Finite Group Databasebeta

← C43×#60491 #24980508

Subgroups — C43×#60491 #24980508

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3458C211yesmaximal, characteristic
2C2×C43×#519C211yesmaximal, characteristic
3C43×#3082C2116yesmaximal, complemented
4C43×#3078C218yesmaximal, complemented
5C43×#2911C212yesmaximal
6C43×#2905C211yesmaximal, characteristic
7C2×C43×#419C212yesmaximal
8C23×Q8×C43C2211yescharacteristic
9C22×M16×C43C2212yes—
10C43×#544—22no—
11C43×#544C2218yes—
12C43×#543—22no—
13C43×#533—24no—
14C43×#533C2214yes—
15C43×#519—24no—
16C43×#519C2218yes—
17C2×C4×Q8×C43—22no—
18C2×C4×Q8×C43C2214yes—
19C2×#117×C43—22no—
20C2×#117×C43C2212yes—
21C2×#117×C43C2211yescharacteristic
22C2×#117×C43C2211yescharacteristic
23C43×#479C22132yescomplemented
24C43×#477C22116yescomplemented
25C43×#475C22116yescomplemented
26C43×#428C2218yes—
27C43×#428C2218yes—
28C43×#427C2218yes—
29C43×#424C2218yes—
30C43×#423C2214yes—
31C43×#419C2218yes—
32C43×#419C2218yes—
33C2×#103×C43C2218yes—
34C22×Q8×C43—21no—
35C22×Q8×C43—22no—
36C22×Q8×C43—24no—
37C22×Q8×C43Q818yescomplemented
38C22×Q8×C43C2312yes—
39C22×Q8×C43C2314yes—
40C23×C4×C43—21no—
41C23×C4×C43C2311yescharacteristic
42C2×M16×C43—28no—
43C2×M16×C43C2314yes—
44C2×M16×C43C2314yes—
45C22×C8×C43C2314yes—
46C4⋊Q8×C43—28no—
47C4⋊Q8×C43C2318yes—
48#125×C43—28no—
49#125×C43C2318yes—
50C22⋊Q8×C43—28no—
51C22⋊Q8×C43—216no—
52C4×Q8×C43—216no—
53C4×Q8×C43—28no—
54C4×Q8×C43—28no—
55C4×Q8×C43C23116yes—
56#117×C43—22no—
57#117×C43—22no—
58#117×C43—22no—
59#117×C43—216no—
60#117×C43D414yes—
61#117×C43C2314yes—
62#117×C43C2314yes—
63#117×C43C2314yes—
64#117×C43C2314yes—
65C2×C4⋊C4×C43—24no—
66C2×C4⋊C4×C43D412yes—
67C2×C4⋊C4×C43C2312yes—
68C2×C4⋊C4×C43C2314yes—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43D412yes—
72C2×C42×C43—24no—
73C2×C42×C43—21no—
74C2×C42×C43—22no—
75C2×C42×C43C2312yes—
76#107×C43C23116yes—
77#106×C43C23116yes—
78C4⋊C8×C43C23116yes—
79#103×C43C23132yes—
80C24×C43C2×D411yescharacteristic
81C2×Q8×C43—28no—
82C2×Q8×C43—216no—
83C2×Q8×C43—22no—
84C2×Q8×C43—24no—
85C2×Q8×C43—28no—
86C2×Q8×C43—28no—
87C2×Q8×C43—24no—
88C2×Q8×C43C2×Q818yes—
89C2×Q8×C43C2×Q8116yes—
90C2×Q8×C43C2414yes—
91C22×C4×C43—28no—
92C22×C4×C43—22no—
93C22×C4×C43—24no—
94C22×C4×C43—22no—
95C22×C4×C43—24no—
96C22×C4×C43C2×D414yes—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2×Q814yes—
100C22×C4×C43#4114yes—
101C22×C4×C43C2411yescharacteristic
102C22×C4×C43C2412yes—
103M16×C43—28no—
104M16×C43—28no—
105C2×C8×C43—28no—
106C2×C8×C43C2418yes—
107C4⋊C4×C43—216no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—24no—
110C4⋊C4×C43—28no—
111C4⋊C4×C43—216no—
112C4⋊C4×C43C2×D418yes—
113C4⋊C4×C43C2418yes—
114C4⋊C4×C43C2414yes—
115C22⋊C4×C43—24no—
116C22⋊C4×C43—24no—
117C22⋊C4×C43—24no—
