Finite Group Databasebeta

← C43×#60175 #24980192

Subgroups — C43×#60175 #24980192

Order 11008.

2650 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#578C211yesmaximal, characteristic
2C4×2−1+4×C43C212yesmaximal, complemented
3C43×#2952C213yesmaximal, complemented
4C43×#2950C213yesmaximal, complemented
5C43×#2947C216yesmaximal, complemented
6C4×#137×C43C216yesmaximal, complemented
7C43×#2943C213yesmaximal, complemented
8C2×C43×#441C213yesmaximal, complemented
9C43×#2912C211yesmaximal, characteristic, complemented
10C43×#2898C212yesmaximal, complemented
11C43×#2875C211yesmaximal, characteristic, complemented
12C2×2−1+4×C43C2212yes—
13C43×#578C4116yescomplemented
14C2×#137×C43C2216yes—
15C2×#135×C43C2213yes—
16C22×Q16×C43C2213yes—
17C2×#131×C43C2211yescharacteristic
18C2×#131×C43C2211yescharacteristic
19C43×#520—26no—
20C43×#520C2216yes—
21C43×#520C2212yes—
22C43×#519—22no—
23C43×#519C2216yes—
24C4×#41×C43—26no—
25C4×#41×C43C2216yes—
26C4×#41×C43C2211yescharacteristic
27C2×C4×Q8×C43—22no—
28C2×C4×Q8×C43C2216yes—
29C43×#442C2211yescharacteristic
30C43×#442C2213yes—
31C43×#441C2213yes—
32C43×#441C2216yes—
33C43×#441C2216yes—
34C43×#441C2216yes—
35C43×#441C2213yes—
36C43×#440C2216yes—
37C43×#440C2216yes—
38C4×Q16×C43C22112yes—
39C4×SD16×C43C22112yes—
40C43×#428C2216yes—
41C43×#427C2213yes—
42C2×#106×C43C2213yes—
43C43×#419C2216yes—
44C43×#417C2216yes—
45C43×#416C2216yes—
46C2×#103×C43C2216yes—
47C43×#405C2213yes—
48C43×#405C2213yes—
49C4×M16×C43C2213yes—
50C2×#97×C43C2213yes—
512−1+4×C43—28no—
522−1+4×C43C2×C4116yescomplemented
53C2×#41×C43—26no—
54C2×#41×C43C2316yes—
55C2×#41×C43C2311yescharacteristic
56C22×Q8×C43—22no—
57C22×Q8×C43C2316yes—
58#137×C43C2×C4148yescomplemented
59#135×C43C2×C4124yescomplemented
60C2×Q16×C43C2×C4124yescomplemented
61C2×Q16×C43C2313yes—
62C2×Q16×C43C2316yes—
63C2×SD16×C43C2316yes—
64C2×D8×C43C2311yescharacteristic
65#131×C43—24no—
66#131×C43C2×C418yescomplemented
67C2×M16×C43C2313yes—
68C2×M16×C43C2313yes—
69C22×C8×C43C2313yes—
70C22×C8×C43C2313yes—
71C4×Q8×C43—22no—
72C4×Q8×C43—26no—
73C4×Q8×C43—26no—
74C4×Q8×C43—26no—
75C4×Q8×C43—26no—
76C4×Q8×C43D412yes—
77C4×Q8×C43C2316yes—
78C4×Q8×C43C23112yes—
79C4×Q8×C43C2316yes—
80C4×D4×C43—26no—
81C4×D4×C43—26no—
82C4×D4×C43—26no—
83C4×D4×C43—212no—
84C4×D4×C43D416yes—
85C4×D4×C43C2312yes—
86C4×D4×C43C2316yes—
87#117×C43—26no—
88#117×C43—212no—
89#117×C43—26no—
90#117×C43C2316yes—
91#117×C43C2313yes—
92C2×C4⋊C4×C43—26no—
93C2×C4⋊C4×C43—26no—
94C2×C4⋊C4×C43C2316yes—
95C2×C42×C43—26no—
96C2×C42×C43—26no—
97C2×C42×C43C2313yes—
98#107×C43C2316yes—
99#106×C43C2313yes—
100#106×C43C2316yes—
101#106×C43C2311yescharacteristic
102#103×C43C2316yes—
103#103×C43C23112yes—
104#103×C43C2316yes—
105#102×C43C2312yes—
106#102×C43C2316yes—
