Finite Group Databasebeta

← C43×#9330 #24929347

Subgroups — C43×#9330 #24929347

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3112C211yesmaximal, characteristic
2C43×#2320C211yesmaximal, characteristic, complemented
3C43×#1980C211yesmaximal, characteristic
4C43×#1505C211yesmaximal, characteristic
5C43×#1491C211yesmaximal, characteristic, complemented
6C43×#1300C211yesmaximal, characteristic, complemented
7C43×#1285C211yesmaximal, characteristic, complemented
8C43×#532C2211yescharacteristic
9C2×C4×Q8×C43C2211yescharacteristic
10C43×#480—21no—
11C43×#477C412yescomplemented
12C43×#460C412yescomplemented
13C43×#448—21no—
14C43×#440—22no—
15C43×#432C2211yescharacteristic
16C43×#432C2211yescharacteristic
17C2×#104×C43—22no—
18C4×M16×C43C2211yescharacteristic
19C43×#391—21no—
20C43×#389—21no—
21C43×#387—22no—
22C43×#383—21no—
23C43×#382—21no—
24C4×C4⋊C4×C43C2211yescharacteristic
25C43×#376C2211yescharacteristic
26C43×#327—21no—
27C43×#327—21no—
28C43×Q8⋊C8—22no—
29C2×#41×C43—21no—
30C22×Q8×C43D411yescharacteristic
31C2×SD16×C43—22no—
32C2×M16×C43—21no—
33C4⋊Q8×C43C2×C411yescharacteristic
34#127×C43C2×C411yescharacteristic
35#124×C43—21no—
36#121×C43—21no—
37#121×C43—21no—
38C4×Q8×C43—21no—
39C4×Q8×C43—21no—
40C4×Q8×C43C2×C412yes—
41C4×Q8×C43D412yes—
42C4×D4×C43—21no—
43C4×D4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—22no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C42×C43—21no—
49C2×C42×C43—21no—
50C2×C42×C43D412yes—
51C2×C42×C43C2311yescharacteristic
52#107×C43—22no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43C2×C412yes—
55#104×C43—44no—
56#103×C43—22no—
57#102×C43—22no—
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#97×C43—21no—
61#97×C43—21no—
62#97×C43—21no—
63C4×C8×C43—21no—
64#95×C43—22no—
65#95×C43—22no—
66#95×C43—22no—
67#95×C43—21no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71#41×C43—42no—
72#41×C43—42no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—42no—
76C2×Q8×C43C22⋊C412yes—
77C2×D4×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—41no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90SD16×C43—44no—
91M16×C43—22no—
92M16×C43—41no—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—82no—
103C4⋊C4×C43C22⋊C412yes—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C42×C43—22no—
107C42×C43—22no—
108C42×C43—42no—
109C42×C43—42no—
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114C23×C43—41no—
115C23×C43#12011yescharacteristic
116Q8×C43—22no—
117Q8×C43—22no—
118Q8×C43—42no—
119Q8×C43—42no—
120D4×C43—42no—
121D4×C43—42no—
122D4×C43—81no—
123D4×C43—81no—
124D4×C43—81no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—42no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—82no—
145C2×C4×C43C2×C22⋊C411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12311yescharacteristic
151C8×C43—42no—
152C8×C43—42no—
153C8×C43—81no—
154#9330C4311yesmaximal, characteristic, direct product factor, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—81no—
158C22×C43—81no—
159C22×C43—81no—
160C22×C43#38611yescharacteristic
161C22×C43#45311yescharacteristic
162C22×C43#45411yescharacteristic
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—42no—
169C4×C43—42no—
170C4×C43—81no—
171C4×C43—82no—
172C4×C43—81no—
173C4×C43—81no—
174C4×C43#42112yes—
175#3112C2×C4311yescharacteristic
176#2320C2×C4311yescharacteristic, complemented
177#1980C2×C4311yescharacteristic
178#1505C2×C4311yescharacteristic
179#1491C2×C4311yescharacteristic, complemented
180#1300C2×C4311yescharacteristic, complemented
