Finite Group Databasebeta

← C43×#9012 #24929029

Subgroups — C43×#9012 #24929029

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2975C211yesmaximal, characteristic
2C43×#2395C211yesmaximal, characteristic
3C43×#1826C212yesmaximal, complemented
4C4×#99×C43C211yesmaximal, characteristic
5C43×#1297C212yesmaximal, complemented
6C2×C4×D4×C43C2211yescharacteristic
7C2×#117×C43C2211yescharacteristic
8C43×#436—24no—
9C43×#431—21no—
10C2×#99×C43—21no—
11C43×#407—21no—
12C43×#407C2212yes—
13C43×#400C411yescharacteristic, complemented
14C43×#399C411yescharacteristic, complemented
15C43×#398C411yescharacteristic, complemented
16C43×#397—21no—
17C43×#397C411yescharacteristic, complemented
18C43×#394—21no—
19C4×C4⋊C4×C43—21no—
20C4×C22⋊C4×C43—21no—
21C4×C22⋊C4×C43C2212yes—
22C4×C22⋊C4×C43C2211yescharacteristic
23C43×#342—21no—
24C43×#339—24no—
25C22×D4×C43D411yescharacteristic
26C23×C4×C43D411yescharacteristic
27C23×C4×C43C2311yescharacteristic
28C2×M16×C43—22no—
29C2×M16×C43D414yes—
30C4×D4×C43—22no—
31C4×D4×C43—22no—
32#117×C43—22no—
33#117×C43—22no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43C2×C411yescharacteristic
37C2×C4⋊C4×C43C2×C411yescharacteristic
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43C2×C411yescharacteristic
45C2×C22⋊C4×C43D411yescharacteristic
46C2×C42×C43—21no—
47C2×C42×C43—21no—
48C2×C42×C43—22no—
49C2×C42×C43D411yescharacteristic
50C4⋊C8×C43—22no—
51#99×C43—24no—
52C22⋊C8×C43—22no—
53C22⋊C8×C43—22no—
54C22⋊C8×C43—22no—
55C4×C8×C43—22no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—22no—
61#95×C43C2×C411yescharacteristic
62#95×C43C2×C411yescharacteristic
63C24×C43C22⋊C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C2×D4×C43—22no—
66C2×D4×C43—22no—
67C2×D4×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—42no—
75C22×C4×C43—42no—
76C22×C4×C43—42no—
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D412yes—
83C22×C4×C43#4112yes—
84M16×C43—44no—
85M16×C43—82no—
86C2×C8×C43—24no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—42no—
91C4⋊C4×C43—42no—
92C22⋊C4×C43—22no—
93C22⋊C4×C43—24no—
94C22⋊C4×C43—22no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—42no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—42no—
100C42×C43—21no—
101C42×C43—21no—
102C42×C43—42no—
103C42×C43—44no—
104C42×C43—41no—
105C42×C43—41no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C23×C43#12112yes—
117D4×C43—44no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—24no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—44no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—81no—
143C2×C4×C43—82no—
144C2×C4×C43—82no—
145C2×C4×C43#10412yes—
146C2×C4×C43C4×D412yes—
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C8×C43—44no—
150#9012C4311yesmaximal, characteristic, direct product factor, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—22no—
154C22×C43—22no—
155C22×C43—22no—
156C22×C43—42no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—81no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43#38611yescharacteristic
164C22×C43C2×#10411yescharacteristic
165C22×C43#42111yescharacteristic
166C4×C43—22no—
167C4×C43—21no—
168C4×C43—22no—
169C4×C43—42no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—81no—
173C4×C43—84no—
174C4×C43—81no—
175C4×C43—81no—
176C4×C43#45812yes—
177#2975C2×C4311yescharacteristic
178#2395C2×C4311yescharacteristic
179#1826C2×C4312yescomplemented
180C4×#99C2×C4311yescharacteristic
181#1297C2×C4312yescomplemented
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—42no—