107#97×C43C2311yescharacteristic
108#97×C43C2313yes—
109#97×C43C2313yes—
110#97×C43C2313yes—
111C4×C8×C43C2316yes—
112#41×C43—248no—
113#41×C43—212no—
114#41×C43C22×C4124yes—
115#41×C43C22×C414yes—
116#41×C43#4114yes—
117C2×Q8×C43—216no—
118C2×Q8×C43—26no—
119C2×Q8×C43—212no—
120C2×Q8×C43C22×C4124yes—
121C2×Q8×C43C2×D411yescharacteristic
122C2×Q8×C43C2416yes—
123C2×D4×C43—26no—
124C2×D4×C43C2×D413yes—
125C2×D4×C43C2412yes—
126C22×C4×C43—26no—
127C22×C4×C43—22no—
128C22×C4×C43—26no—
129C22×C4×C43—26no—
130C22×C4×C43—26no—
131C22×C4×C43C2×D416yes—
132C22×C4×C43C2413yes—
133Q16×C43C22×C4112yes—
134Q16×C43C22×C4124yes—
135SD16×C43C22×C4124yes—
136D8×C43C22×C414yes—
137M16×C43—26no—
138M16×C43C22×C4112yes—
139C2×C8×C43—26no—
140C2×C8×C43C22×C4112yes—
141C2×C8×C43C2413yes—
142C2×C8×C43C2411yescharacteristic
143C2×C8×C43C2413yes—
144C2×C8×C43C2411yescharacteristic
145C4⋊C4×C43—26no—
146C4⋊C4×C43—212no—
147C4⋊C4×C43—26no—
148C4⋊C4×C43—26no—
149C4⋊C4×C43C2×D416yes—
150C4⋊C4×C43C2416yes—
151C4⋊C4×C43C2412yes—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—26no—
154C22⋊C4×C43—26no—
155C22⋊C4×C43C2×D416yes—
156C42×C43—26no—
157C42×C43—26no—
158C42×C43—212no—
159C42×C43—26no—
160C42×C43C2×D416yes—
161C42×C43C2413yes—
162C42×C43C2411yescharacteristic
163C23×C43—22no—
164C23×C43C22×D413yes—
165Q8×C43—224no—
166Q8×C43—26no—
167Q8×C43C4×D414yes—
168Q8×C43C23×C4112yes—
169D4×C43—224no—
170D4×C43—22no—
171D4×C43C4×D4112yes—
172D4×C43C23×C414yes—
173C2×C4×C43—224no—
174C2×C4×C43—26no—
175C2×C4×C43—224no—
176C2×C4×C43—22no—
177C2×C4×C43—26no—
178C2×C4×C43—46no—
179C2×C4×C43—44no—
180C2×C4×C43—86no—
181C2×C4×C43—86no—
182C2×C4×C43C23×C416yes—
183C2×C4×C43C22×D412yes—
184C2×C4×C43C22×D416yes—
185C2×C4×C43C22×D413yes—
186C2×C4×C43C2×#4116yes—
187C2×C4×C43C2511yescharacteristic
188C8×C43—21no—
189C8×C43—23no—
190C8×C43C23×C412yes—
191C8×C43C23×C416yes—
192#60175C4311yesmaximal, characteristic, direct product factor, Sylow
193C22×C43—26no—
194C22×C43—24no—
195C22×C43—42no—
196C22×C43—42no—
197C22×C43C2×C4×D416yes—
198C22×C43C23×D411yescharacteristic
199C4×C43—22no—
200C4×C43—26no—
201C4×C43—212no—
202C4×C43—42no—
203C4×C43—46no—
204C4×C43C2×C4×D416yes—
205C4×C43C24×C411yescharacteristic
206C4×C43C22×#4111yescharacteristic
207C2×#578C2×C4311yescharacteristic
208C4×2−1+4C2×C4312yescomplemented
209#2952C2×C4313yescomplemented
210#2950C2×C4313yescomplemented
211#2947C2×C4316yescomplemented
212C4×#137C2×C4316yescomplemented
213#2943C2×C4313yescomplemented
214C2×#441C2×C4313yescomplemented
215#2912C2×C4311yescharacteristic, complemented
216#2898C2×C4312yescomplemented
217#2875C2×C4311yescharacteristic, complemented
218C2×C43—26no—
219C2×C43—44no—
220C2×C43C22×C4×D411yescharacteristic
221C2×C43#358612yes—
222C2×2−1+4C22×C4312yes—
