Finite Group Databasebeta

← C43×#12926 #24932943

Subgroups — C43×#12926 #24932943

Order 11008.

400 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2913C211yesmaximal, characteristic
2C43×#2159C211yesmaximal, characteristic, complemented
3C2×C43×#367C211yesmaximal, characteristic, complemented
4C2×C43×#350C211yesmaximal, characteristic
5C43×#1816C211yesmaximal, characteristic
6C43×#1387C211yesmaximal, characteristic, complemented
7C43×#1382C211yesmaximal, characteristic, complemented
8C2×#131×C43C2211yescharacteristic
9C43×#520—21no—
10C2×M32×C43C2211yescharacteristic
11C22×C16×C43C2211yescharacteristic
12C2×#108×C43C2211yescharacteristic
13C43×#428—21no—
14C43×#428—22no—
15C43×#427—21no—
16C43×#427C2211yescharacteristic
17C2×#107×C43—21no—
18C2×#107×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C43×#417—21no—
21C43×#367—22no—
22C43×#367—21no—
23C43×#366—21no—
24C43×#350C414yescomplemented
25C43×#343—21no—
26C2×#41×C43D411yescharacteristic
27#131×C43—21no—
28#131×C43—21no—
29#131×C43C2×C412yes—
30#131×C43Q812yes—
31C2×M16×C43—21no—
32C2×M16×C43—21no—
33C2×M16×C43D411yescharacteristic
34C22×C8×C43—21no—
35C22×C8×C43C2311yescharacteristic
36C4×Q8×C43—41no—
37C4×D4×C43—42no—
38C4×D4×C43—41no—
39#117×C43—22no—
40#117×C43—21no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44M32×C43—21no—
45M32×C43C2×C412yescomplemented
46C2×C16×C43—21no—
47C2×C16×C43—21no—
48C2×C16×C43—21no—
49C2×C16×C43C2×C412yescomplemented
50#108×C43—21no—
51#108×C43—21no—
52#107×C43—22no—
53#107×C43—21no—
54#107×C43—21no—
55#107×C43—21no—
56#107×C43D411yescharacteristic
57#107×C43D411yescharacteristic
58#107×C43D412yes—
59#106×C43—22no—
60#106×C43—21no—
61#103×C43—41no—
62#102×C43—41no—
63#41×C43—21no—
64#41×C43—21no—
65#41×C43C4⋊C412yes—
66#41×C43Q1612yes—
67C2×Q8×C43D811yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43D811yescharacteristic
70C22×C4×C43—21no—
71C22×C4×C43—42no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75M16×C43—21no—
76M16×C43—22no—
77M16×C43—22no—
78M16×C43—41no—
79M16×C43—41no—
80M16×C43C4⋊C412yes—
81C2×C8×C43—21no—
82C2×C8×C43—22no—
83C2×C8×C43—22no—
84C2×C8×C43—41no—
85C2×C8×C43C22×C411yescharacteristic
86C2×C8×C43C2×D411yescharacteristic
87C2×C8×C43C2×D411yescharacteristic
88C2×C8×C43C2×Q811yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C4⋊C4×C43—21no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—42no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—41no—
100C42×C43—42no—
101C42×C43—41no—
102C16×C43—22no—
103C16×C43—22no—
104C23×C43—21no—
105C23×C43AGL(1,ℤ/8)11yescharacteristic
106Q8×C43—21no—
107Q8×C43#10712yes—
108D4×C43—22no—
109D4×C43—22no—
110D4×C43—21no—
111D4×C43#10712yes—
112C2×C4×C43—21no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—41no—
116C2×C4×C43—42no—
117C2×C4×C43—41no—
118C2×C4×C43—81no—
119C2×C4×C43—161no—
120C2×C4×C43—162no—
121C2×C4×C43—161no—
122C2×C4×C43C2×C4⋊C411yescharacteristic
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12311yescharacteristic
125C2×C4×C43C2×D811yescharacteristic
126C2×C4×C43C2×Q1611yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C8×C43—22no—
129C8×C43—81no—
130C8×C43C4×D411yescharacteristic
131C8×C43C4×D411yescharacteristic
132C8×C43C22⋊Q811yescharacteristic
133C8×C43C22⋊Q811yescharacteristic
134#12926C4311yesmaximal, characteristic, direct product factor, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—22no—
138C22×C43—41no—
139C22×C43—41no—
140C22×C43#42811yescharacteristic
141C22×C43#44711yescharacteristic
142C22×C43#48411yescharacteristic
143C4×C43—22no—
144C4×C43—81no—
145C4×C43—82no—
146C4×C43—81no—
147C4×C43—161no—
148C4×C43#38511yescharacteristic
149C4×C43C2×#10711yescharacteristic
150C4×C43#45111yescharacteristic
151C4×C43#48011yescharacteristic
152#2913C2×C4311yescharacteristic
153#2159C2×C4311yescharacteristic, complemented
154C2×#367C2×C4311yescharacteristic, complemented
155C2×#350C2×C4311yescharacteristic
156#1816C2×C4311yescharacteristic
157#1387C2×C4311yescharacteristic, complemented
