Finite Group Databasebeta

← C2×C43×#2906 #24980115

Subgroups — C2×C43×#2906 #24980115

Order 11008.

2810 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
1C22×#131×C43C212yesmaximal
2C2×C4×#41×C43C211yesmaximal, characteristic
3C43×#2906C2116yesmaximal, direct product factor
4C2×C43×#424C216yesmaximal, complemented
5C2×C43×#423C213yesmaximal, complemented
6C22×C4⋊C8×C43C213yesmaximal, complemented
7C22×#41×C43C2211yescharacteristic
8C2×#131×C43—216no—
9C2×#131×C43C22116yes—
10C22×M16×C43C2216yes—
11C23×C8×C43C2216yes—
12C4×#41×C43C418yes—
13C4×#41×C43C2218yes—
14C2×C4×Q8×C43C411yescharacteristic
15C2×C4×Q8×C43C411yescharacteristic
16C2×C4×D4×C43C413yes—
17C2×C4×D4×C43C413yes—
18C2×#117×C43C2213yes—
19C22×C42×C43C2213yes—
20C43×#424C22148yescomplemented
21C43×#423C22124yescomplemented
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2213yes—
24C2×C4⋊C8×C43C2216yes—
25C2×C4⋊C8×C43C2216yes—
26C2×C4⋊C8×C43C22124yescomplemented
27C2×#41×C43C2×C414yes—
28C2×#41×C43D418yes—
29C2×#41×C43Q818yes—
30C2×#41×C43C2314yes—
31C22×Q8×C43C2×C411yescharacteristic
32C22×D4×C43C2×C413yes—
33C23×C4×C43C2×C413yes—
34C23×C4×C43C2×C413yes—
35C23×C4×C43C2313yes—
36#131×C43—264no—
37C2×M16×C43—224no—
38C2×M16×C43C23124yes—
39C22×C8×C43—224no—
40C22×C8×C43C23124yes—
41C22×C8×C43C2312yes—
42C22×C8×C43C2316yes—
43C4×Q8×C43C2×C418yes—
44C4×Q8×C43C2×C418yes—
45C4×D4×C43C2×C4124yes—
46C4×D4×C43C2×C4124yes—
47#117×C43C2×C4112yes—
48#117×C43C23112yes—
49C2×C4⋊C4×C43C2×C413yes—
50C2×C4⋊C4×C43C2×C413yes—
51C2×C22⋊C4×C43C2×C416yes—
52C2×C42×C43C2×C413yes—
53C2×C42×C43C2×C413yes—
54C2×C42×C43C2×C4112yes—
55C2×C42×C43C23112yes—
56C2×C42×C43C2311yescharacteristic
57C2×C42×C43C2313yes—
58C4⋊C8×C43C2314yes—
59C4⋊C8×C43C23112yes—
60C4⋊C8×C43C23124yes—
61C4⋊C8×C43C23124yes—
62C24×C43C22×C413yes—
63#41×C43C4⋊C4132yes—
64#41×C43C2×D4116yes—
65#41×C43C2×Q8116yes—
66C2×Q8×C43C4⋊C418yes—
67C2×Q8×C43C22×C414yes—
68C2×D4×C43C4⋊C4124yes—
69C2×D4×C43C22×C4112yes—
70C22×C4×C43—212no—
71C22×C4×C43—46no—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C22×C413yes—
74C22×C4×C43C22×C413yes—
75C22×C4×C43C22×C4112yes—
76C22×C4×C43C22×C4112yes—
77C22×C4×C43C22×C413yes—
78C22×C4×C43C22×C416yes—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D4112yes—
81C22×C4×C43C2×Q8112yes—
82C22×C4×C43C2416yes—
83C22×C4×C43C2411yescharacteristic
84M16×C43—248no—
85C2×C8×C43—24no—
86C2×C8×C43—212no—
87C2×C8×C43—248no—
88C2×C8×C43C2414yes—
89C2×C8×C43C24112yes—
90C4⋊C4×C43C22×C4112yes—
91C4⋊C4×C43C22×C4112yes—
92C22⋊C4×C43C22×C4124yes—
93C42×C43C22×C412yes—
94C42×C43C22×C416yes—
95C42×C43C22×C4112yes—
96C42×C43C22×C4112yes—
97C42×C43C2412yes—
98C42×C43C2416yes—
99C23×C43—26no—
100C23×C43—26no—
101C23×C43C2×C4⋊C4112yes—
102C23×C43C23×C416yes—
103C23×C43C23×C411yescharacteristic
104Q8×C43C2×C4⋊C4116yes—
105D4×C43C2×C4⋊C4148yes—
106C2×C4×C43—26no—
107C2×C4×C43—22no—
108C2×C4×C43—26no—
