Finite Group Databasebeta

← C43×#28670 #24948687

Subgroups — C43×#28670 #24948687

Order 11008.

698 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3165C211yesmaximal, characteristic, complemented
2C43×#3138C211yesmaximal, characteristic
3C2×C43×#486C211yesmaximal, characteristic
4C43×#2960C211yesmaximal, characteristic, complemented
5C43×#2063C214yesmaximal, complemented
6C43×#1997C211yesmaximal, characteristic, complemented
7C43×#1965C211yesmaximal, characteristic
8C43×#1931C214yesmaximal, complemented
9C4×#108×C43C211yesmaximal, characteristic, complemented
10C43×#533C2211yescharacteristic
11C2×C4⋊Q8×C43C2211yescharacteristic
12C2×#127×C43C2211yescharacteristic
13C43×#501—22no—
14C43×#500—21no—
15C43×#498—21no—
16C43×#490—22no—
17C43×#486—21no—
18C43×#486—21no—
19C43×#486—21no—
20C43×#486—21no—
21C43×#486—21no—
22C43×#486—21no—
23C43×#446—21no—
24C43×#446—21no—
25C8×Q8×C43—21no—
26C8×Q8×C43—21no—
27C2×#108×C43C2212yes—
28C43×#428C2214yes—
29C43×#424C2212yes—
30C43×#423C2211yescharacteristic
31C43×#418C2214yes—
32C2×#102×C43C2212yes—
33C2×#102×C43C2212yes—
34C2×#100×C43C2214yes—
35C43×#405C2212yes—
36C4×M16×C43C2211yescharacteristic
37C4×M16×C43C2211yescharacteristic
38C2×C4×C8×C43C2211yescharacteristic
39C43×#343C2214yes—
40C43×#341C2212yes—
41C22×Q8×C43—21no—
42C22×D4×C43—21no—
43C22×D4×C43—21no—
44C22×D4×C43C2312yes—
45C2×M16×C43C2312yes—
46C2×M16×C43C2312yes—
47C2×M16×C43C2312yes—
48C22×C8×C43C2311yescharacteristic
49C22×C8×C43C2311yescharacteristic
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43D411yescharacteristic
55C4⋊Q8×C43D411yescharacteristic
56#127×C43—21no—
57#127×C43—21no—
58#127×C43—21no—
59#127×C43—21no—
60#125×C43D412yes—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43—21no—
65#117×C43C2312yes—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43C2312yes—
68C2×C42×C43C2311yescharacteristic
69#108×C43—24no—
70#107×C43—24no—
71#106×C43—24no—
72C4⋊C8×C43—22no—
73C4⋊C8×C43—22no—
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76#102×C43—22no—
77#102×C43—22no—
78#102×C43—22no—
79#102×C43—22no—
80#102×C43—24no—
81#102×C43—24no—
82#100×C43—28no—
83#97×C43—22no—
84#97×C43—21no—
85#97×C43—21no—
86C4×C8×C43—22no—
87C4×C8×C43—21no—
88C4×C8×C43—21no—
89C4×C8×C43D411yescharacteristic
90C4×C8×C43D411yescharacteristic
91C4×C8×C43D411yescharacteristic
92C4×C8×C43D411yescharacteristic
93C24×C43—22no—
94C2×Q8×C43—21no—
95C2×Q8×C43—21no—
96C2×Q8×C43—41no—
97C2×Q8×C43—41no—
98C2×Q8×C43—82no—
99C2×D4×C43—22no—
100C2×D4×C43—22no—
101C2×D4×C43—24no—
102C2×D4×C43—24no—
103C2×D4×C43—41no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C2×D4×C43—41no—
107C2×D4×C43—82no—
108C2×D4×C43—82no—
109C22×C4×C43—22no—
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43C2411yescharacteristic
113M16×C43—22no—
114M16×C43—24no—
115M16×C43—22no—
116M16×C43—22no—
117M16×C43#4114yes—
118C2×C8×C43—22no—
119C2×C8×C43—22no—
120C2×C8×C43—22no—
121C2×C8×C43—22no—
122C2×C8×C43—22no—
123C2×C8×C43C2×D411yescharacteristic
124C2×C8×C43C2×D411yescharacteristic
125C2×C8×C43C2×D411yescharacteristic
126C2×C8×C43C2×D411yescharacteristic
