Finite Group Databasebeta

← C43×#13128 #24933145

Subgroups — C43×#13128 #24933145

Order 11008.

328 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#364C211yesmaximal, characteristic, complemented
2C2×C43×#349C211yesmaximal, characteristic
3C2×C43×#349C211yesmaximal, characteristic
4C2×C43×#347C211yesmaximal, characteristic, complemented
5C43×#1753C211yesmaximal, characteristic
6C43×#1376C211yesmaximal, characteristic, complemented
7C43×#1375C211yesmaximal, characteristic, complemented
8C22×M16×C43C2211yescharacteristic
9C2×M32×C43C2211yescharacteristic
10C2×M32×C43C2211yescharacteristic
11C2×M32×C43C2211yescharacteristic
12C2×M32×C43C2211yescharacteristic
13C2×C22⋊C8×C43C411yescharacteristic
14C2×#97×C43C2211yescharacteristic
15C2×C4×C8×C43C2211yescharacteristic
16C4×C22⋊C4×C43C411yescharacteristic
17C43×#364—22no—
18C43×#349—22no—
19C43×#349—22no—
20C43×#347—22no—
21C43×#336C411yescharacteristic
22C43×#336C411yescharacteristic
23C23×C4×C43C2×C411yescharacteristic
24C2×M16×C43—21no—
25C2×M16×C43—21no—
26C2×M16×C43—21no—
27C2×M16×C43—21no—
28C2×M16×C43—21no—
29C2×M16×C43—21no—
30C22×C8×C43C2×C411yescharacteristic
31C22×C8×C43C2×C411yescharacteristic
32C22×C8×C43C2×C411yescharacteristic
33C22×C8×C43C2311yescharacteristic
34C2×C22⋊C4×C43—21no—
35C2×C42×C43C2×C411yescharacteristic
36C2×C42×C43C2×C411yescharacteristic
37M32×C43—21no—
38M32×C43—21no—
39M32×C43—21no—
40M32×C43—21no—
41M32×C43—21no—
42M32×C43—21no—
43M32×C43D412yes—
44M32×C43D412yes—
45C2×C16×C43—21no—
46C2×C16×C43—21no—
47C2×C16×C43—21no—
48C2×C16×C43—21no—
49C22⋊C8×C43—22no—
50#97×C43—21no—
51#97×C43—21no—
52C4×C8×C43—21no—
53C4×C8×C43—21no—
54#95×C43—21no—
55C24×C43M1611yescharacteristic
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43M1611yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66M16×C43—41no—
67M16×C43—41no—
68M16×C43—41no—
69M16×C43—41no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43—21no—
75C2×C8×C43—21no—
76C2×C8×C43—21no—
77C2×C8×C43—21no—
78C2×C8×C43M1612yes—
79C2×C8×C43C2×D411yescharacteristic
80C2×C8×C43C2×D411yescharacteristic
81C2×C8×C43#4111yescharacteristic
82C2×C8×C43#4111yescharacteristic
83C2×C8×C43#4111yescharacteristic
84C2×C8×C43#4111yescharacteristic
85C22⋊C4×C43—42no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—21no—
90C16×C43—22no—
91C16×C43—22no—
92C16×C43—41no—
93C16×C43—41no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43C2×M1611yescharacteristic
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43#11711yescharacteristic
114C2×C4×C43C4×D411yescharacteristic
115C2×C4×C43C4×D411yescharacteristic
116C2×C4×C43C2×M1611yescharacteristic
117C2×C4×C43#13111yescharacteristic
118C2×C4×C43#13111yescharacteristic
119C8×C43—22no—
120C8×C43—41no—
121C8×C43—41no—
122C8×C43#12111yescharacteristic
123C8×C43#12311yescharacteristic
124C8×C43#12411yescharacteristic
125C8×C43#12611yescharacteristic
126#13128C4311yesmaximal, characteristic, direct product factor, Sylow
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—41no—
130C22×C43—41no—
131C22×C43—41no—
132C22×C43—81no—
133C22×C43—81no—
134C22×C43#43211yescharacteristic
135C22×C43#43511yescharacteristic
136C22×C43#43511yescharacteristic
137C4×C43—42no—
138C4×C43—41no—
139C4×C43—81no—
140C4×C43#38811yescharacteristic
141C4×C43#43311yescharacteristic
142C4×C43#43511yescharacteristic
143C4×C43#43611yescharacteristic
144C2×#364C2×C4311yescharacteristic, complemented
145C2×#349C2×C4311yescharacteristic
146C2×#349C2×C4311yescharacteristic
147C2×#347C2×C4311yescharacteristic, complemented
148#1753C2×C4311yescharacteristic