109C2×C4×C43—224no—
110C2×C4×C43—412no—
111C2×C4×C43C2×C4⋊C4112yes—
112C2×C4×C43C2×C4⋊C4124yes—
113C2×C4×C43#13114yescomplemented
114C2×C4×C43C23×C412yes—
115C2×C4×C43C23×C416yes—
116C2×C4×C43C23×C416yes—
117C2×C4×C43C23×C411yescharacteristic
118C2×C4×C43C23×C416yes—
119C2×C4×C43C23×C412yes—
120C2×C4×C43C22×D412yes—
121C2×C4×C43C22×D4112yes—
122C2×C4×C43C22×Q812yes—
123C2×C4×C43C22×Q8112yes—
124C2×C4×C43C2511yescharacteristic
125C8×C43—24no—
126C8×C43—212no—
127C2×#2906C4311yesmaximal, characteristic, direct product factor, Sylow
128C22×C43—224no—
129C22×C43—26no—
130C22×C43—26no—
131C22×C43C22×C4⋊C4112yes—
132C22×C43C22×C4⋊C412yes—
133C22×C43C2×#13112yes—
134C22×C43#56812yes—
135C22×C43C24×C411yescharacteristic
136C4×C43—26no—
137C4×C43—22no—
138C4×C43—26no—
139C4×C43C22×C4⋊C412yes—
140C4×C43C22×C4⋊C4112yes—
141C4×C43C2×#13114yescomplemented
142C4×C43C23×D411yescharacteristic
143C4×C43C23×Q811yescharacteristic
144C22×#131C2×C4312yes—
145C2×C4×#41C2×C4311yescharacteristic
146#2906C2×C43116yesdirect product factor
147C2×#424C2×C4316yescomplemented
148C2×#423C2×C4313yescomplemented
149C22×C4⋊C8C2×C4313yescomplemented
150C2×C43—212no—
151C2×C43#290614yesdirect product factor
152C2×C43C23×C4⋊C411yescharacteristic
153C2×C43C22×#13111yescharacteristic
154C2×C43C2×#56811yescharacteristic
155C22×#41C22×C4311yescharacteristic
156C2×#131—216no—
157C2×#131C22×C43116yes—
158C22×M16C22×C4316yes—
159C23×C8C22×C4316yes—
160C4×#41C4×C4318yes—
161C4×#41C22×C4318yes—
162C2×C4×Q8C4×C4311yescharacteristic
163C2×C4×Q8C4×C4311yescharacteristic
164C2×C4×D4C4×C4313yes—
165C2×C4×D4C4×C4313yes—
166C2×#117C22×C4313yes—
167C22×C42C22×C4313yes—
168#424C22×C43148yescomplemented
169#423C22×C43124yescomplemented
170C2×C4⋊C8C22×C4311yescharacteristic
171C2×C4⋊C8C22×C4313yes—
172C2×C4⋊C8C22×C4316yes—
173C2×C4⋊C8C22×C4316yes—
174C2×C4⋊C8C22×C43124yescomplemented
175C43C2×#290611yescharacteristic, direct product factor, Sylow
176C2×#41C2×C4×C4314yes—
177C2×#41D4×C4318yes—
178C2×#41Q8×C4318yes—
179C2×#41C23×C4314yes—
180C22×Q8C2×C4×C4311yescharacteristic
181C22×D4C2×C4×C4313yes—
182C23×C4C2×C4×C4313yes—
183C23×C4C2×C4×C4313yes—
184C23×C4C23×C4313yes—
185#131—264no—
186C2×M16—224no—
187C2×M16C23×C43124yes—
188C22×C8—224no—
189C22×C8C23×C4312yes—
190C22×C8C23×C4316yes—
191C22×C8C23×C43124yes—
192C4×Q8C2×C4×C4318yes—
193C4×Q8C2×C4×C4318yes—
194C4×D4C2×C4×C43124yes—
195C4×D4C2×C4×C43124yes—
196#117C2×C4×C43112yes—
197#117C23×C43112yes—
198C2×C4⋊C4C2×C4×C4313yes—
199C2×C4⋊C4C2×C4×C4313yes—
200C2×C22⋊C4C2×C4×C4316yes—
201C2×C42C2×C4×C4313yes—
202C2×C42C2×C4×C4313yes—
203C2×C42C2×C4×C43112yes—
204C2×C42C23×C4313yes—
205C2×C42C23×C43112yes—
206C2×C42C23×C4311yescharacteristic
207C4⋊C8C23×C4314yes—
208C4⋊C8C23×C43112yes—
209C4⋊C8C23×C43124yes—
210C4⋊C8C23×C43124yes—
211C24C22×C4×C4313yes—
212#41C4⋊C4×C43132yes—
213#41C2×D4×C43116yes—
214#41C2×Q8×C43116yes—
215C2×Q8C4⋊C4×C4318yes—
