Finite Group Databasebeta

← C43×#29858 #24949875

Subgroups — C43×#29858 #24949875

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#486C211yesmaximal, characteristic, complemented
2C43×#3079C211yesmaximal, characteristic, complemented
3C43×#3038C211yesmaximal, characteristic
4C43×#2922C211yesmaximal, characteristic, complemented
5C43×#2063C214yesmaximal, complemented
6C43×#2051C214yesmaximal, complemented
7C43×#1997C211yesmaximal, characteristic, complemented
8C43×#1965C211yesmaximal, characteristic, complemented
9C43×#1848C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C43C2212yes—
11C2×C4⋊Q8×C43C2211yescharacteristic
12C2×#127×C43C2211yescharacteristic
13C4×#41×C43C2211yescharacteristic
14C43×#486—22no—
15C43×#486—22no—
16C43×#477—21no—
17C43×#476—21no—
18C43×#475—21no—
19C43×#474—21no—
20C43×#460—21no—
21C43×#460—21no—
22C43×#459—21no—
23C43×#459—21no—
24C43×#433—22no—
25C43×#431—22no—
26C2×#108×C43C2214yes—
27C43×#428C2212yes—
28C43×#424C2212yes—
29C43×#423C2211yescharacteristic
30C43×#423C2211yescharacteristic
31C43×#418C2212yes—
32C43×#417C2212yes—
33C2×#102×C43C2214yes—
34C2×#100×C43C2214yes—
35C43×#408C2212yes—
36C4×M16×C43C2211yescharacteristic
37C2×C4×C8×C43C2211yescharacteristic
38C43×#343C2214yes—
39C2×#41×C43C2311yescharacteristic
40C22×Q8×C43—21no—
41C22×D4×C43—21no—
42C22×D4×C43—21no—
43C22×D4×C43C2312yes—
44AGL(1,ℤ/8)×C43—44no—
45C2×SD16×C43—22no—
46C2×D8×C43—22no—
47C2×M16×C43C2312yes—
48C2×M16×C43C2312yes—
49C2×M16×C43C2312yes—
50C22×C8×C43C2312yes—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55#127×C43—21no—
56#127×C43—21no—
57#127×C43—21no—
58#127×C43—21no—
59C4×Q8×C43D411yescharacteristic
60C4×Q8×C43D411yescharacteristic
61C4×D4×C43—21no—
62C4×D4×C43—21no—
63C4×D4×C43D411yescharacteristic
64C4×D4×C43D411yescharacteristic
65#117×C43—21no—
66#117×C43C2311yescharacteristic
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43C2312yes—
69C2×C42×C43—21no—
70C2×C42×C43C2311yescharacteristic
71#108×C43—44no—
72#107×C43—22no—
73#106×C43—22no—
74C4⋊C8×C43—24no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C4⋊C8×C43—21no—
79#103×C43—22no—
80#102×C43—22no—
81#102×C43—28no—
82#102×C43—22no—
83#102×C43—22no—
84#100×C43—44no—
85C22⋊C8×C43—24no—
86#97×C43—21no—
87C4×C8×C43—21no—
88C4×C8×C43D412yes—
89C4×C8×C43D412yes—
90C24×C43—22no—
91#41×C43—22no—
92#41×C43—22no—
93C2×Q8×C43—41no—
94C2×Q8×C43—41no—
95C2×Q8×C43—82no—
96C2×Q8×C43C2×D411yescharacteristic
97C2×D4×C43—21no—
98C2×D4×C43—22no—
99C2×D4×C43—22no—
100C2×D4×C43—24no—
101C2×D4×C43—24no—
102C2×D4×C43—41no—
103C2×D4×C43—41no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C2×D4×C43—82no—
107C2×D4×C43—82no—
108C2×D4×C43C2×D411yescharacteristic
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43C2411yescharacteristic
116SD16×C43—44no—
117D8×C43—44no—
118M16×C43—22no—
119M16×C43—24no—
120M16×C43—24no—
121M16×C43—22no—
122C2×C8×C43—22no—
123C2×C8×C43—22no—
124C2×C8×C43—22no—
125C2×C8×C43—22no—
126C2×C8×C43—22no—
127C2×C8×C43C2×D414yes—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—22no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43C2×D411yescharacteristic
135C4⋊C4×C43C2×D411yescharacteristic