149#1376C2×C4311yescharacteristic, complemented
150#1375C2×C4311yescharacteristic, complemented
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—81no—
154C2×C43#192411yescharacteristic
155C2×C43#216511yescharacteristic
156C2×C43#216611yescharacteristic
157C22×M16C22×C4311yescharacteristic
158C2×M32C22×C4311yescharacteristic
159C2×M32C22×C4311yescharacteristic
160C2×M32C22×C4311yescharacteristic
161C2×M32C22×C4311yescharacteristic
162C2×C22⋊C8C4×C4311yescharacteristic
163C2×#97C22×C4311yescharacteristic
164C2×C4×C8C22×C4311yescharacteristic
165C4×C22⋊C4C4×C4311yescharacteristic
166#364—22no—
167#349—22no—
168#349—22no—
169#347—22no—
170#336C4×C4311yescharacteristic
171#336C4×C4311yescharacteristic
172C43#1312811yescharacteristic, direct product factor, Sylow
173C23×C4C2×C4×C4311yescharacteristic
174C2×M16—21no—
175C2×M16—21no—
176C2×M16—21no—
177C2×M16—21no—
178C2×M16—21no—
179C2×M16—21no—
180C22×C8C2×C4×C4311yescharacteristic
181C22×C8C2×C4×C4311yescharacteristic
182C22×C8C2×C4×C4311yescharacteristic
183C22×C8C23×C4311yescharacteristic
184C2×C22⋊C4—21no—
185C2×C42C2×C4×C4311yescharacteristic
186C2×C42C2×C4×C4311yescharacteristic
187M32—21no—
188M32—21no—
189M32—21no—
190M32—21no—
191M32—21no—
192M32—21no—
193M32D4×C4312yes—
194M32D4×C4312yes—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—21no—
199C22⋊C8—22no—
200#97—21no—
201#97—21no—
202C4×C8—21no—
203C4×C8—21no—
204#95—21no—
205C24M16×C4311yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4M16×C4311yescharacteristic
215C22×C4C22×C4×C4311yescharacteristic
216M16—41no—
217M16—41no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8M16×C4312yes—
229C2×C8C2×D4×C4311yescharacteristic
230C2×C8C2×D4×C4311yescharacteristic
231C2×C8#41×C4311yescharacteristic
232C2×C8#41×C4311yescharacteristic
233C2×C8#41×C4311yescharacteristic
234C2×C8#41×C4311yescharacteristic
235C22⋊C4—42no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C16—22no—
241C16—22no—
242C16—41no—
243C16—41no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23C2×M16×C4311yescharacteristic
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4#117×C4311yescharacteristic
264C2×C4C4×D4×C4311yescharacteristic
265C2×C4C4×D4×C4311yescharacteristic
266C2×C4C2×M16×C4311yescharacteristic
267C2×C4#131×C4311yescharacteristic
268C2×C4#131×C4311yescharacteristic
269C8—22no—
270C8—41no—
271C8—41no—
272C8#121×C4311yescharacteristic
273C8#123×C4311yescharacteristic
274C8#124×C4311yescharacteristic
275C8#126×C4311yescharacteristic
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22C43×#43211yescharacteristic
284C22C43×#43511yescharacteristic
285C22C43×#43511yescharacteristic
286C4—42no—
287C4—41no—
288C4—81no—
289C4C43×#38811yescharacteristic
290C4C43×#43311yescharacteristic
291C4C43×#43511yescharacteristic
292C4C43×#43611yescharacteristic
293C2—21no—
294C2—21no—
295C2—81no—
296C2C43×#192411yescharacteristic
297C2C43×#216511yescharacteristic
298C2C43×#216611yescharacteristic
subgroupG/H
centerC2×C4×C43#117
commutatorC22×C4C22×C4×C43
Frattini, cosocleC22×C8C23×C43
socleC22×C43#432
prime radicalC24×C43M16
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×#97×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#364C2semidirect
4. C2×C43×#347C2semidirect
6. C43×#1376C2semidirect
7. C43×#1375C2semidirect
126. #13128C43direct (N × H)
144. C2×#364C2×C43semidirect
147. C2×#347C2×C43semidirect
149. #1376C2×C43semidirect
150. #1375C2×C43semidirect
172. C43#13128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3642
C2×C43×#3492
C2×C43×#3472
C43×#17532
C43×#13762
C43×#13752
#1312843