127C4⋊C4×C43—22no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43C2×D412yes—
136C4⋊C4×C43C2×D412yes—
137C22⋊C4×C43—22no—
138C42×C43—22no—
139C42×C43C2×D411yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43C2×D411yescharacteristic
142C42×C43C2×D411yescharacteristic
143C23×C43—42no—
144C23×C43—44no—
145C23×C43—82no—
146C23×C43—82no—
147C23×C43C2×#4111yescharacteristic
148Q8×C43—42no—
149Q8×C43—42no—
150Q8×C43—82no—
151Q8×C43—82no—
152D4×C43—42no—
153D4×C43—42no—
154D4×C43—44no—
155D4×C43—82no—
156D4×C43—82no—
157D4×C43—82no—
158D4×C43—82no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43—22no—
163C2×C4×C43—42no—
164C2×C4×C43—82no—
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43C22×D411yescharacteristic
170C2×C4×C43C22×D411yescharacteristic
171C2×C4×C43C2×#4112yes—
172C2×C4×C432−1+412yes—
173C8×C43—21no—
174C8×C43—21no—
175C8×C43—21no—
176C8×C43—21no—
177C8×C43—24no—
178C8×C43—42no—
179C8×C43—42no—
180#28670C4311yesmaximal, characteristic, direct product factor, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—82no—
184C22×C43—82no—
185C22×C43—82no—
186C22×C43—164no—
187C22×C43C2×#12111yescharacteristic
188C22×C43#55612yes—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—42no—
192C4×C43—42no—
193C4×C43—82no—
194C4×C43#47112yes—
195C4×C43#47212yes—
196C4×C43#53211yescharacteristic
197C4×C43#53611yescharacteristic
198C4×C43#54812yes—
199#3165C2×C4311yescharacteristic, complemented
200#3138C2×C4311yescharacteristic
201C2×#486C2×C4311yescharacteristic
202#2960C2×C4311yescharacteristic, complemented
203#2063C2×C4314yescomplemented
204#1997C2×C4311yescharacteristic, complemented
205#1965C2×C4311yescharacteristic
206#1931C2×C4314yescomplemented
207C4×#108C2×C4311yescharacteristic, complemented
208C2×C43—22no—
209C2×C43—162no—
210C2×C43#254511yescharacteristic
211C2×C43C2×#47111yescharacteristic
212C2×C43C2×#47211yescharacteristic
213#533C22×C4311yescharacteristic
214C2×C4⋊Q8C22×C4311yescharacteristic
215C2×#127C22×C4311yescharacteristic
216#501—22no—
217#500—21no—
218#498—21no—
219#490—22no—
220#486—21no—
221#486—21no—
222#486—21no—
223#486—21no—
224#486—21no—
225#486—21no—
226#446—21no—
227#446—21no—
228C8×Q8—21no—
229C8×Q8—21no—
230C2×#108C22×C4312yes—
231#428C22×C4314yes—
232#424C22×C4312yes—
233#423C22×C4311yescharacteristic
234#418C22×C4314yes—
235C2×#102C22×C4312yes—
236C2×#102C22×C4312yes—
237C2×#100C22×C4314yes—
238#405C22×C4312yes—
239C4×M16C22×C4311yescharacteristic
240C4×M16C22×C4311yescharacteristic
241C2×C4×C8C22×C4311yescharacteristic
242#343C22×C4314yes—
243#341C22×C4312yes—
244C43#2867011yescharacteristic, direct product factor, Sylow
245C22×Q8—21no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4C23×C4312yes—
249C2×M16C23×C4312yes—
250C2×M16C23×C4312yes—
251C2×M16C23×C4312yes—
252C22×C8C23×C4311yescharacteristic
253C22×C8C23×C4311yescharacteristic
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8D4×C4311yescharacteristic
259C4⋊Q8D4×C4311yescharacteristic
260#127—21no—
261#127—21no—
262#127—21no—
263#127—21no—
264#125D4×C4312yes—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269#117C23×C4312yes—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C23×C4312yes—
