Finite Group Databasebeta

← C43×#9888 #24929905

Subgroups — C43×#9888 #24929905

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2857C211yesmaximal, characteristic
2C43×#1749C211yesmaximal, characteristic
3C43×#1434C211yesmaximal, characteristic
4C43×#1294C214yesmaximal
5C2×C4⋊Q8×C43C411yescharacteristic, complemented
6C2×C22⋊Q8×C43—21no—
7C22×C42×C43C2211yescharacteristic
8C2×C22⋊C8×C43C2212yes—
9C2×#97×C43—21no—
10C43×#391—21no—
11C43×#389—21no—
12C43×#389C412yescomplemented
13C43×#384C411yescharacteristic, complemented
14C43×#380—21no—
15C43×#380C2212yes—
16C2×#95×C43—21no—
17C2×#95×C43—21no—
18C2×#95×C43C2212yes—
19C43×#336—21no—
20C22×Q8×C43—21no—
21C23×C4×C43—22no—
22C23×C4×C43D411yescharacteristic
23C23×C4×C43D411yescharacteristic
24C23×C4×C43C2311yescharacteristic
25C22×C8×C43—22no—
26C4⋊Q8×C43—42no—
27C22⋊Q8×C43—44no—
28C2×C4⋊C4×C43—21no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43C2×C412yes—
33C2×C4⋊C4×C43C2×C412yes—
34C2×C22⋊C4×C43—22no—
35C2×C42×C43—42no—
36C2×C42×C43C2×C411yescharacteristic
37C2×C42×C43C2×C411yescharacteristic
38C2×C42×C43D411yescharacteristic
39C2×C42×C43D411yescharacteristic
40C22⋊C8×C43—22no—
41C22⋊C8×C43Q814yescomplemented
42#97×C43—42no—
43#95×C43—24no—
44#95×C43—22no—
45#95×C43—22no—
46#95×C43—24no—
47#95×C43—42no—
48C24×C43C2×D411yescharacteristic
49C2×Q8×C43—42no—
50C2×Q8×C43—42no—
51C2×Q8×C43—42no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—24no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43—42no—
68C22×C4×C43—42no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×Q812yes—
76C22×C4×C43#4112yes—
77C2×C8×C43—24no—
78C2×C8×C43—42no—
79C2×C8×C43—42no—
80C4⋊C4×C43—42no—
81C4⋊C4×C43—42no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43—42no—
84C4⋊C4×C43—44no—
85C4⋊C4×C43—42no—
86C22⋊C4×C43—44no—
87C42×C43—22no—
88C42×C43—22no—
89C42×C43—41no—
90C42×C43—41no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43C2×C22⋊C411yescharacteristic
96C23×C43#12411yescharacteristic
97C23×C43C4⋊Q811yescharacteristic
98C23×C43AGL(1,ℤ/8)12yes—
99C23×C43#13712yes—
100Q8×C43—84no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—42no—
116C2×C4×C43—42no—
117C2×C4×C43—44no—
118C2×C4×C43—44no—
119C2×C4×C43—44no—
120C2×C4×C43—44no—
121C2×C4×C43—44no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—82no—
129C2×C4×C43—82no—
130C2×C4×C43—82no—
131C2×C4×C43—82no—
132C2×C4×C43#9912yes—
133C2×C4×C43#10412yes—
134C2×C4×C43C4×Q812yes—
135C2×C4×C43C22⋊Q812yes—
136C8×C43—44no—
137#9888C4311yesmaximal, characteristic, direct product factor, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—22no—
146C22×C43#39111yescharacteristic
147C22×C43C2×#9911yescharacteristic
148C22×C43#41011yescharacteristic
149C22×C43#41811yescharacteristic
150C22×C43#41911yescharacteristic
151C22×C43C2×#10411yescharacteristic
152C22×C43#42111yescharacteristic
153C22×C43#48912yes—
154C22×C43#50112yes—
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—22no—
158C4×C43—22no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—84no—
162C4×C43—82no—
163C4×C43—82no—
164#2857C2×C4311yescharacteristic
165#1749C2×C4311yescharacteristic
166#1434C2×C4311yescharacteristic
167#1294C2×C4314yes—
168C2×C43—22no—
169C2×C43—22no—
170C2×C43#150611yescharacteristic
