Finite Group Databasebeta

← C43×#13153 #24933170

Subgroups — C43×#13153 #24933170

Order 11008.

328 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#360C211yesmaximal, characteristic
2C43×#2139C211yesmaximal, characteristic
3C2×C43×#347C211yesmaximal, characteristic, complemented
4C43×#1975C211yesmaximal, characteristic
5C43×#1943C211yesmaximal, characteristic, complemented
6C43×#1387C211yesmaximal, characteristic, complemented
7C43×#1383C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C2×M32×C43C2211yescharacteristic
10C2×M32×C43C2211yescharacteristic
11C2×#108×C43C2211yescharacteristic
12C2×#107×C43C2211yescharacteristic
13C2×#106×C43C2211yescharacteristic
14C2×#104×C43—21no—
15C43×#408—21no—
16C2×#97×C43C2211yescharacteristic
17C43×#389—21no—
18C43×#360—22no—
19C43×#358C412yescomplemented
20C43×#357C412yescomplemented
21C43×#347—22no—
22C43×#340—21no—
23C2×#41×C43—21no—
24#135×C43—21no—
25#135×C43—21no—
26#135×C43—21no—
27#135×C43—21no—
28C2×Q16×C43C2×C411yescharacteristic
29C2×SD16×C43—21no—
30C2×D8×C43C2×C411yescharacteristic
31C2×M16×C43—21no—
32C22×C8×C43D411yescharacteristic
33C22×C8×C43C2311yescharacteristic
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—41no—
37C2×C42×C43D411yescharacteristic
38M32×C43—21no—
39M32×C43—21no—
40M32×C43—21no—
41M32×C43D412yes—
42C2×C16×C43—21no—
43C2×C16×C43C2×C412yes—
44#108×C43—21no—
45#108×C43—21no—
46#107×C43—21no—
47#107×C43C2×C412yes—
48#106×C43—21no—
49#106×C43—21no—
50#104×C43—42no—
51C22⋊C8×C43—42no—
52#97×C43—21no—
53#97×C43—21no—
54#95×C43—41no—
55#41×C43—41no—
56#41×C43—41no—
57#41×C43—41no—
58#41×C43—41no—
59C2×Q8×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—41no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43C2×D411yescharacteristic
67Q16×C43—21no—
68Q16×C43—21no—
69SD16×C43—41no—
70SD16×C43—41no—
71D8×C43—21no—
72D8×C43—21no—
73M16×C43—41no—
74M16×C43—41no—
75C2×C8×C43—21no—
76C2×C8×C43—21no—
77C2×C8×C43—21no—
78C2×C8×C43—41no—
79C2×C8×C43C22×C411yescharacteristic
80C2×C8×C43C2×D411yescharacteristic
81C2×C8×C43#4111yescharacteristic
82C2×C8×C43#4111yescharacteristic
83C2×C8×C43#4111yescharacteristic
84C2×C8×C43#4111yescharacteristic
85C4⋊C4×C43—22no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—82no—
90C42×C43—21no—
91C42×C43—21no—
92C16×C43—22no—
93C16×C43—22no—
94C23×C43—41no—
95C23×C43AGL(1,ℤ/8)11yescharacteristic
96Q8×C43—41no—
97Q8×C43—41no—
98D4×C43—41no—
99D4×C43—41no—
100D4×C43—81no—
101D4×C43—81no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—42no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—81no—
108C2×C4×C43—81no—
109C2×C4×C43—81no—
110C2×C4×C43—81no—
111C2×C4×C43—81no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43C4×D411yescharacteristic
115C2×C4×C43#12111yescharacteristic
116C2×C4×C43#12411yescharacteristic
117C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C8×C43—41no—
121C8×C43—81no—
122C8×C43#11711yescharacteristic
123C8×C43C4×D411yescharacteristic
124C8×C43#12311yescharacteristic
125C8×C43#12611yescharacteristic
126#13153C4311yesmaximal, characteristic, direct product factor, Sylow
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—81no—
130C22×C43—81no—
131C22×C43—81no—
132C22×C43#44211yescharacteristic
133C22×C43#46911yescharacteristic
134C22×C43#48911yescharacteristic
135C4×C43—81no—
136C4×C43—82no—
137C4×C43—81no—
138C4×C43—161no—
139C4×C43#38811yescharacteristic
140C4×C43#44011yescharacteristic
141C4×C43#46811yescharacteristic
142C4×C43#49011yescharacteristic
143C2×#360C2×C4311yescharacteristic
144#2139C2×C4311yescharacteristic
145C2×#347C2×C4311yescharacteristic, complemented
146#1975C2×C4311yescharacteristic
147#1943C2×C4311yescharacteristic, complemented
148#1387C2×C4311yescharacteristic, complemented
