Finite Group Databasebeta

← C43×#13329 #24933346

Subgroups — C43×#13329 #24933346

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q32×C43C211yesmaximal, characteristic, complemented
2C22×SD32×C43C211yesmaximal, characteristic
3C2×C43×#495C211yesmaximal, characteristic
4C2×C43×#358C211yesmaximal, characteristic, complemented
5C2×C43×#357C211yesmaximal, characteristic
6C43×#1969C211yesmaximal, characteristic, complemented
7C43×#1374C211yesmaximal, characteristic, complemented
8C22×Q16×C43C2211yescharacteristic
9C22×Q16×C43C2211yescharacteristic
10C22×SD16×C43—21no—
11C22×D8×C43C2211yescharacteristic
12C2×#124×C43—21no—
13C2×Q32×C43—22no—
14C2×Q32×C43—22no—
15C2×Q32×C43—22no—
16C2×SD32×C43—22no—
17C2×SD32×C43—22no—
18C2×SD32×C43—22no—
19C22×C16×C43C2211yescharacteristic
20C22×C16×C43C2211yescharacteristic
21C43×#495—22no—
22C43×#495—22no—
23C2×#107×C43C2211yescharacteristic
24C2×#103×C43—21no—
25C2×C4×C8×C43C2211yescharacteristic
26C43×#391—21no—
27C43×#358—22no—
28C43×#357—22no—
29C22×Q8×C43—21no—
30C22×Q8×C43—21no—
31C22×D4×C43—21no—
32C2×Q16×C43—21no—
33C2×Q16×C43—21no—
34C2×Q16×C43—21no—
35C2×Q16×C43—21no—
36C2×Q16×C43—21no—
37C2×Q16×C43—21no—
38C2×Q16×C43—21no—
39C2×Q16×C43—21no—
40C2×Q16×C43—21no—
41C2×Q16×C43—21no—
42C2×Q16×C43D412yes—
43C2×Q16×C43D412yes—
44C2×SD16×C43—24no—
45C2×SD16×C43—42no—
46C2×SD16×C43—42no—
47C2×D8×C43—21no—
48C2×D8×C43—21no—
49C2×D8×C43—21no—
50C2×D8×C43—21no—
51C2×D8×C43—21no—
52C2×D8×C43D412yes—
53C22×C8×C43D411yescharacteristic
54C22×C8×C43C2311yescharacteristic
55#124×C43—24no—
56#124×C43—42no—
57C2×C4⋊C4×C43—21no—
58C2×C22⋊C4×C43—42no—
59C2×C42×C43D411yescharacteristic
60Q32×C43—28no—
61SD32×C43—28no—
62C2×C16×C43—21no—
63C2×C16×C43—21no—
64C2×C16×C43—21no—
65C2×C16×C43—21no—
66C2×C16×C43D412yes—
67C2×C16×C43D412yes—
68#107×C43—21no—
69#107×C43—21no—
70#103×C43—42no—
71C4×C8×C43—21no—
72C4×C8×C43—21no—
73#95×C43—42no—
74C24×C43—41no—
75C2×Q8×C43—22no—
76C2×Q8×C43—22no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C2×Q8×C43—41no—
83C2×Q8×C43—41no—
84C2×Q8×C43—41no—
85C2×Q8×C43—41no—
86C2×Q8×C43—41no—
87C2×D4×C43—22no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43D812yes—
97C22×C4×C43C2×D411yescharacteristic
98Q16×C43—22no—
99Q16×C43—22no—
100Q16×C43—22no—
101Q16×C43—22no—
102Q16×C43—41no—
103Q16×C43—41no—
104Q16×C43—41no—
105Q16×C43—41no—
106SD16×C43—48no—
107D8×C43—22no—
108D8×C43—22no—
109D8×C43—41no—
110D8×C43—41no—
111C2×C8×C43—21no—
112C2×C8×C43—21no—
113C2×C8×C43D812yes—
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43C2×D411yescharacteristic
117C2×C8×C43C2×D411yescharacteristic
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43#4111yescharacteristic
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C22⋊C4×C43—48no—
123C42×C43—21no—
124C42×C43—21no—
125C16×C43—22no—
126C16×C43—22no—
127C23×C43—42no—
128C23×C43—81no—
129C23×C43—81no—
130C23×C43—82no—
131C23×C43—82no—
132C23×C43C2×D811yescharacteristic
133Q8×C43—42no—
134Q8×C43—42no—
135Q8×C43—42no—
136Q8×C43—42no—
137Q8×C43—81no—
138Q8×C43—81no—
139Q8×C43—81no—
140Q8×C43—81no—
141D4×C43—42no—
142D4×C43—42no—
143D4×C43—81no—
144D4×C43—81no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—82no—
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12711yescharacteristic
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C8×C43—22no—
163C8×C43#12011yescharacteristic
164C8×C43#12011yescharacteristic
165C8×C43#12111yescharacteristic
166C8×C43#12111yescharacteristic
167#13329C4311yesmaximal, characteristic, direct product factor, Sylow
168C22×C43—84no—
169C22×C43—82no—
170C22×C43—162no—
171C22×C43—161no—
172C22×C43—161no—
173C22×C43#44711yescharacteristic
174C22×C43#45911yescharacteristic
175C22×C43#49311yescharacteristic
176C22×C43#50812yes—
177C22×C43#51012yes—
178C4×C43—42no—
179C4×C43—82no—
180C4×C43—82no—
181C4×C43—161no—
182C4×C43#39211yescharacteristic
183C4×C43#44711yescharacteristic
184C4×C43#45911yescharacteristic
185C4×C43#49611yescharacteristic
186C22×Q32C2×C4311yescharacteristic, complemented
187C22×SD32C2×C4311yescharacteristic
188C2×#495C2×C4311yescharacteristic
189C2×#358C2×C4311yescharacteristic, complemented