181#1285C2×C4311yescharacteristic, complemented
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—161no—
185C2×C43#188311yescharacteristic
186C2×C43#189711yescharacteristic
187C2×C43#190511yescharacteristic
188#532C22×C4311yescharacteristic
189C2×C4×Q8C22×C4311yescharacteristic
190#480—21no—
191#477C4×C4312yescomplemented
192#460C4×C4312yescomplemented
193#448—21no—
194#440—22no—
195#432C22×C4311yescharacteristic
196#432C22×C4311yescharacteristic
197C2×#104—22no—
198C4×M16C22×C4311yescharacteristic
199#391—21no—
200#389—21no—
201#387—22no—
202#383—21no—
203#382—21no—
204C4×C4⋊C4C22×C4311yescharacteristic
205#376C22×C4311yescharacteristic
206#327—21no—
207#327—21no—
208Q8⋊C8—22no—
209C43#933011yescharacteristic, direct product factor, Sylow
210C2×#41—21no—
211C22×Q8D4×C4311yescharacteristic
212C2×SD16—22no—
213C2×M16—21no—
214C4⋊Q8C2×C4×C4311yescharacteristic
215#127C2×C4×C4311yescharacteristic
216#124—21no—
217#121—21no—
218#121—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8C2×C4×C4312yes—
222C4×Q8D4×C4312yes—
223C4×D4—21no—
224C4×D4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4D4×C4311yescharacteristic
229C2×C42—21no—
230C2×C42—21no—
231C2×C42D4×C4312yes—
232C2×C42C23×C4311yescharacteristic
233#107—22no—
234C4⋊C8—21no—
235C4⋊C8C2×C4×C4312yes—
236#104—44no—
237#103—22no—
238#102—22no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241#97—21no—
242#97—21no—
243#97—21no—
244C4×C8—21no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—21no—
249#95—21no—
250#95D4×C4311yescharacteristic
251#95D4×C4311yescharacteristic
252#41—42no—
253#41—42no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—42no—
257C2×Q8C22⋊C4×C4312yes—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4C2×D4×C4311yescharacteristic
269C22×C4C2×D4×C4311yescharacteristic
270C22×C4C2×D4×C4311yescharacteristic
271SD16—44no—
272M16—22no—
273M16—41no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—42no—
283C4⋊C4—82no—
284C4⋊C4C22⋊C4×C4312yes—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—22no—
288C42—22no—
289C42—42no—
290C42—42no—
291C42C22×C4×C4311yescharacteristic
292C42C2×D4×C4311yescharacteristic
293C42#41×C4311yescharacteristic
294C42#41×C4311yescharacteristic
295C23—41no—
296C23#120×C4311yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—42no—
300Q8—42no—
301D4—42no—
302D4—42no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4C2×C22⋊C4×C4311yescharacteristic
327C2×C4C4×D4×C4311yescharacteristic
328C2×C4C4×D4×C4311yescharacteristic
329C2×C4#121×C4311yescharacteristic
330C2×C4#121×C4311yescharacteristic
331C2×C4#123×C4311yescharacteristic
332C8—42no—
333C8—42no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C43×#38611yescharacteristic
341C22C43×#45311yescharacteristic
342C22C43×#45411yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—81no—
351C4—82no—
352C4—81no—
353C4—81no—
354C4C43×#42112yes—
355C2—21no—
356C2—21no—
357C2—161no—
358C2C43×#188311yescharacteristic
359C2C43×#189711yescharacteristic
360C2C43×#190511yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2320C2semidirect
5. C43×#1491C2semidirect
6. C43×#1300C2semidirect
7. C43×#1285C2semidirect
11. C43×#477C4semidirect
12. C43×#460C4semidirect
154. #9330C43direct (N × H)
176. #2320C2×C43semidirect
179. #1491C2×C43semidirect
180. #1300C2×C43semidirect
181. #1285C2×C43semidirect
191. #477C4×C43semidirect
192. #460C4×C43semidirect
209. C43#9330direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31122
C43×#23202
C43×#19802
C43×#15052
C43×#14912
C43×#13002
C43×#12852
#933043