Finite Group Databasebeta

← C2×C43×#2072 #24943642

Subgroups — C2×C43×#2072 #24943642

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#103×C43C212yesmaximal
2C2×C43×#391C211yesmaximal, characteristic
3C2×C43×#384C211yesmaximal, characteristic
4C43×#2072C218yesmaximal, direct product factor
5C2×C43×#340C212yesmaximal
6C2×C43×#336C211yesmaximal, characteristic
7C23×Q8×C43C2211yescharacteristic
8C23×C8×C43C2212yes—
9C22×C4⋊C4×C43—21no—
10C22×C4⋊C4×C43—21no—
11C22×C4⋊C4×C43C2212yes—
12C22×C4⋊C4×C43C2211yescharacteristic
13C22×C42×C43C2211yescharacteristic
14C2×#103×C43—28no—
15C2×#103×C43C2218yes—
16C43×#391—22no—
17C43×#391C2214yes—
18C43×#384—22no—
19C43×#384C2214yes—
20C2×#95×C43—21no—
21C2×#95×C43—21no—
22C43×#340C2218yes—
23C43×#336C2214yes—
24C22×Q8×C43—21no—
25C22×Q8×C43—22no—
26C22×Q8×C43—24no—
27C22×Q8×C43—24no—
28C22×Q8×C43D414yes—
29C22×Q8×C43C2312yes—
30C23×C4×C43—21no—
31C23×C4×C43—22no—
32C23×C4×C43—21no—
33C23×C4×C43D411yescharacteristic
34C23×C4×C43D411yescharacteristic
35C23×C4×C43C2311yescharacteristic
36C22×C8×C43—24no—
37C22×C8×C43—24no—
38C22×C8×C43—24no—
39C22×C8×C43C2314yes—
40C2×C4⋊C4×C43—24no—
41C2×C4⋊C4×C43—24no—
42C2×C4⋊C4×C43—24no—
43C2×C4⋊C4×C43—24no—
44C2×C4⋊C4×C43—24no—
45C2×C4⋊C4×C43—22no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—44no—
48C2×C4⋊C4×C43—44no—
49C2×C4⋊C4×C43C2312yes—
50C2×C4⋊C4×C43C2314yes—
51C2×C42×C43—24no—
52C2×C42×C43D412yes—
53C2×C42×C43C2312yes—
54#103×C43—216no—
55#95×C43—24no—
56#95×C43—24no—
57C24×C43C2×D411yescharacteristic
58C2×Q8×C43—24no—
59C2×Q8×C43—22no—
60C2×Q8×C43—216no—
61C2×Q8×C43—24no—
62C2×Q8×C43—24no—
63C2×Q8×C43—42no—
64C2×Q8×C43—42no—
65C2×Q8×C43—48no—
66C2×Q8×C43C2×D414yes—
67C22×C4×C43—24no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—22no—
71C22×C4×C43—22no—
72C22×C4×C43—22no—
73C22×C4×C43—22no—
74C22×C4×C43—24no—
75C22×C4×C43—44no—
76C22×C4×C43—42no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43—44no—
80C22×C4×C43—44no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43SD1614yes—
84C22×C4×C43Q1614yes—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4112yes—
90C22×C4×C43#4114yes—
91C22×C4×C43#4114yes—
92C22×C4×C43C2411yescharacteristic
93C2×C8×C43—24no—
94C2×C8×C43—24no—
95C2×C8×C43—24no—
96C2×C8×C43—48no—
97C4⋊C4×C43—24no—
98C4⋊C4×C43—24no—
99C4⋊C4×C43—24no—
100C4⋊C4×C43—48no—
101C4⋊C4×C43—44no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—48no—
104C42×C43—24no—
105C42×C43—24no—
106C23×C43#12112yes—
107C23×C43#12312yes—
108C23×C43#12412yes—
109C23×C43C2×SD1612yes—
110C23×C43C2×Q1612yes—
111C23×C43AGL(1,ℤ/8)12yes—
112C23×C43#13712yes—
113C23×C43C22×D411yescharacteristic
114Q8×C43—28no—
115Q8×C43—44no—
116Q8×C43—48no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—28no—
122C2×C4×C43—28no—
123C2×C4×C43—24no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—48no—
127C2×C4×C43—44no—
128C2×C4×C43—42no—
129C2×C4×C43—44no—
130C2×C4×C43—44no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—88no—
134C2×C4×C43—84no—
135C2×C4×C43#12112yes—
136C2×C4×C43#12318yes—
137C2×C4×C43#12312yes—
138C2×C4×C43#12412yes—
139C2×C4×C43#12618yes—
140C2×C4×C43C2×SD1614yes—
141C2×C4×C43C2×Q1614yes—
142C2×C4×C43C22×D411yescharacteristic
143C2×C4×C43C2×#4112yes—
144C2×C4×C43C2×#4112yes—
145C2×C4×C43C2×#4111yescharacteristic
146C8×C43—44no—
147C2×#2072C4311yesmaximal, characteristic, direct product factor, Sylow
148C22×C43#39714yes—
149C22×C43#46014yes—
150C22×C43#46214yes—
151C22×C43#48314yes—
152C22×C43#48414yes—
153C22×C43#48714yes—
154C22×C43#48914yes—
155C22×C43C2×#12111yescharacteristic
156C22×C43C2×#12311yescharacteristic
157C22×C43C2×#12411yescharacteristic
158C22×C43C22×SD1611yescharacteristic
159C22×C43C22×Q1611yescharacteristic
160C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
161C22×C43C2×#13711yescharacteristic
162C4×C43—24no—
163C4×C43—24no—
164C4×C43—44no—
165C4×C43—82no—
166C4×C43—84no—
167C4×C43#39714yes—
168C4×C43C2×#12312yes—
169C4×C43C2×#12612yes—
170C22×#103C2×C4312yes—
171C2×#391C2×C4311yescharacteristic
172C2×#384C2×C4311yescharacteristic
173#2072C2×C4318yesdirect product factor
174C2×#340C2×C4312yes—