149#1383C2×C4311yescharacteristic, complemented
150C2×C43—21no—
151C2×C43—21no—
152C2×C43—161no—
153C2×C43#193611yescharacteristic
154C2×C43#218011yescharacteristic
155C2×C43AGL(1,ℤ/16)11yescharacteristic
156C2×#135C22×C4311yescharacteristic
157C2×M32C22×C4311yescharacteristic
158C2×M32C22×C4311yescharacteristic
159C2×#108C22×C4311yescharacteristic
160C2×#107C22×C4311yescharacteristic
161C2×#106C22×C4311yescharacteristic
162C2×#104—21no—
163#408—21no—
164C2×#97C22×C4311yescharacteristic
165#389—21no—
166#360—22no—
167#358C4×C4312yescomplemented
168#357C4×C4312yescomplemented
169#347—22no—
170#340—21no—
171C43#1315311yescharacteristic, direct product factor, Sylow
172C2×#41—21no—
173#135—21no—
174#135—21no—
175#135—21no—
176#135—21no—
177C2×Q16C2×C4×C4311yescharacteristic
178C2×SD16—21no—
179C2×D8C2×C4×C4311yescharacteristic
180C2×M16—21no—
181C22×C8D4×C4311yescharacteristic
182C22×C8C23×C4311yescharacteristic
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—41no—
186C2×C42D4×C4311yescharacteristic
187M32—21no—
188M32—21no—
189M32—21no—
190M32D4×C4312yes—
191C2×C16—21no—
192C2×C16C2×C4×C4312yes—
193#108—21no—
194#108—21no—
195#107—21no—
196#107C2×C4×C4312yes—
197#106—21no—
198#106—21no—
199#104—42no—
200C22⋊C8—42no—
201#97—21no—
202#97—21no—
203#95—41no—
204#41—41no—
205#41—41no—
206#41—41no—
207#41—41no—
208C2×Q8—21no—
209C2×D4—21no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4C2×D4×C4311yescharacteristic
216Q16—21no—
217Q16—21no—
218SD16—41no—
219SD16—41no—
220D8—21no—
221D8—21no—
222M16—41no—
223M16—41no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—41no—
228C2×C8C22×C4×C4311yescharacteristic
229C2×C8C2×D4×C4311yescharacteristic
230C2×C8#41×C4311yescharacteristic
231C2×C8#41×C4311yescharacteristic
232C2×C8#41×C4311yescharacteristic
233C2×C8#41×C4311yescharacteristic
234C4⋊C4—22no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—82no—
239C42—21no—
240C42—21no—
241C16—22no—
242C16—22no—
243C23—41no—
244C23AGL(1,ℤ/8)×C4311yescharacteristic
245Q8—41no—
246Q8—41no—
247D4—41no—
248D4—41no—
249D4—81no—
250D4—81no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4C4×D4×C4311yescharacteristic
264C2×C4#121×C4311yescharacteristic
265C2×C4#124×C4311yescharacteristic
266C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
267C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
268C2×C4#137×C4311yescharacteristic
269C8—41no—
270C8—81no—
271C8#117×C4311yescharacteristic
272C8C4×D4×C4311yescharacteristic
273C8#123×C4311yescharacteristic
274C8#126×C4311yescharacteristic
275C22—21no—
276C22—21no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22C43×#44211yescharacteristic
281C22C43×#46911yescharacteristic
282C22C43×#48911yescharacteristic
283C4—81no—
284C4—82no—
285C4—81no—
286C4—161no—
287C4C43×#38811yescharacteristic
288C4C43×#44011yescharacteristic
289C4C43×#46811yescharacteristic
290C4C43×#49011yescharacteristic
291C2—21no—
292C2—21no—
293C2—161no—
294C2C43×#193611yescharacteristic
295C2C43×#218011yescharacteristic
296C2C43×AGL(1,ℤ/16)11yescharacteristic
subgroupG/H
center, socleC22×C43#442
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC2×#135×C43C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×#97×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C43×#347C2semidirect
5. C43×#1943C2semidirect
6. C43×#1387C2semidirect
7. C43×#1383C2semidirect
19. C43×#358C4semidirect
20. C43×#357C4semidirect
126. #13153C43direct (N × H)
145. C2×#347C2×C43semidirect
147. #1943C2×C43semidirect
148. #1387C2×C43semidirect
149. #1383C2×C43semidirect
167. #358C4×C43semidirect
168. #357C4×C43semidirect
171. C43#13153direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3602
C43×#21392
C2×C43×#3472
C43×#19752
C43×#19432
C43×#13872
C43×#13832
#1315343