223#578C4×C43116yescomplemented
224C2×#137C22×C4316yes—
225C2×#135C22×C4313yes—
226C22×Q16C22×C4313yes—
227C2×#131C22×C4311yescharacteristic
228C2×#131C22×C4311yescharacteristic
229#520—26no—
230#520C22×C4316yes—
231#520C22×C4312yes—
232#519—22no—
233#519C22×C4316yes—
234C4×#41—26no—
235C4×#41C22×C4316yes—
236C4×#41C22×C4311yescharacteristic
237C2×C4×Q8—22no—
238C2×C4×Q8C22×C4316yes—
239#442C22×C4311yescharacteristic
240#442C22×C4313yes—
241#441C22×C4313yes—
242#441C22×C4316yes—
243#441C22×C4316yes—
244#441C22×C4316yes—
245#441C22×C4313yes—
246#440C22×C4316yes—
247#440C22×C4316yes—
248C4×Q16C22×C43112yes—
249C4×SD16C22×C43112yes—
250#428C22×C4316yes—
251#427C22×C4313yes—
252C2×#106C22×C4313yes—
253#419C22×C4316yes—
254#417C22×C4316yes—
255#416C22×C4316yes—
256C2×#103C22×C4316yes—
257#405C22×C4313yes—
258#405C22×C4313yes—
259C4×M16C22×C4313yes—
260C2×#97C22×C4313yes—
261C43#6017511yescharacteristic, direct product factor, Sylow
2622−1+4—28no—
2632−1+4C2×C4×C43116yescomplemented
264C2×#41—26no—
265C2×#41C23×C4316yes—
266C2×#41C23×C4311yescharacteristic
267C22×Q8—22no—
268C22×Q8C23×C4316yes—
269#137C2×C4×C43148yescomplemented
270#135C2×C4×C43124yescomplemented
271C2×Q16C2×C4×C43124yescomplemented
272C2×Q16C23×C4313yes—
273C2×Q16C23×C4316yes—
274C2×SD16C23×C4316yes—
275C2×D8C23×C4311yescharacteristic
276#131—24no—
277#131C2×C4×C4318yescomplemented
278C2×M16C23×C4313yes—
279C2×M16C23×C4313yes—
280C22×C8C23×C4313yes—
281C22×C8C23×C4313yes—
282C4×Q8—22no—
283C4×Q8—26no—
284C4×Q8—26no—
285C4×Q8—26no—
286C4×Q8—26no—
287C4×Q8D4×C4312yes—
288C4×Q8C23×C4316yes—
289C4×Q8C23×C43112yes—
290C4×Q8C23×C4316yes—
291C4×D4—26no—
292C4×D4—26no—
293C4×D4—26no—
294C4×D4—212no—
295C4×D4D4×C4316yes—
296C4×D4C23×C4312yes—
297C4×D4C23×C4316yes—
298#117—26no—
299#117—212no—
300#117—26no—
301#117C23×C4316yes—
302#117C23×C4313yes—
303C2×C4⋊C4—26no—
304C2×C4⋊C4—26no—
305C2×C4⋊C4C23×C4316yes—
306C2×C42—26no—
307C2×C42—26no—
308C2×C42C23×C4313yes—
309#107C23×C4316yes—
310#106C23×C4313yes—
311#106C23×C4316yes—
312#106C23×C4311yescharacteristic
313#103C23×C4316yes—
314#103C23×C43112yes—
315#103C23×C4316yes—
316#102C23×C4312yes—
317#102C23×C4316yes—
318#97C23×C4311yescharacteristic
319#97C23×C4313yes—
320#97C23×C4313yes—
321#97C23×C4313yes—
322C4×C8C23×C4316yes—
323#41—248no—
324#41—212no—
325#41C22×C4×C43124yes—
326#41C22×C4×C4314yes—
327#41#41×C4314yes—
328C2×Q8—216no—
329C2×Q8—26no—
330C2×Q8—212no—
331C2×Q8C22×C4×C43124yes—
332C2×Q8C2×D4×C4311yescharacteristic
333C2×Q8C24×C4316yes—
334C2×D4—26no—
335C2×D4C2×D4×C4313yes—
336C2×D4C24×C4312yes—
337C22×C4—26no—
338C22×C4—26no—
339C22×C4—26no—
340C22×C4—22no—
341C22×C4—26no—
342C22×C4C2×D4×C4316yes—
343C22×C4C24×C4313yes—
344Q16C22×C4×C43112yes—
345Q16C22×C4×C43124yes—
346SD16C22×C4×C43124yes—