175C2×#336C2×C4311yescharacteristic
176C2×C43#207218yesdirect product factor
177C2×C43C2×#39711yescharacteristic
178C2×C43C2×#46011yescharacteristic
179C2×C43C2×#46211yescharacteristic
180C2×C43C2×#48311yescharacteristic
181C2×C43C2×#48411yescharacteristic
182C2×C43C2×#48711yescharacteristic
183C2×C43C2×#48911yescharacteristic
184C23×Q8C22×C4311yescharacteristic
185C23×C8C22×C4312yes—
186C22×C4⋊C4—21no—
187C22×C4⋊C4—21no—
188C22×C4⋊C4C22×C4312yes—
189C22×C4⋊C4C22×C4311yescharacteristic
190C22×C42C22×C4311yescharacteristic
191C2×#103—28no—
192C2×#103C22×C4318yes—
193#391—22no—
194#391C22×C4314yes—
195#384—22no—
196#384C22×C4314yes—
197C2×#95—21no—
198C2×#95—21no—
199#340C22×C4318yes—
200#336C22×C4314yes—
201C43C2×#207211yescharacteristic, direct product factor, Sylow
202C22×Q8—21no—
203C22×Q8—22no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8D4×C4314yes—
207C22×Q8C23×C4312yes—
208C23×C4—21no—
209C23×C4—22no—
210C23×C4—21no—
211C23×C4D4×C4311yescharacteristic
212C23×C4D4×C4311yescharacteristic
213C23×C4C23×C4311yescharacteristic
214C22×C8—24no—
215C22×C8—24no—
216C22×C8—24no—
217C22×C8C23×C4314yes—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—44no—
226C2×C4⋊C4—44no—
227C2×C4⋊C4C23×C4312yes—
228C2×C4⋊C4C23×C4314yes—
229C2×C42—24no—
230C2×C42D4×C4312yes—
231C2×C42C23×C4312yes—
232#103—216no—
233#95—24no—
234#95—24no—
235C24C2×D4×C4311yescharacteristic
236C2×Q8—24no—
237C2×Q8—22no—
238C2×Q8—216no—
239C2×Q8—24no—
240C2×Q8—24no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—48no—
244C2×Q8C2×D4×C4314yes—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—44no—
256C22×C4—42no—
257C22×C4—44no—
258C22×C4—44no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4SD16×C4314yes—
262C22×C4Q16×C4314yes—
263C22×C4C2×D4×C4312yes—
264C22×C4C2×D4×C4312yes—
265C22×C4C2×D4×C4311yescharacteristic
266C22×C4C2×D4×C4312yes—
267C22×C4#41×C4312yes—
268C22×C4#41×C4314yes—
269C22×C4#41×C4314yes—
270C22×C4C24×C4311yescharacteristic
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—48no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—48no—
279C4⋊C4—44no—
280C4⋊C4—42no—
281C4⋊C4—48no—
282C42—24no—
283C42—24no—
284C23#121×C4312yes—
285C23#123×C4312yes—
286C23#124×C4312yes—
287C23C2×SD16×C4312yes—
288C23C2×Q16×C4312yes—
289C23AGL(1,ℤ/8)×C4312yes—
290C23#137×C4312yes—
291C23C22×D4×C4311yescharacteristic
292Q8—28no—
293Q8—44no—
294Q8—48no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—24no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—48no—
305C2×C4—44no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—88no—
312C2×C4—84no—
313C2×C4#121×C4312yes—
314C2×C4#123×C4318yes—
315C2×C4#123×C4312yes—
316C2×C4#124×C4312yes—
317C2×C4#126×C4318yes—
318C2×C4C2×SD16×C4314yes—
319C2×C4C2×Q16×C4314yes—
320C2×C4C22×D4×C4311yescharacteristic
321C2×C4C2×#41×C4312yes—
322C2×C4C2×#41×C4312yes—
323C2×C4C2×#41×C4311yescharacteristic
324C8—44no—
325C22C43×#39714yes—
326C22C43×#46014yes—
327C22C43×#46214yes—
328C22C43×#48314yes—
329C22C43×#48414yes—
330C22C43×#48714yes—
331C22C43×#48914yes—
332C22C2×#121×C4311yescharacteristic
333C22C2×#123×C4311yescharacteristic
334C22C2×#124×C4311yescharacteristic
335C22C22×SD16×C4311yescharacteristic
336C22C22×Q16×C4311yescharacteristic
337C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
338C22C2×#137×C4311yescharacteristic
339C4—24no—
340C4—24no—
341C4—44no—
342C4—82no—
343C4—84no—
344C4C43×#39714yes—
345C4C2×#123×C4312yes—
346C4C2×#126×C4312yes—
347C2C43×#207218yesdirect product factor
348C2C2×C43×#39711yescharacteristic
349C2C2×C43×#46011yescharacteristic
350C2C2×C43×#46211yescharacteristic
351C2C2×C43×#48311yescharacteristic
352C2C2×C43×#48411yescharacteristic
353C2C2×C43×#48711yescharacteristic
354C2C2×C43×#48911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C43C2×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#2072C2direct (N × H)
147. C2×#2072C43direct (N × H)
173. #2072C2×C43direct (N × H)
176. C2×C43#2072direct (N × H)
201. C43C2×#2072direct (N × H)
347. C2C43×#2072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#103×C432
C2×C43×#3912
C2×C43×#3842
C43×#20722
C2×C43×#3402
C2×C43×#3362
C2×#207243