C2×C43#190711yescharacteristic
233C2×AGL(1,ℤ/8)C4×C4311yescharacteristic
234C4×#41C22×C4311yescharacteristic
235C2×C4×D4C22×C4311yescharacteristic
236#446—21no—
237#442—21no—
238#440—21no—
239C4×SD16—21no—
240C4×D8—21no—
241#436—21no—
242#435—22no—
243#431—21no—
244#431C22×C4311yescharacteristic
245#431C22×C4311yescharacteristic
246#428C4×C4311yescharacteristic
247C2×C4⋊C8C22×C4311yescharacteristic
248#418C4×C4311yescharacteristic
249#417C4×C4311yescharacteristic
250C4×M16—21no—
251C4×M16C22×C4311yescharacteristic
252C2×C4×C8C22×C4311yescharacteristic
253Q8⋊C8—21no—
254D4⋊C8—21no—
255D4⋊C8—21no—
256D4⋊C8—21no—
257#323—22no—
258C43#909711yescharacteristic, direct product factor, Sylow
259C2×#41C2×C4×C4311yescharacteristic
260C22×D4C2×C4×C4311yescharacteristic
261C23×C4—21no—
262AGL(1,ℤ/8)—22no—
263AGL(1,ℤ/8)—22no—
264C2×SD16—21no—
265C2×D8—21no—
266C2×M16—22no—
267C2×M16C2×C4×C4311yescharacteristic
268C2×M16C2×C4×C4311yescharacteristic
269C22×C8—21no—
270C22×C8—21no—
271C4×Q8D4×C4311yescharacteristic
272C4×Q8D4×C4311yescharacteristic
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4D4×C4311yescharacteristic
280C4×D4D4×C4311yescharacteristic
281#117—21no—
282#117C2×C4×C4311yescharacteristic
283C2×C4⋊C4C2×C4×C4311yescharacteristic
284C2×C22⋊C4—21no—
285C2×C42—21no—
286C2×C42C23×C4311yescharacteristic
287#107—21no—
288#106—21no—
289C4⋊C8—22no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294#103—21no—
295#102—21no—
296#102—21no—
297#102—21no—
298C22⋊C8—22no—
299C22⋊C8—21no—
300C22⋊C8D4×C4312yes—
301#97—22no—
302#97—21no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—21no—
306C4×C8—21no—
307C4×C8D4×C4311yescharacteristic
308C4×C8D4×C4311yescharacteristic
309C24—21no—
310#41—21no—
311#41—21no—
312#41—21no—
313#41—21no—
314C2×Q8C22⋊C4×C4311yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4C22⋊C4×C4311yescharacteristic
322C2×D4M16×C4312yescomplemented
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—81no—
330C22×C4—81no—
331C22×C4C22×C4×C4311yescharacteristic
332C22×C4C2×D4×C4311yescharacteristic
333C22×C4#41×C4311yescharacteristic
334SD16—24no—
335D8—24no—
336M16—21no—
337M16—21no—
338M16—21no—
339M16—44no—
340M16M16×C4312yescomplemented
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—22no—
346C2×C8—42no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—81no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4C22⋊C4×C4311yescharacteristic
355C4⋊C4C22⋊C4×C4311yescharacteristic
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—21no—
362C42—21no—
363C42—21no—
364C42C2×D4×C4311yescharacteristic
365C42C2×D4×C4311yescharacteristic
366C42C2×D4×C4311yescharacteristic
367C42#41×C4311yescharacteristic
368C23—21no—
369C23—22no—
370C23—41no—
371C23—41no—
372C23—81no—
373C23—81no—
374C23C4×D4×C4311yescharacteristic
375Q8—21no—
376Q8—21no—
377D4—21no—
378D4—22no—
379D4—21no—
380D4—22no—
381D4—41no—
382D4—41no—
383D4—41no—
384D4—41no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4C2×C22⋊C4×C4311yescharacteristic
402C2×C4C4×D4×C4311yescharacteristic
403C2×C4#120×C4311yescharacteristic
404C2×C4#121×C4311yescharacteristic
405C2×C4#121×C4311yescharacteristic
406C2×C4#123×C4311yescharacteristic
407C2×C4C2×M16×C4311yescharacteristic
408C2×C4C2×M16×C4311yescharacteristic
409C2×C4#131×C4311yescharacteristic
410C2×C4#131×C4311yescharacteristic
411C8—22no—
412C8—22no—
413C8—41no—
414C8—42no—
415C8—41no—
416C8—81no—
417C8—81no—
418C22—21no—
419C22—21no—
420C22—41no—
421C22—42no—
422C22—41no—
423C22—41no—
424C22—82no—
425C22—82no—
426C22—81no—
427C22—81no—
428C22C43×#38611yescharacteristic
429C22C43×#43511yescharacteristic
430C22C43×#43611yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—81no—
438C4C43×#40711yescharacteristic
439C4C43×#40811yescharacteristic
440C4C43×#43511yescharacteristic
441C4C43×#43611yescharacteristic
442C4C43×#47111yescharacteristic
443C4C43×#47211yescharacteristic
444C2—21no—
445C2—21no—
446C2—81no—
447C2—82no—
448C2C43×#187011yescharacteristic
449C2C43×#190611yescharacteristic
450C2C43×#190711yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#386
prime radicalC2×AGL(1,ℤ/8)×C43C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2965C2semidirect
3. C43×#1477C2semidirect
4. C2×C43×D4⋊C8C2semidirect
5. C43×#1460C2semidirect
6. C43×#1283C2semidirect
7. C43×#1278C2semidirect
96. C2×D4×C43M16semidirect
114. M16×C43M16semidirect
192. #9097C43direct (N × H)
219. #2965C2×C43semidirect
221. #1477C2×C43semidirect
222. C2×D4⋊C8C2×C43semidirect
223. #1460C2×C43semidirect
224. #1283C2×C43semidirect
225. #1278C2×C43semidirect
258. C43#9097direct (N × H)
322. C2×D4M16×C43semidirect
340. M16M16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#29652
C4×AGL(1,ℤ/8)×C432
C43×#14772
C2×C43×D4⋊C82
C43×#14602
C43×#12832
C43×#12782
#909743