347D8C22×C4×C4314yes—
348M16—26no—
349M16C22×C4×C43112yes—
350C2×C8—26no—
351C2×C8C22×C4×C43112yes—
352C2×C8C24×C4313yes—
353C2×C8C24×C4311yescharacteristic
354C2×C8C24×C4313yes—
355C2×C8C24×C4311yescharacteristic
356C4⋊C4—26no—
357C4⋊C4—212no—
358C4⋊C4—26no—
359C4⋊C4—26no—
360C4⋊C4C2×D4×C4316yes—
361C4⋊C4C24×C4316yes—
362C4⋊C4C24×C4312yes—
363C22⋊C4—26no—
364C22⋊C4—22no—
365C22⋊C4—26no—
366C22⋊C4C2×D4×C4316yes—
367C42—26no—
368C42—26no—
369C42—212no—
370C42—26no—
371C42C2×D4×C4316yes—
372C42C24×C4313yes—
373C42C24×C4311yescharacteristic
374C23—22no—
375C23C22×D4×C4313yes—
376Q8—224no—
377Q8—26no—
378Q8C4×D4×C4314yes—
379Q8C23×C4×C43112yes—
380D4—224no—
381D4—22no—
382D4C4×D4×C43112yes—
383D4C23×C4×C4314yes—
384C2×C4—224no—
385C2×C4—26no—
386C2×C4—224no—
387C2×C4—22no—
388C2×C4—26no—
389C2×C4—46no—
390C2×C4—44no—
391C2×C4—86no—
392C2×C4—86no—
393C2×C4C23×C4×C4316yes—
394C2×C4C22×D4×C4312yes—
395C2×C4C22×D4×C4316yes—
396C2×C4C22×D4×C4313yes—
397C2×C4C2×#41×C4316yes—
398C2×C4C25×C4311yescharacteristic
399C8—21no—
400C8—23no—
401C8C23×C4×C4312yes—
402C8C23×C4×C4316yes—
403C22—26no—
404C22—24no—
405C22—42no—
406C22—42no—
407C22C2×C4×D4×C4316yes—
408C22C23×D4×C4311yescharacteristic
409C4—212no—
410C4—22no—
411C4—26no—
412C4—42no—
413C4—46no—
414C4C2×C4×D4×C4316yes—
415C4C24×C4×C4311yescharacteristic
416C4C22×#41×C4311yescharacteristic
417C2—26no—
418C2—44no—
419C2C22×C4×D4×C4311yescharacteristic
420C2C43×#358612yes—
subgroupG/H
center, socleC22×C43C23×D4
commutatorC4C24×C4×C43
Frattini, cosocleC2×C4C25×C43
prime radicalC2×C43×#578C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C4×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×2−1+4×C43C2semidirect
3. C43×#2952C2semidirect
4. C43×#2950C2semidirect
5. C43×#2947C2semidirect
6. C4×#137×C43C2semidirect
7. C43×#2943C2semidirect
8. C2×C43×#441C2semidirect
9. C43×#2912C2semidirect
10. C43×#2898C2semidirect
11. C43×#2875C2semidirect
13. C43×#578C4semidirect
52. 2−1+4×C43C2×C4semidirect
58. #137×C43C2×C4semidirect
59. #135×C43C2×C4semidirect
60. C2×Q16×C43C2×C4semidirect
66. #131×C43C2×C4semidirect
192. #60175C43direct (N × H)
208. C4×2−1+4C2×C43semidirect
209. #2952C2×C43semidirect
210. #2950C2×C43semidirect
211. #2947C2×C43semidirect
212. C4×#137C2×C43semidirect
213. #2943C2×C43semidirect
214. C2×#441C2×C43semidirect
215. #2912C2×C43semidirect
216. #2898C2×C43semidirect
217. #2875C2×C43semidirect
223. #578C4×C43semidirect
261. C43#60175direct (N × H)
263. 2−1+4C2×C4×C43semidirect
269. #137C2×C4×C43semidirect
270. #135C2×C4×C43semidirect
271. C2×Q16C2×C4×C43semidirect
277. #131C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5782
C4×2−1+4×C432
C43×#29522
C43×#29502
C43×#29472
C4×#137×C432
C43×#29432
C2×C43×#4412
C43×#29122
C43×#28982
C43×#28752
#6017543