171C2×C43#150711yescharacteristic
172C2×C43#151111yescharacteristic
173C2×C43#151411yescharacteristic
174C2×C43#198611yescharacteristic
175C2×C43#199311yescharacteristic
176C2×C43#199611yescharacteristic
177C2×C4⋊Q8C4×C4311yescharacteristic, complemented
178C2×C22⋊Q8—21no—
179C22×C42C22×C4311yescharacteristic
180C2×C22⋊C8C22×C4312yes—
181C2×#97—21no—
182#391—21no—
183#389—21no—
184#389C4×C4312yescomplemented
185#384C4×C4311yescharacteristic, complemented
186#380—21no—
187#380C22×C4312yes—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95C22×C4312yes—
191#336—21no—
192C43#988811yescharacteristic, direct product factor, Sylow
193C22×Q8—21no—
194C23×C4—22no—
195C23×C4D4×C4311yescharacteristic
196C23×C4D4×C4311yescharacteristic
197C23×C4C23×C4311yescharacteristic
198C22×C8—22no—
199C4⋊Q8—42no—
200C22⋊Q8—44no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C4312yes—
206C2×C4⋊C4C2×C4×C4312yes—
207C2×C22⋊C4—22no—
208C2×C42—42no—
209C2×C42C2×C4×C4311yescharacteristic
210C2×C42C2×C4×C4311yescharacteristic
211C2×C42D4×C4311yescharacteristic
212C2×C42D4×C4311yescharacteristic
213C22⋊C8—22no—
214C22⋊C8Q8×C4314yescomplemented
215#97—42no—
216#95—24no—
217#95—22no—
218#95—22no—
219#95—24no—
220#95—42no—
221C24C2×D4×C4311yescharacteristic
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—42no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4C22⋊C4×C4311yescharacteristic
243C22×C4C22⋊C4×C4311yescharacteristic
244C22×C4C22⋊C4×C4311yescharacteristic
245C22×C4C22⋊C4×C4311yescharacteristic
246C22×C4C22×C4×C4311yescharacteristic
247C22×C4C2×D4×C4311yescharacteristic
248C22×C4C2×Q8×C4312yes—
249C22×C4#41×C4312yes—
250C2×C8—24no—
251C2×C8—42no—
252C2×C8—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C22⋊C4—44no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42—41no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C2×C22⋊C4×C4311yescharacteristic
269C23#124×C4311yescharacteristic
270C23C4⋊Q8×C4311yescharacteristic
271C23AGL(1,ℤ/8)×C4312yes—
272C23#137×C4312yes—
273Q8—84no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4#99×C4312yes—
306C2×C4#104×C4312yes—
307C2×C4C4×Q8×C4312yes—
308C2×C4C22⋊Q8×C4312yes—
309C8—44no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22C43×#39111yescharacteristic
319C22C2×#99×C4311yescharacteristic
320C22C43×#41011yescharacteristic
321C22C43×#41811yescharacteristic
322C22C43×#41911yescharacteristic
323C22C2×#104×C4311yescharacteristic
324C22C43×#42111yescharacteristic
325C22C43×#48912yes—
326C22C43×#50112yes—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—84no—
334C4—82no—
335C4—82no—
336C2—22no—
337C2—22no—
338C2C43×#150611yescharacteristic
339C2C43×#150711yescharacteristic
340C2C43×#151111yescharacteristic
341C2C43×#151411yescharacteristic
342C2C43×#198611yescharacteristic
343C2C43×#199311yescharacteristic
344C2C43×#199611yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C43C4semidirect
12. C43×#389C4semidirect
13. C43×#384C4semidirect
41. C22⋊C8×C43Q8semidirect
137. #9888C43direct (N × H)
177. C2×C4⋊Q8C4×C43semidirect
184. #389C4×C43semidirect
185. #384C4×C43semidirect
192. C43#9888direct (N × H)
214. C22⋊C8Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#28572
C43×#17492
C43×#14342
C43×#12942
#988843