272C2×C42C23×C4311yescharacteristic
273#108—24no—
274#107—24no—
275#106—24no—
276C4⋊C8—22no—
277C4⋊C8—22no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280#102—22no—
281#102—22no—
282#102—22no—
283#102—22no—
284#102—24no—
285#102—24no—
286#100—28no—
287#97—22no—
288#97—21no—
289#97—21no—
290C4×C8—22no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8D4×C4311yescharacteristic
294C4×C8D4×C4311yescharacteristic
295C4×C8D4×C4311yescharacteristic
296C4×C8D4×C4311yescharacteristic
297C24—22no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—82no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—24no—
306C2×D4—24no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—82no—
312C2×D4—82no—
313C22×C4—22no—
314C22×C4#41×C4311yescharacteristic
315C22×C4#41×C4311yescharacteristic
316C22×C4C24×C4311yescharacteristic
317M16—22no—
318M16—24no—
319M16—22no—
320M16—22no—
321M16#41×C4314yes—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8C2×D4×C4311yescharacteristic
328C2×C8C2×D4×C4311yescharacteristic
329C2×C8C2×D4×C4311yescharacteristic
330C2×C8C2×D4×C4311yescharacteristic
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4C2×D4×C4312yes—
340C4⋊C4C2×D4×C4312yes—
341C22⋊C4—22no—
342C42—22no—
343C42C2×D4×C4311yescharacteristic
344C42C2×D4×C4311yescharacteristic
345C42C2×D4×C4311yescharacteristic
346C42C2×D4×C4311yescharacteristic
347C23—42no—
348C23—44no—
349C23—82no—
350C23—82no—
351C23C2×#41×C4311yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—82no—
355Q8—82no—
356D4—42no—
357D4—42no—
358D4—44no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4—82no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4#121×C4311yescharacteristic
370C2×C4#121×C4311yescharacteristic
371C2×C4#121×C4311yescharacteristic
372C2×C4#121×C4311yescharacteristic
373C2×C4C22×D4×C4311yescharacteristic
374C2×C4C22×D4×C4311yescharacteristic
375C2×C4C2×#41×C4312yes—
376C2×C42−1+4×C4312yes—
377C8—21no—
378C8—21no—
379C8—21no—
380C8—21no—
381C8—24no—
382C8—42no—
383C8—42no—
384C22—21no—
385C22—21no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—164no—
390C22C2×#121×C4311yescharacteristic
391C22C43×#55612yes—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—42no—
396C4—82no—
397C4C43×#47112yes—
398C4C43×#47212yes—
399C4C43×#53211yescharacteristic
400C4C43×#53611yescharacteristic
401C4C43×#54812yes—
402C2—22no—
403C2—162no—
404C2C43×#254511yescharacteristic
405C2C2×C43×#47111yescharacteristic
406C2C2×C43×#47211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#127×C43C22
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. C43×#3165C2semidirect
4. C43×#2960C2semidirect
5. C43×#2063C2semidirect
6. C43×#1997C2semidirect
8. C43×#1931C2semidirect
9. C4×#108×C43C2semidirect
180. #28670C43direct (N × H)
199. #3165C2×C43semidirect
202. #2960C2×C43semidirect
203. #2063C2×C43semidirect
204. #1997C2×C43semidirect
206. #1931C2×C43semidirect
207. C4×#108C2×C43semidirect
244. C43#28670direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31652
C43×#31382
C2×C43×#4862
C43×#29602
C43×#20632
C43×#19972
C43×#19652
C43×#19312
C4×#108×C432
#2867043