185C2×C43—81no—
186C2×C43#187111yescharacteristic
187C2×C43#188411yescharacteristic
188C2×C43#189011yescharacteristic
189C2×C4×D4C22×C4311yescharacteristic
190C2×#117C22×C4311yescharacteristic
191#436—24no—
192#431—21no—
193C2×#99—21no—
194#407—21no—
195#407C22×C4312yes—
196#400C4×C4311yescharacteristic, complemented
197#399C4×C4311yescharacteristic, complemented
198#398C4×C4311yescharacteristic, complemented
199#397—21no—
200#397C4×C4311yescharacteristic, complemented
201#394—21no—
202C4×C4⋊C4—21no—
203C4×C22⋊C4—21no—
204C4×C22⋊C4C22×C4312yes—
205C4×C22⋊C4C22×C4311yescharacteristic
206#342—21no—
207#339—24no—
208C43#901211yescharacteristic, direct product factor, Sylow
209C22×D4D4×C4311yescharacteristic
210C23×C4D4×C4311yescharacteristic
211C23×C4C23×C4311yescharacteristic
212C2×M16—22no—
213C2×M16D4×C4314yes—
214C4×D4—22no—
215C4×D4—22no—
216#117—22no—
217#117—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×C4×C4311yescharacteristic
221C2×C4⋊C4C2×C4×C4311yescharacteristic
222C2×C4⋊C4C2×C4×C4311yescharacteristic
223C2×C22⋊C4—22no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4C2×C4×C4311yescharacteristic
229C2×C22⋊C4D4×C4311yescharacteristic
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—22no—
233C2×C42D4×C4311yescharacteristic
234C4⋊C8—22no—
235#99—24no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239C4×C8—22no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—22no—
245#95C2×C4×C4311yescharacteristic
246#95C2×C4×C4311yescharacteristic
247C24C22⋊C4×C4311yescharacteristic
248C24C2×D4×C4311yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4C22⋊C4×C4311yescharacteristic
262C22×C4C22⋊C4×C4311yescharacteristic
263C22×C4C22⋊C4×C4311yescharacteristic
264C22×C4C22×C4×C4311yescharacteristic
265C22×C4C2×D4×C4312yes—
266C22×C4C2×D4×C4311yescharacteristic
267C22×C4#41×C4312yes—
268M16—44no—
269M16—82no—
270C2×C8—24no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—24no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C42—21no—
285C42—21no—
286C42—42no—
287C42—44no—
288C42—41no—
289C42—41no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×C22⋊C4×C4311yescharacteristic
300C23#121×C4312yes—
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—44no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4#104×C4312yes—
330C2×C4C4×D4×C4312yes—
331C2×C4#120×C4311yescharacteristic
332C2×C4#123×C4311yescharacteristic
333C8—44no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22C43×#38611yescharacteristic
347C22C2×#104×C4311yescharacteristic
348C22C43×#42111yescharacteristic
349C4—22no—
350C4—21no—
351C4—22no—
352C4—42no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—84no—
357C4—81no—
358C4—81no—
359C4C43×#45812yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2C43×#187111yescharacteristic
365C2C43×#188411yescharacteristic
366C2C43×#189011yescharacteristic
subgroupG/H
centerC2×C4×C43#120
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
socleC22×C43#386
prime radicalC22×D4×C43D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#1826C2semidirect
5. C43×#1297C2semidirect
13. C43×#400C4semidirect
14. C43×#399C4semidirect
15. C43×#398C4semidirect
17. C43×#397C4semidirect
150. #9012C43direct (N × H)
179. #1826C2×C43semidirect
181. #1297C2×C43semidirect
196. #400C4×C43semidirect
197. #399C4×C43semidirect
198. #398C4×C43semidirect
200. #397C4×C43semidirect
208. C43#9012direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#29752
C43×#23952
C43×#18262
C4×#99×C432
C43×#12972
#901243