Finite Group Databasebeta

← C43×#9418 #24929435

Subgroups — C43×#9418 #24929435

Order 11008.

402 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3182C211yesmaximal, characteristic
2C43×#2987C211yesmaximal, characteristic, complemented
3C43×#1536C211yesmaximal, characteristic
4C43×#1515C211yesmaximal, characteristic, complemented
5C43×#1514C211yesmaximal, characteristic
6C43×#1291C211yesmaximal, characteristic, complemented
7C43×#1288C211yesmaximal, characteristic, complemented
8C43×#533C2211yescharacteristic
9C43×#532C2211yescharacteristic
10C43×#500C411yescharacteristic, complemented
11C43×#492C411yescharacteristic, complemented
12C43×#487C411yescharacteristic, complemented
13C43×#486C411yescharacteristic, complemented
14C43×#468—22no—
15C43×#446—22no—
16C43×#446—22no—
17C43×#440—22no—
18C43×#433—22no—
19C43×#432C2211yescharacteristic
20C43×#432C2211yescharacteristic
21C43×#432C2211yescharacteristic
22C4×M16×C43C2211yescharacteristic
23C43×#383C2211yescharacteristic
24C43×#329—22no—
25C43×#328—22no—
26C43×#327—22no—
27C2×#41×C43—21no—
28C2×SD16×C43—22no—
29C2×M16×C43—21no—
30C4⋊Q8×C43C2×C411yescharacteristic
31C4⋊Q8×C43C2×C411yescharacteristic
32C4⋊Q8×C43C2×C411yescharacteristic
33#127×C43C2×C411yescharacteristic
34#125×C43—21no—
35#124×C43—21no—
36C22⋊Q8×C43—21no—
37C22⋊Q8×C43D412yes—
38#121×C43—21no—
39#121×C43—21no—
40C4×Q8×C43—21no—
41C4×Q8×C43D412yes—
42C4×D4×C43—21no—
43C4×D4×C43—21no—
44#117×C43—21no—
45C2×C42×C43C2311yescharacteristic
46#107×C43—22no—
47C4⋊C8×C43—24no—
48C4⋊C8×C43—21no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43—21no—
51#103×C43—22no—
52#102×C43—22no—
53C22⋊C8×C43—21no—
54C22⋊C8×C43—21no—
55C22⋊C8×C43D412yes—
56#97×C43—22no—
57#97×C43—21no—
58#97×C43—21no—
59#97×C43—21no—
60#97×C43D412yes—
61C4×C8×C43—22no—
62C4×C8×C43C2×C411yescharacteristic
63C4×C8×C43C2×C411yescharacteristic
64#95×C43—21no—
65#95×C43—21no—
66#95×C43—21no—
67#41×C43—82no—
68C2×Q8×C43—21no—
69C2×Q8×C43—21no—
70C2×Q8×C43C22⋊C412yes—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—41no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80SD16×C43—44no—
81M16×C43—42no—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—22no—
85C2×C8×C43—22no—
86C2×C8×C43—41no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43C22⋊C412yes—
95C22⋊C4×C43—22no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C42×C43—22no—
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103C23×C43—41no—
104C23×C43#12111yescharacteristic
105Q8×C43—42no—
106Q8×C43—81no—
107Q8×C43—81no—
108D4×C43—42no—
109D4×C43—81no—
110D4×C43—81no—
111D4×C43—82no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—82no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43C2×C22⋊C411yescharacteristic
123C2×C4×C43C4×D411yescharacteristic
124C2×C4×C43C4×D411yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12311yescharacteristic
128C8×C43—22no—
129C8×C43—42no—
130C8×C43—42no—
131C8×C43—41no—
132C8×C43—81no—
133#9418C4311yesmaximal, characteristic, direct product factor, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—81no—
138C22×C43—81no—
139C22×C43—81no—
140C22×C43#38611yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—42no—
148C4×C43—42no—
149C4×C43—81no—
150C4×C43—161no—
151#3182C2×C4311yescharacteristic
152#2987C2×C4311yescharacteristic, complemented
153#1536C2×C4311yescharacteristic
154#1515C2×C4311yescharacteristic, complemented
155#1514C2×C4311yescharacteristic
156#1291C2×C4311yescharacteristic, complemented
