Finite Group Databasebeta

← C43×#13122 #24933139

Subgroups — C43×#13122 #24933139

Order 11008.

326 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#364C211yesmaximal, characteristic, complemented
2C2×C43×#350C211yesmaximal, characteristic
3C43×#2113C211yesmaximal, characteristic
4C43×#2108C211yesmaximal, characteristic, complemented
5C43×#1764C211yesmaximal, characteristic
6C43×#1379C211yesmaximal, characteristic, complemented
7C43×#1374C211yesmaximal, characteristic, complemented
8C2×#131×C43C2211yescharacteristic
9C2×M32×C43C2211yescharacteristic
10C2×M32×C43C2211yescharacteristic
11C22×C16×C43C2211yescharacteristic
12C22×C16×C43C2211yescharacteristic
13C2×#104×C43C411yescharacteristic
14C43×#416C411yescharacteristic
15C43×#405C2211yescharacteristic
16C2×C4×C8×C43C2211yescharacteristic
17C43×#364—22no—
18C43×#350—22no—
19C43×C22⋊C16—21no—
20C43×C22⋊C16—21no—
21C43×#346—21no—
22C4×C16×C43—21no—
23C43×#341C411yescharacteristic
24C43×#339C411yescharacteristic
25C2×#41×C43C2×C411yescharacteristic
26#131×C43—21no—
27#131×C43—21no—
28#131×C43—21no—
29#131×C43—21no—
30C2×M16×C43—21no—
31C2×M16×C43C2×C411yescharacteristic
32C2×M16×C43C2×C411yescharacteristic
33C22×C8×C43—21no—
34C22×C8×C43C2×C411yescharacteristic
35C22×C8×C43C2311yescharacteristic
36#117×C43C2×C411yescharacteristic
37C2×C42×C43C2×C411yescharacteristic
38M32×C43—21no—
39M32×C43—21no—
40M32×C43—21no—
41M32×C43D412yes—
42C2×C16×C43—21no—
43C2×C16×C43—21no—
44C2×C16×C43—21no—
45C2×C16×C43—21no—
46C2×C16×C43—21no—
47C2×C16×C43—21no—
48C2×C16×C43—21no—
49C2×C16×C43D411yescharacteristic
50C2×C16×C43D411yescharacteristic
51#104×C43—22no—
52#103×C43C811yescharacteristic
53#103×C43C811yescharacteristic
54#102×C43C811yescharacteristic
55#102×C43C811yescharacteristic
56#97×C43—21no—
57C4×C8×C43—21no—
58C4×C8×C43—21no—
59C4×C8×C43—21no—
60#41×C43—21no—
61#41×C43—21no—
62#41×C43—21no—
63#41×C43—21no—
64C2×Q8×C43C2×C811yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43C2×C811yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70M16×C43—21no—
71M16×C43—21no—
72M16×C43—21no—
73M16×C43—41no—
74M16×C43—41no—
75M16×C43M1612yes—
76C2×C8×C43—21no—
77C2×C8×C43—21no—
78C2×C8×C43—21no—
79C2×C8×C43—21no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43C2×C811yescharacteristic
83C2×C8×C43C2×C811yescharacteristic
84C2×C8×C43C2×D411yescharacteristic
85C2×C8×C43C2×D411yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C2×C8×C43#4111yescharacteristic
88C2×C8×C43#4111yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C4⋊C4×C43C2×C811yescharacteristic
91C4⋊C4×C43C2×C811yescharacteristic
92C22⋊C4×C43—21no—
93C42×C43—21no—
94C42×C43—21no—
95C42×C43—21no—
96C16×C43—22no—
97C16×C43—21no—
98C16×C43—21no—
99C16×C43—41no—
100C16×C43—41no—
101C23×C43—21no—
102C23×C43#13111yescharacteristic
103Q8×C43—21no—
104Q8×C43—21no—
105D4×C43—21no—
106D4×C43—21no—
107D4×C43—41no—
108D4×C43—41no—
109C2×C4×C43—22no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43#11711yescharacteristic
118C2×C4×C43C4×D411yescharacteristic
119C2×C4×C43C4×D411yescharacteristic
120C2×C4×C43C22×C811yescharacteristic
121C2×C4×C43C2×M1611yescharacteristic
122C2×C4×C43#13111yescharacteristic
123C8×C43—21no—
124C8×C43—21no—
125C8×C43—22no—
126C8×C43—41no—
127C8×C43#12111yescharacteristic
128C8×C43#12311yescharacteristic
129C8×C43#12411yescharacteristic
130C8×C43#12611yescharacteristic
131#13122C4311yesmaximal, characteristic, direct product factor, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43#43311yescharacteristic
138C22×C43C8×D411yescharacteristic
139C22×C43#43611yescharacteristic
140C4×C43—42no—
141C4×C43—41no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43#38811yescharacteristic
145C4×C43#43111yescharacteristic
146C4×C43C8×D411yescharacteristic
147C4×C43#43511yescharacteristic
148C2×#364C2×C4311yescharacteristic, complemented
149C2×#350C2×C4311yescharacteristic
150#2113C2×C4311yescharacteristic
151#2108C2×C4311yescharacteristic, complemented
152#1764C2×C4311yescharacteristic
153#1379C2×C4311yescharacteristic, complemented