136C22⋊C4×C43—21no—
137C22⋊C4×C43—21no—
138C22⋊C4×C43—21no—
139C42×C43—21no—
140C42×C43—21no—
141C42×C43—21no—
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43C2×D411yescharacteristic
146C23×C43—21no—
147C23×C43—42no—
148C23×C43—44no—
149C23×C43—82no—
150C23×C43—82no—
151C23×C43C2×#4111yescharacteristic
152Q8×C43—21no—
153Q8×C43—21no—
154Q8×C43—82no—
155Q8×C43—82no—
156D4×C43—21no—
157D4×C43—21no—
158D4×C43—42no—
159D4×C43—42no—
160D4×C43—42no—
161D4×C43—44no—
162D4×C43—82no—
163D4×C43—82no—
164D4×C43—82no—
165D4×C43—82no—
166C2×C4×C43—22no—
167C2×C4×C43—22no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—42no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43—42no—
175C2×C4×C43—82no—
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43C22×D411yescharacteristic
181C2×C4×C43C22×D411yescharacteristic
182C2×C4×C43H(5,𝔽2)12yes—
183C2×C4×C432−1+412yes—
184C8×C43—24no—
185C8×C43—42no—
186C8×C43—42no—
187C8×C43—42no—
188#29858C4311yesmaximal, characteristic, direct product factor, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—82no—
195C22×C43—82no—
196C22×C43—82no—
197C22×C43—164no—
198C22×C43C2×#12111yescharacteristic
199C22×C43#54212yes—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—41no—
203C4×C43—41no—
204C4×C43—41no—
205C4×C43—82no—
206C4×C43#47112yes—
207C4×C43#47212yes—
208C4×C43#53511yescharacteristic
209C4×C43#53611yescharacteristic
210C4×C43#53712yes—
211C2×#486C2×C4311yescharacteristic, complemented
212#3079C2×C4311yescharacteristic, complemented
213#3038C2×C4311yescharacteristic
214#2922C2×C4311yescharacteristic, complemented
215#2063C2×C4314yescomplemented
216#2051C2×C4314yescomplemented
217#1997C2×C4311yescharacteristic, complemented
218#1965C2×C4311yescharacteristic, complemented
219#1848C2×C4311yescharacteristic, complemented
220C2×C43—22no—
221C2×C43—81no—
222C2×C43—162no—
223C2×C43#262011yescharacteristic
224C2×C43C2×#47111yescharacteristic
225C2×C43C2×#47211yescharacteristic
226C2×AGL(1,ℤ/8)C22×C4312yes—
227C2×C4⋊Q8C22×C4311yescharacteristic
228C2×#127C22×C4311yescharacteristic
229C4×#41C22×C4311yescharacteristic
230#486—22no—
231#486—22no—
232#477—21no—
233#476—21no—
234#475—21no—
235#474—21no—
236#460—21no—
237#460—21no—
238#459—21no—
239#459—21no—
240#433—22no—
241#431—22no—
242C2×#108C22×C4314yes—
243#428C22×C4312yes—
244#424C22×C4312yes—
245#423C22×C4311yescharacteristic
246#423C22×C4311yescharacteristic
247#418C22×C4312yes—
248#417C22×C4312yes—
249C2×#102C22×C4314yes—
250C2×#100C22×C4314yes—
251#408C22×C4312yes—
252C4×M16C22×C4311yescharacteristic
253C2×C4×C8C22×C4311yescharacteristic
254#343C22×C4314yes—
255C43#2985811yescharacteristic, direct product factor, Sylow
256C2×#41C23×C4311yescharacteristic
257C22×Q8—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4C23×C4312yes—
261AGL(1,ℤ/8)—44no—
262C2×SD16—22no—
263C2×D8—22no—
264C2×M16C23×C4312yes—
265C2×M16C23×C4312yes—
266C2×M16C23×C4312yes—
267C22×C8C23×C4312yes—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272#127—21no—
273#127—21no—
274#127—21no—
275#127—21no—
276C4×Q8D4×C4311yescharacteristic
277C4×Q8D4×C4311yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D4×C4311yescharacteristic