157#1288C2×C4311yescharacteristic, complemented
158C2×C43—41no—
159C2×C43—161no—
160C2×C43#188411yescharacteristic
161C2×C43#190311yescharacteristic
162C2×C43#190511yescharacteristic
163#533C22×C4311yescharacteristic
164#532C22×C4311yescharacteristic
165#500C4×C4311yescharacteristic, complemented
166#492C4×C4311yescharacteristic, complemented
167#487C4×C4311yescharacteristic, complemented
168#486C4×C4311yescharacteristic, complemented
169#468—22no—
170#446—22no—
171#446—22no—
172#440—22no—
173#433—22no—
174#432C22×C4311yescharacteristic
175#432C22×C4311yescharacteristic
176#432C22×C4311yescharacteristic
177C4×M16C22×C4311yescharacteristic
178#383C22×C4311yescharacteristic
179#329—22no—
180#328—22no—
181#327—22no—
182C43#941811yescharacteristic, direct product factor, Sylow
183C2×#41—21no—
184C2×SD16—22no—
185C2×M16—21no—
186C4⋊Q8C2×C4×C4311yescharacteristic
187C4⋊Q8C2×C4×C4311yescharacteristic
188C4⋊Q8C2×C4×C4311yescharacteristic
189#127C2×C4×C4311yescharacteristic
190#125—21no—
191#124—21no—
192C22⋊Q8—21no—
193C22⋊Q8D4×C4312yes—
194#121—21no—
195#121—21no—
196C4×Q8—21no—
197C4×Q8D4×C4312yes—
198C4×D4—21no—
199C4×D4—21no—
200#117—21no—
201C2×C42C23×C4311yescharacteristic
202#107—22no—
203C4⋊C8—24no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207#103—22no—
208#102—22no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211C22⋊C8D4×C4312yes—
212#97—22no—
213#97—21no—
214#97—21no—
215#97—21no—
216#97D4×C4312yes—
217C4×C8—22no—
218C4×C8C2×C4×C4311yescharacteristic
219C4×C8C2×C4×C4311yescharacteristic
220#95—21no—
221#95—21no—
222#95—21no—
223#41—82no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8C22⋊C4×C4312yes—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4C2×D4×C4311yescharacteristic
234C22×C4C2×D4×C4311yescharacteristic
235C22×C4#41×C4311yescharacteristic
236SD16—44no—
237M16—42no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4C22⋊C4×C4312yes—
251C22⋊C4—22no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C42—22no—
255C42C22×C4×C4311yescharacteristic
256C42C2×D4×C4311yescharacteristic
257C42C2×D4×C4311yescharacteristic
258C42#41×C4311yescharacteristic
259C23—41no—
260C23#121×C4311yescharacteristic
261Q8—42no—
262Q8—81no—
263Q8—81no—
264D4—42no—
265D4—81no—
266D4—81no—
267D4—82no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—82no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4C2×C22⋊C4×C4311yescharacteristic
279C2×C4C4×D4×C4311yescharacteristic
280C2×C4C4×D4×C4311yescharacteristic
281C2×C4#120×C4311yescharacteristic
282C2×C4#121×C4311yescharacteristic
283C2×C4#123×C4311yescharacteristic
284C8—22no—
285C8—41no—
286C8—42no—
287C8—42no—
288C8—81no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22C43×#38611yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—81no—
305C4—161no—
306C2—41no—
307C2—161no—
308C2C43×#188411yescharacteristic
309C2C43×#190311yescharacteristic
310C2C43×#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×#2987C2semidirect
4. C43×#1515C2semidirect
6. C43×#1291C2semidirect
7. C43×#1288C2semidirect
10. C43×#500C4semidirect
11. C43×#492C4semidirect
12. C43×#487C4semidirect
13. C43×#486C4semidirect
133. #9418C43direct (N × H)
152. #2987C2×C43semidirect
154. #1515C2×C43semidirect
156. #1291C2×C43semidirect
157. #1288C2×C43semidirect
165. #500C4×C43semidirect
166. #492C4×C43semidirect
167. #487C4×C43semidirect
168. #486C4×C43semidirect
182. C43#9418direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31822
C43×#29872
C43×#15362
C43×#15152
C43×#15142
C43×#12912
C43×#12882
#941843