118C22⋊C4×C43C2×D418yes—
119C42×C43—216no—
120C42×C43—24no—
121C42×C43—24no—
122C42×C43—24no—
123C42×C43C2×D414yes—
124C42×C43C2414yes—
125C23×C43—42no—
126C23×C43C22⋊Q814yes—
127C23×C43C22×D412yes—
128C23×C43C22×D411yescharacteristic
129Q8×C43—28no—
130Q8×C43—216no—
131Q8×C43—24no—
132Q8×C43—88no—
133Q8×C43C22×Q818yes—
134C2×C4×C43—28no—
135C2×C4×C43—216no—
136C2×C4×C43—24no—
137C2×C4×C43—24no—
138C2×C4×C43—28no—
139C2×C4×C43—44no—
140C2×C4×C43—44no—
141C2×C4×C43—84no—
142C2×C4×C43C22⋊Q814yes—
143C2×C4×C43C22⋊Q818yes—
144C2×C4×C43C22×D418yes—
145C2×C4×C43C22×D411yescharacteristic
146C2×C4×C43C22×D412yes—
147C2×C4×C43C22×Q812yes—
148C2×C4×C43C22×Q814yes—
149C2×C4×C43C2×#4114yes—
150C2×C4×C43C2×#4112yes—
151C2×C4×C43C2511yescharacteristic
152C8×C43—28no—
153#60491C4311yesmaximal, characteristic, direct product factor, Sylow
154C22×C43—22no—
155C22×C43—24no—
156C22×C43—44no—
157C22×C43C2×C22⋊Q814yes—
158C22×C43C2×C22⋊Q812yes—
159C22×C43C23×D411yescharacteristic
160C4×C43—28no—
161C4×C43—28no—
162C4×C43—44no—
163C4×C43—48no—
164C4×C43C2×C22⋊Q812yes—
165C4×C43C2×C22⋊Q814yes—
166C4×C43C23×Q811yescharacteristic
167C4×C43C22×#4111yescharacteristic
168#3458C2×C4311yescharacteristic
169C2×#519C2×C4311yescharacteristic
170#3082C2×C43116yescomplemented
171#3078C2×C4318yescomplemented
172#2911C2×C4312yes—
173#2905C2×C4311yescharacteristic
174C2×#419C2×C4312yes—
175C2×C43—22no—
176C2×C43—24no—
177C2×C43C22×C22⋊Q811yescharacteristic
178C2×C43#358612yes—
179C23×Q8C22×C4311yescharacteristic
180C22×M16C22×C4312yes—
181#544—22no—
182#544C22×C4318yes—
183#543—22no—
184#533—24no—
185#533C22×C4314yes—
186#519—24no—
187#519C22×C4318yes—
188C2×C4×Q8—22no—
189C2×C4×Q8C22×C4314yes—
190C2×#117—22no—
191C2×#117C22×C4312yes—
192C2×#117C22×C4311yescharacteristic
193C2×#117C22×C4311yescharacteristic
194#479C22×C43132yescomplemented
195#477C22×C43116yescomplemented
196#475C22×C43116yescomplemented
197#428C22×C4318yes—
198#428C22×C4318yes—
199#427C22×C4318yes—
200#424C22×C4318yes—
201#423C22×C4314yes—
202#419C22×C4318yes—
203#419C22×C4318yes—
204C2×#103C22×C4318yes—
205C43#6049111yescharacteristic, direct product factor, Sylow
206C22×Q8—21no—
207C22×Q8—22no—
208C22×Q8—24no—
209C22×Q8Q8×C4318yescomplemented
210C22×Q8C23×C4312yes—
211C22×Q8C23×C4314yes—
212C23×C4—21no—
213C23×C4C23×C4311yescharacteristic
214C2×M16—28no—
215C2×M16C23×C4314yes—
216C2×M16C23×C4314yes—
217C22×C8C23×C4314yes—
218C4⋊Q8—28no—
219C4⋊Q8C23×C4318yes—
220#125—28no—
221#125C23×C4318yes—
222C22⋊Q8—28no—
223C22⋊Q8—216no—
224C4×Q8—216no—
225C4×Q8—28no—
226C4×Q8—28no—
227C4×Q8C23×C43116yes—
228#117—22no—
229#117—22no—
230#117—22no—
231#117—216no—
232#117D4×C4314yes—
233#117C23×C4314yes—
234#117C23×C4314yes—
235#117C23×C4314yes—
236#117C23×C4314yes—