216C2×Q8C22×C4×C4314yes—
217C2×D4C4⋊C4×C43124yes—
218C2×D4C22×C4×C43112yes—
219C22×C4—212no—
220C22×C4—46no—
221C22×C4C22×C4×C4311yescharacteristic
222C22×C4C22×C4×C4313yes—
223C22×C4C22×C4×C4313yes—
224C22×C4C22×C4×C43112yes—
225C22×C4C22×C4×C43112yes—
226C22×C4C22×C4×C4313yes—
227C22×C4C22×C4×C4316yes—
228C22×C4C22×C4×C4311yescharacteristic
229C22×C4C2×D4×C43112yes—
230C22×C4C2×Q8×C43112yes—
231C22×C4C24×C4311yescharacteristic
232C22×C4C24×C4316yes—
233M16—248no—
234C2×C8—24no—
235C2×C8—212no—
236C2×C8—248no—
237C2×C8C24×C4314yes—
238C2×C8C24×C43112yes—
239C4⋊C4C22×C4×C43112yes—
240C4⋊C4C22×C4×C43112yes—
241C22⋊C4C22×C4×C43124yes—
242C42C22×C4×C4312yes—
243C42C22×C4×C4316yes—
244C42C22×C4×C43112yes—
245C42C22×C4×C43112yes—
246C42C24×C4312yes—
247C42C24×C4316yes—
248C23—26no—
249C23—26no—
250C23C2×C4⋊C4×C43112yes—
251C23C23×C4×C4316yes—
252C23C23×C4×C4311yescharacteristic
253Q8C2×C4⋊C4×C43116yes—
254D4C2×C4⋊C4×C43148yes—
255C2×C4—26no—
256C2×C4—22no—
257C2×C4—26no—
258C2×C4—224no—
259C2×C4—412no—
260C2×C4C2×C4⋊C4×C43112yes—
261C2×C4C2×C4⋊C4×C43124yes—
262C2×C4#131×C4314yescomplemented
263C2×C4C23×C4×C4312yes—
264C2×C4C23×C4×C4316yes—
265C2×C4C23×C4×C4316yes—
266C2×C4C23×C4×C4311yescharacteristic
267C2×C4C23×C4×C4316yes—
268C2×C4C23×C4×C4312yes—
269C2×C4C22×D4×C4312yes—
270C2×C4C22×D4×C43112yes—
271C2×C4C22×Q8×C4312yes—
272C2×C4C22×Q8×C43112yes—
273C2×C4C25×C4311yescharacteristic
274C8—24no—
275C8—212no—
276C22—224no—
277C22—26no—
278C22—26no—
279C22C22×C4⋊C4×C43112yes—
280C22C22×C4⋊C4×C4312yes—
281C22C2×#131×C4312yes—
282C22C43×#56812yes—
283C22C24×C4×C4311yescharacteristic
284C4—26no—
285C4—22no—
286C4—26no—
287C4C22×C4⋊C4×C4312yes—
288C4C22×C4⋊C4×C43112yes—
289C4C2×#131×C4314yescomplemented
290C4C23×D4×C4311yescharacteristic
291C4C23×Q8×C4311yescharacteristic
292C2—212no—
293C2C43×#290614yesdirect product factor
294C2C23×C4⋊C4×C4311yescharacteristic
295C2C22×#131×C4311yescharacteristic
296C2C2×C43×#56811yescharacteristic
subgroupG/H
centerC22×C4×C43C24
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC23×C43C23×C4
prime radicalC22×#41×C43C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2906C2direct (N × H)
4. C2×C43×#424C2semidirect
5. C2×C43×#423C2semidirect
6. C22×C4⋊C8×C43C2semidirect
20. C43×#424C22semidirect
21. C43×#423C22semidirect
26. C2×C4⋊C8×C43C22semidirect
113. C2×C4×C43#131semidirect
127. C2×#2906C43direct (N × H)
141. C4×C43C2×#131semidirect
146. #2906C2×C43direct (N × H)
147. C2×#424C2×C43semidirect
148. C2×#423C2×C43semidirect
149. C22×C4⋊C8C2×C43semidirect
151. C2×C43#2906direct (N × H)
168. #424C22×C43semidirect
169. #423C22×C43semidirect
174. C2×C4⋊C8C22×C43semidirect
175. C43C2×#2906direct (N × H)
262. C2×C4#131×C43semidirect
289. C4C2×#131×C43semidirect
293. C2C43×#2906direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131×C432
C2×C4×#41×C432
C43×#29062
C2×C43×#4242
C2×C43×#4232
C22×C4⋊C8×C432
C2×#290643