158#1382C2×C4311yescharacteristic, complemented
159C2×C43—21no—
160C2×C43—21no—
161C2×C43—42no—
162C2×C43#185211yescharacteristic
163C2×C43#219311yescharacteristic
164C2×C43#219411yescharacteristic
165C2×#131C22×C4311yescharacteristic
166#520—21no—
167C2×M32C22×C4311yescharacteristic
168C22×C16C22×C4311yescharacteristic
169C2×#108C22×C4311yescharacteristic
170#428—21no—
171#428—22no—
172#427—21no—
173#427C22×C4311yescharacteristic
174C2×#107—21no—
175C2×#107C22×C4311yescharacteristic
176C2×#107C22×C4311yescharacteristic
177#417—21no—
178#367—22no—
179#367—21no—
180#366—21no—
181#350C4×C4314yescomplemented
182#343—21no—
183C43#1292611yescharacteristic, direct product factor, Sylow
184C2×#41D4×C4311yescharacteristic
185#131—21no—
186#131—21no—
187#131C2×C4×C4312yes—
188#131Q8×C4312yes—
189C2×M16—21no—
190C2×M16—21no—
191C2×M16D4×C4311yescharacteristic
192C22×C8—21no—
193C22×C8C23×C4311yescharacteristic
194C4×Q8—41no—
195C4×D4—42no—
196C4×D4—41no—
197#117—22no—
198#117—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202M32—21no—
203M32C2×C4×C4312yescomplemented
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16C2×C4×C4312yescomplemented
208#108—21no—
209#108—21no—
210#107—22no—
211#107—21no—
212#107—21no—
213#107—21no—
214#107D4×C4311yescharacteristic
215#107D4×C4311yescharacteristic
216#107D4×C4312yes—
217#106—22no—
218#106—21no—
219#103—41no—
220#102—41no—
221#41—21no—
222#41—21no—
223#41C4⋊C4×C4312yes—
224#41Q16×C4312yes—
225C2×Q8D8×C4311yescharacteristic
226C2×D4—21no—
227C2×D4D8×C4311yescharacteristic
228C22×C4—21no—
229C22×C4—42no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4C2×D4×C4311yescharacteristic
233M16—21no—
234M16—22no—
235M16—22no—
236M16—41no—
237M16—41no—
238M16C4⋊C4×C4312yes—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8C22×C4×C4311yescharacteristic
244C2×C8C2×D4×C4311yescharacteristic
245C2×C8C2×D4×C4311yescharacteristic
246C2×C8C2×Q8×C4311yescharacteristic
247C2×C8#41×C4311yescharacteristic
248C2×C8#41×C4311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—21no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C42—42no—
259C42—41no—
260C16—22no—
261C16—22no—
262C23—21no—
263C23AGL(1,ℤ/8)×C4311yescharacteristic
264Q8—21no—
265Q8#107×C4312yes—
266D4—22no—
267D4—22no—
268D4—21no—
269D4#107×C4312yes—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—161no—
278C2×C4—162no—
279C2×C4—161no—
280C2×C4C2×C4⋊C4×C4311yescharacteristic
281C2×C4#120×C4311yescharacteristic
282C2×C4#123×C4311yescharacteristic
283C2×C4C2×D8×C4311yescharacteristic
284C2×C4C2×Q16×C4311yescharacteristic
285C2×C4#137×C4311yescharacteristic
286C8—22no—
287C8—81no—
288C8C4×D4×C4311yescharacteristic
289C8C4×D4×C4311yescharacteristic
290C8C22⋊Q8×C4311yescharacteristic
291C8C22⋊Q8×C4311yescharacteristic
292C22—21no—
293C22—21no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22C43×#42811yescharacteristic
298C22C43×#44711yescharacteristic
299C22C43×#48411yescharacteristic
300C4—22no—
301C4—81no—
302C4—82no—
303C4—81no—
304C4—161no—
305C4C43×#38511yescharacteristic
306C4C2×#107×C4311yescharacteristic
307C4C43×#45111yescharacteristic
308C4C43×#48011yescharacteristic
309C2—21no—
310C2—21no—
311C2—42no—
312C2C43×#185211yescharacteristic
313C2C43×#219311yescharacteristic
314C2C43×#219411yescharacteristic
subgroupG/H
center, socleC22×C43#447
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC2×#41×C43D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×#131×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2159C2semidirect
3. C2×C43×#367C2semidirect
6. C43×#1387C2semidirect
7. C43×#1382C2semidirect
24. C43×#350C4semidirect
45. M32×C43C2×C4semidirect
49. C2×C16×C43C2×C4semidirect
134. #12926C43direct (N × H)
153. #2159C2×C43semidirect
154. C2×#367C2×C43semidirect
157. #1387C2×C43semidirect
158. #1382C2×C43semidirect
181. #350C4×C43semidirect
183. C43#12926direct (N × H)
203. M32C2×C4×C43semidirect
207. C2×C16C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#29132
C43×#21592
C2×C43×#3672
C2×C43×#3502
C43×#18162
C43×#13872
C43×#13822
#1292643