190C2×#357C2×C4311yescharacteristic
191#1969C2×C4311yescharacteristic, complemented
192#1374C2×C4311yescharacteristic, complemented
193C2×C43—162no—
194C2×C43#201111yescharacteristic
195C2×C43#218912yes—
196C2×C43#221112yes—
197C2×C43#224911yescharacteristic
198C2×C43#225111yescharacteristic
199C22×Q16C22×C4311yescharacteristic
200C22×Q16C22×C4311yescharacteristic
201C22×SD16—21no—
202C22×D8C22×C4311yescharacteristic
203C2×#124—21no—
204C2×Q32—22no—
205C2×Q32—22no—
206C2×Q32—22no—
207C2×SD32—22no—
208C2×SD32—22no—
209C2×SD32—22no—
210C22×C16C22×C4311yescharacteristic
211C22×C16C22×C4311yescharacteristic
212#495—22no—
213#495—22no—
214C2×#107C22×C4311yescharacteristic
215C2×#103—21no—
216C2×C4×C8C22×C4311yescharacteristic
217#391—21no—
218#358—22no—
219#357—22no—
220C43#1332911yescharacteristic, direct product factor, Sylow
221C22×Q8—21no—
222C22×Q8—21no—
223C22×D4—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16—21no—
228C2×Q16—21no—
229C2×Q16—21no—
230C2×Q16—21no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16D4×C4312yes—
235C2×Q16D4×C4312yes—
236C2×SD16—24no—
237C2×SD16—42no—
238C2×SD16—42no—
239C2×D8—21no—
240C2×D8—21no—
241C2×D8—21no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8D4×C4312yes—
245C22×C8D4×C4311yescharacteristic
246C22×C8C23×C4311yescharacteristic
247#124—24no—
248#124—42no—
249C2×C4⋊C4—21no—
250C2×C22⋊C4—42no—
251C2×C42D4×C4311yescharacteristic
252Q32—28no—
253SD32—28no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16D4×C4312yes—
259C2×C16D4×C4312yes—
260#107—21no—
261#107—21no—
262#103—42no—
263C4×C8—21no—
264C4×C8—21no—
265#95—42no—
266C24—41no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4D8×C4312yes—
289C22×C4C2×D4×C4311yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—22no—
293Q16—22no—
294Q16—41no—
295Q16—41no—
296Q16—41no—
297Q16—41no—
298SD16—48no—
299D8—22no—
300D8—22no—
301D8—41no—
302D8—41no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8D8×C4312yes—
306C2×C8C2×D4×C4311yescharacteristic
307C2×C8C2×D4×C4311yescharacteristic
308C2×C8C2×D4×C4311yescharacteristic
309C2×C8C2×D4×C4311yescharacteristic
310C2×C8C2×D4×C4311yescharacteristic
311C2×C8#41×C4311yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—48no—
315C42—21no—
316C42—21no—
317C16—22no—
318C16—22no—
319C23—42no—
320C23—82no—
321C23—82no—
322C23—81no—
323C23—81no—
324C23C2×D8×C4311yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—42no—
329Q8—81no—
330Q8—81no—
331Q8—81no—
332Q8—81no—
333D4—42no—
334D4—42no—
335D4—81no—
336D4—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4—81no—
348C2×C4#120×C4311yescharacteristic
349C2×C4#121×C4311yescharacteristic
350C2×C4#127×C4311yescharacteristic
351C2×C4C2×D8×C4311yescharacteristic
352C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
353C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
354C8—22no—
355C8#120×C4311yescharacteristic
356C8#120×C4311yescharacteristic
357C8#121×C4311yescharacteristic
358C8#121×C4311yescharacteristic
359C22—84no—
360C22—82no—
361C22—162no—
362C22—161no—
363C22—161no—
364C22C43×#44711yescharacteristic
365C22C43×#45911yescharacteristic
366C22C43×#49311yescharacteristic
367C22C43×#50812yes—
368C22C43×#51012yes—
369C4—42no—
370C4—82no—
371C4—82no—
372C4—161no—
373C4C43×#39211yescharacteristic
374C4C43×#44711yescharacteristic
375C4C43×#45911yescharacteristic
376C4C43×#49611yescharacteristic
377C2—162no—
378C2C43×#201111yescharacteristic
379C2C43×#218912yes—
380C2C43×#221112yes—
381C2C43×#224911yescharacteristic
382C2C43×#225111yescharacteristic
subgroupG/H
center, socleC23×C43C2×D8
commutator, Frattini, cosocleC22×C8C23×C43
prime radicalC22×D8×C43C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ C2×C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×Q32×C43C2semidirect
4. C2×C43×#358C2semidirect
6. C43×#1969C2semidirect
7. C43×#1374C2semidirect
167. #13329C43direct (N × H)
186. C22×Q32C2×C43semidirect
189. C2×#358C2×C43semidirect
191. #1969C2×C43semidirect
192. #1374C2×C43semidirect
220. C43#13329direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q32×C432
C22×SD32×C432
C2×C43×#4952
C2×C43×#3582
C2×C43×#3572
C43×#19692
C43×#13742
#1332943