154#1374C2×C4311yescharacteristic, complemented
155C2×C43—21no—
156C2×C43—21no—
157C2×C43—81no—
158C2×C43#192311yescharacteristic
159C2×C43#217011yescharacteristic
160C2×C43#217111yescharacteristic
161C2×#131C22×C4311yescharacteristic
162C2×M32C22×C4311yescharacteristic
163C2×M32C22×C4311yescharacteristic
164C22×C16C22×C4311yescharacteristic
165C22×C16C22×C4311yescharacteristic
166C2×#104C4×C4311yescharacteristic
167#416C4×C4311yescharacteristic
168#405C22×C4311yescharacteristic
169C2×C4×C8C22×C4311yescharacteristic
170#364—22no—
171#350—22no—
172C22⋊C16—21no—
173C22⋊C16—21no—
174#346—21no—
175C4×C16—21no—
176#341C4×C4311yescharacteristic
177#339C4×C4311yescharacteristic
178C43#1312211yescharacteristic, direct product factor, Sylow
179C2×#41C2×C4×C4311yescharacteristic
180#131—21no—
181#131—21no—
182#131—21no—
183#131—21no—
184C2×M16—21no—
185C2×M16C2×C4×C4311yescharacteristic
186C2×M16C2×C4×C4311yescharacteristic
187C22×C8—21no—
188C22×C8C2×C4×C4311yescharacteristic
189C22×C8C23×C4311yescharacteristic
190#117C2×C4×C4311yescharacteristic
191C2×C42C2×C4×C4311yescharacteristic
192M32—21no—
193M32—21no—
194M32—21no—
195M32D4×C4312yes—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—21no—
201C2×C16—21no—
202C2×C16—21no—
203C2×C16D4×C4311yescharacteristic
204C2×C16D4×C4311yescharacteristic
205#104—22no—
206#103C8×C4311yescharacteristic
207#103C8×C4311yescharacteristic
208#102C8×C4311yescharacteristic
209#102C8×C4311yescharacteristic
210#97—21no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—21no—
214#41—21no—
215#41—21no—
216#41—21no—
217#41—21no—
218C2×Q8C2×C8×C4311yescharacteristic
219C2×D4—21no—
220C2×D4C2×C8×C4311yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C22×C4×C4311yescharacteristic
224M16—21no—
225M16—21no—
226M16—21no—
227M16—41no—
228M16—41no—
229M16M16×C4312yes—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8C2×C8×C4311yescharacteristic
237C2×C8C2×C8×C4311yescharacteristic
238C2×C8C2×D4×C4311yescharacteristic
239C2×C8C2×D4×C4311yescharacteristic
240C2×C8#41×C4311yescharacteristic
241C2×C8#41×C4311yescharacteristic
242C2×C8#41×C4311yescharacteristic
243C2×C8#41×C4311yescharacteristic
244C4⋊C4C2×C8×C4311yescharacteristic
245C4⋊C4C2×C8×C4311yescharacteristic
246C22⋊C4—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C16—22no—
251C16—21no—
252C16—21no—
253C16—41no—
254C16—41no—
255C23—21no—
256C23#131×C4311yescharacteristic
257Q8—21no—
258Q8—21no—
259D4—21no—
260D4—21no—
261D4—41no—
262D4—41no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4#117×C4311yescharacteristic
272C2×C4C4×D4×C4311yescharacteristic
273C2×C4C4×D4×C4311yescharacteristic
274C2×C4C22×C8×C4311yescharacteristic
275C2×C4C2×M16×C4311yescharacteristic
276C2×C4#131×C4311yescharacteristic
277C8—21no—
278C8—21no—
279C8—22no—
280C8—41no—
281C8#121×C4311yescharacteristic
282C8#123×C4311yescharacteristic
283C8#124×C4311yescharacteristic
284C8#126×C4311yescharacteristic
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22C43×#43311yescharacteristic
291C22C8×D4×C4311yescharacteristic
292C22C43×#43611yescharacteristic
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4C43×#38811yescharacteristic
298C4C43×#43111yescharacteristic
299C4C8×D4×C4311yescharacteristic
300C4C43×#43511yescharacteristic
301C2—21no—
302C2—21no—
303C2—81no—
304C2C43×#192311yescharacteristic
305C2C43×#217011yescharacteristic
306C2C43×#217111yescharacteristic
subgroupG/H
centerC2×C8×C43C2×D4
commutatorC2×C4C22×C8×C43
Frattini, cosocleC22×C8C23×C43
socleC22×C43C8×D4
prime radicalC2×#41×C43C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8×C43 ◁ C22×C16×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#364C2semidirect
4. C43×#2108C2semidirect
6. C43×#1379C2semidirect
7. C43×#1374C2semidirect
131. #13122C43direct (N × H)
148. C2×#364C2×C43semidirect
151. #2108C2×C43semidirect
153. #1379C2×C43semidirect
154. #1374C2×C43semidirect
178. C43#13122direct (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×#3502
C43×#21132
C43×#21082
C43×#17642
C43×#13792
C43×#13742
#1312243