237C2×C4⋊C4—24no—
238C2×C4⋊C4D4×C4312yes—
239C2×C4⋊C4C23×C4312yes—
240C2×C4⋊C4C23×C4314yes—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4D4×C4312yes—
244C2×C42—24no—
245C2×C42—21no—
246C2×C42—22no—
247C2×C42C23×C4312yes—
248#107C23×C43116yes—
249#106C23×C43116yes—
250C4⋊C8C23×C43116yes—
251#103C23×C43132yes—
252C24C2×D4×C4311yescharacteristic
253C2×Q8—28no—
254C2×Q8—216no—
255C2×Q8—22no—
256C2×Q8—24no—
257C2×Q8—28no—
258C2×Q8—28no—
259C2×Q8—24no—
260C2×Q8C2×Q8×C4318yes—
261C2×Q8C2×Q8×C43116yes—
262C2×Q8C24×C4314yes—
263C22×C4—28no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4C2×D4×C4314yes—
269C22×C4C2×D4×C4311yescharacteristic
270C22×C4C2×D4×C4312yes—
271C22×C4C2×Q8×C4314yes—
272C22×C4#41×C4314yes—
273C22×C4C24×C4311yescharacteristic
274C22×C4C24×C4312yes—
275M16—28no—
276M16—28no—
277C2×C8—28no—
278C2×C8C24×C4318yes—
279C4⋊C4—216no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4—28no—
283C4⋊C4—216no—
284C4⋊C4C2×D4×C4318yes—
285C4⋊C4C24×C4318yes—
286C4⋊C4C24×C4314yes—
287C22⋊C4—24no—
288C22⋊C4—24no—
289C22⋊C4—24no—
290C22⋊C4C2×D4×C4318yes—
291C42—216no—
292C42—24no—
293C42—24no—
294C42—24no—
295C42C2×D4×C4314yes—
296C42C24×C4314yes—
297C23—42no—
298C23C22⋊Q8×C4314yes—
299C23C22×D4×C4312yes—
300C23C22×D4×C4311yescharacteristic
301Q8—28no—
302Q8—216no—
303Q8—24no—
304Q8—88no—
305Q8C22×Q8×C4318yes—
306C2×C4—28no—
307C2×C4—216no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—28no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—84no—
314C2×C4C22⋊Q8×C4314yes—
315C2×C4C22⋊Q8×C4318yes—
316C2×C4C22×D4×C4318yes—
317C2×C4C22×D4×C4311yescharacteristic
318C2×C4C22×D4×C4312yes—
319C2×C4C22×Q8×C4312yes—
320C2×C4C22×Q8×C4314yes—
321C2×C4C2×#41×C4314yes—
322C2×C4C2×#41×C4312yes—
323C2×C4C25×C4311yescharacteristic
324C8—28no—
325C22—22no—
326C22—24no—
327C22—44no—
328C22C2×C22⋊Q8×C4314yes—
329C22C2×C22⋊Q8×C4312yes—
330C22C23×D4×C4311yescharacteristic
331C4—28no—
332C4—28no—
333C4—44no—
334C4—48no—
335C4C2×C22⋊Q8×C4312yes—
336C4C2×C22⋊Q8×C4314yes—
337C4C23×Q8×C4311yescharacteristic
338C4C22×#41×C4311yescharacteristic
339C2—22no—
340C2—24no—
341C2C22×C22⋊Q8×C4311yescharacteristic
342C2C43×#358612yes—
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC24×C43C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#3082C2semidirect
4. C43×#3078C2semidirect
23. C43×#479C22semidirect
24. C43×#477C22semidirect
25. C43×#475C22semidirect
37. C22×Q8×C43Q8semidirect
153. #60491C43direct (N × H)
170. #3082C2×C43semidirect
171. #3078C2×C43semidirect
194. #479C22×C43semidirect
195. #477C22×C43semidirect
196. #475C22×C43semidirect
205. C43#60491direct (N × H)
209. C22×Q8Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34582
C2×C43×#5192
C43×#30822
C43×#30782
C43×#29112
C43×#29052
C2×C43×#4192
#6049143