281C4×D4D4×C4311yescharacteristic
282#117—21no—
283#117C23×C4311yescharacteristic
284C2×C4⋊C4—21no—
285C2×C4⋊C4C23×C4312yes—
286C2×C42—21no—
287C2×C42C23×C4311yescharacteristic
288#108—44no—
289#107—22no—
290#106—22no—
291C4⋊C8—24no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296#103—22no—
297#102—22no—
298#102—28no—
299#102—22no—
300#102—22no—
301#100—44no—
302C22⋊C8—24no—
303#97—21no—
304C4×C8—21no—
305C4×C8D4×C4312yes—
306C4×C8D4×C4312yes—
307C24—22no—
308#41—22no—
309#41—22no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—82no—
313C2×Q8C2×D4×C4311yescharacteristic
314C2×D4—21no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—24no—
318C2×D4—24no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—82no—
324C2×D4—82no—
325C2×D4C2×D4×C4311yescharacteristic
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4#41×C4311yescharacteristic
331C22×C4#41×C4311yescharacteristic
332C22×C4C24×C4311yescharacteristic
333SD16—44no—
334D8—44no—
335M16—22no—
336M16—24no—
337M16—24no—
338M16—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8C2×D4×C4314yes—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4C2×D4×C4311yescharacteristic
352C4⋊C4C2×D4×C4311yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42C2×D4×C4311yescharacteristic
360C42C2×D4×C4311yescharacteristic
361C42C2×D4×C4311yescharacteristic
362C42C2×D4×C4311yescharacteristic
363C23—21no—
364C23—42no—
365C23—44no—
366C23—82no—
367C23—82no—
368C23C2×#41×C4311yescharacteristic
369Q8—21no—
370Q8—21no—
371Q8—82no—
372Q8—82no—
373D4—21no—
374D4—21no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—44no—
379D4—82no—
380D4—82no—
381D4—82no—
382D4—82no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4#121×C4311yescharacteristic
394C2×C4#121×C4311yescharacteristic
395C2×C4#121×C4311yescharacteristic
396C2×C4#121×C4311yescharacteristic
397C2×C4C22×D4×C4311yescharacteristic
398C2×C4C22×D4×C4311yescharacteristic
399C2×C4H(5,𝔽2)×C4312yes—
400C2×C42−1+4×C4312yes—
401C8—24no—
402C8—42no—
403C8—42no—
404C8—42no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—164no—
414C22C2×#121×C4311yescharacteristic
415C22C43×#54212yes—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4C43×#47112yes—
423C4C43×#47212yes—
424C4C43×#53511yescharacteristic
425C4C43×#53611yescharacteristic
426C4C43×#53712yes—
427C2—22no—
428C2—81no—
429C2—162no—
430C2C43×#262011yescharacteristic
431C2C2×C43×#47111yescharacteristic
432C2C2×C43×#47211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3038C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#486C2semidirect
2. C43×#3079C2semidirect
4. C43×#2922C2semidirect
5. C43×#2063C2semidirect
6. C43×#2051C2semidirect
7. C43×#1997C2semidirect
8. C43×#1965C2semidirect
9. C43×#1848C2semidirect
188. #29858C43direct (N × H)
211. C2×#486C2×C43semidirect
212. #3079C2×C43semidirect
214. #2922C2×C43semidirect
215. #2063C2×C43semidirect
216. #2051C2×C43semidirect
217. #1997C2×C43semidirect
218. #1965C2×C43semidirect
219. #1848C2×C43semidirect
255. C43#29858direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4862
C43×#30792
C43×#30382
C43×#29222
C43×#20632
C43×#20512
C43×#19972
C43×#19652
C43×#18482
#2985843